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Problem Description : 

Three containers are kept on a horizontal surface. The dimensions of all the containers is given in Fig.1 . The base of each container is kept on a pressure sensor (PS). Each container is placed below a tap. All containers are symmetrical about the central axis. The whole setup is shown in Fig. 2

• Pressure Sensor/ Pressure Transducer:

        For this problem, we have chosen this sensor to measure the pressure                at the base

• Working: 

         More the pressure, more the value sent as output

         Note : In reality, this is known as a force sensor

The pressure sensor is further, a part of the electric circuit shown. The circuit involves :

• Microcontroller – Arduino
• Pressure Sensor
• LED
• LDR
• Multimeter as Ammeter

Hint : LDR stands for ‘Light’ Dependent Resistor

Note : Each container has a separate circuit (Fig.3) for itself attached

Arduino IDE code:

Hint : Understand the problem statement, the setup of the problem, the circuit and the code thoroughly. Note that, you just need to get the gist of what the code is trying to do!

• Based on your understanding,

                Answer the Question Parts shown below

Question Parts :

Part- (a)

The taps above respective containers are turned on and water is allowed to flow into the containers. The experimenter keeps a track of the height of the water column ‘h’ which gets accumulated in the containers w.r.t time and plots the graphs for the same as an observation. (Taps are not identical)*

Graphs are as follows :

• Is there any time instant where the readings of the current values are same on atleast 2 ammeters? And if you find any, then find the volume of water filled in the 3 containers at that time instant.

Part-(b)

Part-(c)

• Draw the simplified schematic circuit diagram and a flowchart which simplifies Fig.3

            (Optional)

Conclusion :

Understand & draw the circuit. Try to understand the motive behind the code. Basically, there is a type of procedure/flow to approach this problem. Try to grab that flow.

Solution has been uploaded !! – SOLUTION

All the Best !!

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The formula sheet is mainly designed for the high school physics students. This sheet would definitely help students to boost up their   JEE Mains preparation. 

Important Note : 

• The Question Formula sheet is basically a set of mini-problems. This would help you to understand the use of the formulae as well
• Keep solving the sheet atleast thrice a week. The more, the better. It will really help you in problem solving
• Don’t refer to the solution sheet (attached separately below) directly. Use the solution sheet as your reference. You might find a shorter way to do the same thing !

Question Sheet :

Chapters Covered :

• Kinematics
• Laws of Motion
• Work, Energy and Power
• Rotational Motion
• Gravitation
• Fluid Mechanics
• Thermodynamics
• Kinetic theory of Gases (KTG)
• Oscillations and Waves

Download the Question sheet file below by clicking here – DOWNLOAD

Conclusion :

Use this formula sheet quite frequently. This work is inspired by my physics teacher. Be consistent in solving it !!

Solution Sheet has been uploaded !! (*Click only when the formula sheet is attempted*) – SOLUTION

Till then, Keep practicing !!

All the Best !!

For Best Experience, View on Desktop/Laptop 

#RC Airplane Series-6

In this article, we are going to learn to do the ESC Calculations. Also, we are going to study about the control systems connections (basically, how are the electronics are connected to each other) !!

Topics Covered :

• What is ESC ?
• How to choose a ESC ?
• How to connect all the electronic components?
• Use of Y-junction (optional)

1. What is ESC ?

ESC stands for Electronic Speed Controller. It’s job is to provide set appropriate voltage across the BLDC motor according to the throttle given on the transmitter. 

• For example, Suppose, I give 25% throttle, so, to get the speed corresponding to 25% throttle, what should be voltage applied across the motor –> this is the job of ESC ! (speed is controlled by controlling current)

• The main thing to understand is that, we will be controlling the voltage across the motor with the help of ESC. We are already aware of the motor kV relation :

• So according to the relation, Varying the voltage will vary the RPM of the motor, which will result in speed variation as well !!

From the example itself, we can understand that choosing a proper ESC is very much crucial so that everything is under control and also safe at the same time 

Wiring connections for ESC :

                                                                                              Fig. Wiring Connections of ESC

2. How to choose ESC ?

Let’s undertand the procedure using an example !

Suppose, we finally choose the motor for our model: 

A2212 10T 1400kV motor

Step-1 : Find out the maximum current which the current draws. If this value is not directly given, it can be calculated from the relation

                                                                                                          P = V x I 

(‘P’ is max. power of motor, ‘V’ is the nominal voltage of our battery used and ‘I’ is the max current from motor)

Step-2 : But we should choose an ESC such that this maximum current value should just be 75% of the actual ESC current which we will be buying. (Read it again !). We call this current as ‘Actual ESC Current’

This implies that we need an ESC which has a rating of 20.25 A. But in reality, there is no such ESC with this current rating being manufactured. So we need to go with an ESC which has a bigger value than 20.25

We can go with 30A ESC or an 40A ESC would also be perfect !!

3. Connections of all Electronics

Now, by this article 6 of RC Airplane Series, we already got to know about all the basic electronic requirements for an RC Airplane. Let’s list it down :

• Motor and Propeller
• LiPo Battery
• ESC (Electronic Speed Controller)
• Receiver (On board)
• Transmitter (Not on board)
• 4 Servos (1 for each ailerons, 1 for elevator, 1 for rudder) 

In this example, let’s say we are using a 6 channel transmitter and receiver

• Usually in most of the cases, we have to attach the connectors to the 2 wires assigned for battery in ESC. For this, we can use XT60 connector which is very commonly used as well. They come in a set of a female and male connector. The female one is to be attached to the ESC while the male one is to be attached to the battery

For more clarity on above figure, you can also refer to the diagram below

4. Why Y-junction wire for ailerons ? (optional)

• If you look into the connection diagram carefully, we can see that the servos attached to the 2 ailerons are connected to a Y-junction wire. This then goes onto connect to the receiver and it uses just one channel on the receiver for 2 servos !!

The reason behind us doing this thing can be learnt from the article – RC Airplane Series-2 : ‘Understanding Control Surfaces’

• In the above article, mainly focus on the ailerons part in order to understand the reasoning behind Y-junction cable. In short, we can summarize it as : 

           In order to get a roll, making the ailerons deflect in opposite sense helps even more. For example, if we need to take right roll, then             on giving just one stimulus through transmitter, the right aileron will deflect upwards while at the same time, the left aileron also                 deflects downwards

One Advantage and One Disadvantage !

Advantage :

• We can get a better roll due to 2 ailerons moving in opposite sense and everything is completed by using just 1 channel

Disadvantage :

• We can’t make the ailerons to be used as flaps since they will always move in opposite sense. (i.e. flaperons is not possible)

Conclusion : 

• So in this RC Airplane-6, we have learnt to do the ESC Calculations. Similar stuff is used while drone designing as well since it also includes BLDC motors whose speed needs to be controlled. 
• Here, we have completed the basic designing of RC Airplane. Hope you enjoyed the Series and got to learn something new through this. But again reminding you, this was just the Basics !! 

RC Airplane Series (All previous Articles)

• Part-1 : What’s in the Wings !
• Part-2 : Understanding the control surfaces !
• Part-3 : Designing your Airplane !!
• Part-4 : Motor and Propeller Selection
• Part-5 : How to choose LiPo Battery ?

Any suggestions from your side are welcomed !!

Keep Learning !!

All the Best !!

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In Part 1 : Dealing with Resistors, we learnt about the Resistor, basically how it works, what are it’s application, how to use in circuit, etc. But we come across the circuits which involve some combinations of resistors. Our aim in this article is to simplify these network and obtain Equivalent Resistance of the network.

Topics Covered :

• What is meant by finding equivalent resistance ?
• Resistor in Series
• Resistor in parallel
• Example on Series – Parallel
• Folding Symmetry & Example
• Mirror Symmetry & Example
• Voltage method (Rearrangement) & Example
• Assignment & Conclusion

1. What is meant by finding equivalent resistance ?

When it comes to circuit solving, we will encounter lot of complex combination of resistors present in the circuit. Finding ‘equivalent’ of such combination of resistors means that, we must be able to replace that whole thing with just a single resistor without changing any of the other parameters (current, potential difference across given points, etc. ) in the circuit.

Fig.1                                             (a)                                                                                                                         (b) 

Note that, in Fig.1 (a) and (b), except the number of resistors, there is no change in other parameters (I remain I, E remains E, delta V remains delta V)

Now, how to actually calculate this value of Req is what we need to study in this article !!

2. Resistors in Series

Resistors are said to be in Series when the current flowing through them is the same. Done !

Now, with reference to above figure, 

Important Note :

From the above relation, we can infer that, we can use series combination if we need a resistance value greater than the individual resistances (i.e. Req > R1 & also Req > R2)

So, Resistors in Series just add up directly !

3. Resistors in Parallel

Resistors are said to be in parallel, when they have same potential difference across them. Done !

Important Note : 

From the above relation, we can infer that we can use parallel combination if we need a resistance value even lower than the individual resistances. (i.e. Req < R1 & also Req < R2)

Breadboard Connections for parallel combination :

4. Example on Series – Parallel

Question -1

Find the equivalent resistance of the given setup across points A and C

Solution : 

Step – 1 : Both the 4ohms resistors are connected across same points B and C. Hence, Both are in parallel combination. Req for just this combination will be 2 ohm

Step-2 : Now, 5ohm and 2 ohm are in series combination. Req of this will be 7ohm

Step-3 : Finally, we have 7 ohm resistor between A and C. This is our final Req between points A and C

Question – 2 :

Solution :

Step 1 : same current passes through AF and FE which makes both the 3 ohm resistors in series. Req for this will be 3+3 = 6 ohms

Step 2 : Two 6 ohm resistors are connected across same points A and E which makes them in parallel. Req for this will be 3ohm 

Step 3 : again both 3 ohm are in series. Req will be 6 ohm

Step 4 : both 6 ohm are in parallel. Req will be 3 ohm

Step-5 : 3 ohm and 3 ohm are in series. Req of this will be 6 ohm

Step-6: two 6 ohm resistors are in parallel. Req of this will be 3 ohms. Keep on simplifying !! 

Step-7 :  3 ohm and 3ohm  are in series

Step-8 : 6 ohm and 3ohm are in parallel. Req of this will be 2ohms.

Final Answer : So, the overall equivalent resistance across points A and B is 2ohm

5. Folding Symmetry

(Example will make everything very clear, but keep the below idea in your mind)

• Step 1 : Consider a line passing through the points across which equivalent resistance needs to be found. Let this line be called AB for now.
• Step 2 : See if any folding symmetry exists. Folding needs to be done about the line AB. (By folding symmetry, we mean that there should be an exact overlap once the folding is done). 
• Step 3 :Once folding symmetry is confirmed, it implies that all the potentials are also identical at the overlapping points

Let’s take an example to understand this !!

Example :

Solution :

Step-1 : We need to find equivalent resistance across A and B. So we draw line AB first

Step-2 : So we fold one portion of the network about AB and see if it coincides with the portion on other side (Just like a folding of chapati about it’s diameter). And here it does !! – Folding symmetry exists !

Step-3 : Now, since Folding symmetry exists,  Vc=Vh (Potential at ‘c’ = Potential at ‘h’) ; Vd = Vg ; Ve = Vf.  This implies that the potential difference for the resistor between points ‘A’ and ‘c’ is equal to the potential difference for the resistor between points ‘A’ and ‘h’. This again tells us that, they are in parallel. So, we can just keep one of those resistors but it’s value will become ‘R/2’

(Read it again !)

(We follow similar process for all the remaining resistors & we get the circuit shown below)

Step-4 : Just solve this like a normal Series- Parallel problem

Final Answer : We get the overall equivalent resistance as 3R/2. So option (b) is correct.

6. Mirror Symmetry

• Just check for mirror symmetry about any line (imaginary is also OK) in the circuit
• If any mirror symmetry exists, then the currents in the mirrored branches should also be same. This point is responsible for simplification of the circuit.

Let’s take an example to understand this even better !

Example : 

Find the equivalent resistance of the circuit shown in the figure about points a and b. Each resistor has a resistance ‘r’

Solution :

Step-1 : 

• Draw the imaginary line about which you find mirror symmetry.
• Consider as if a current ‘i’ enters the whole network through A and gets distributed in branches such that ;                                                i = i1 + i2 + i3
• Because of mirror symmetry, the current in corresponding image branches should also be same and an overall current ‘i’ should come back from B 

Step-2 :

• ‘i1’ flows in AC and as discussed in step-1, ‘i1’ flows in CB as well
• But applying KCL(junction rule) at C, current ‘i1’ should have been distributed in branches cd and cB. but it doesn’t happen as the whole current ‘i1’ goes into branch cB
• This implies that resistor between points c and d is not actually attached at C even though it just appears to be attached. We can just remove it’s connection

Step-3 :

• Similar thing with i2 !!The current in Ad (i2) should have been divided at ‘d’
• But the whole i2 gets passed on to dB which implies that the resistor is actually not connected to ‘d’ as well (because if it was, then current would have been divided)

           Now it is just simple Series-parallel Problem !!

Final Answer : The overall equivalent resistance of the circuit across the points is ‘r/2’

7. Voltage method (Rearrangement) 

This method is to be used when we are not directly seeing any kind of symmetry. This method is basically rearrangement of the network in order to get a clearer view to proceed further 

Remember :

• Potential remains constant along the plain wires.
• Resistors connected across same potentials are in parallel

(Example will make it more clear)

Procedure :

• Step-1 : Distribute the potentials across the whole circuit. Take care that potential should be defined across both the ends of each resistor. Introduce new variables to denote unknown potentials if needed.
• Step-2 : Number the ends of the resistors
• Step-3 : Write down the potentials separately , keeping the points across which the Req is to be found at the two ends
• Step-4 : Place the resistors between their respective potentials

Let’s take an example to understand this even better !!

Example : Find equivalent resistance of the given circuit about points ‘a’ and ‘b’

Solution :

Step-1 :

• As we already mentioned, potential along plain wires remains constant.
• We are unaware of the potential at the center, so we consider it as ‘x’

Step-2 :

• Number all the ends of the resistors. (Complete one resistor first and then proceed to next !)

Step-3 :

• Now, separately write down the potentials 
• Remember that the points/potentials across which you are calculating equivalent resistance should be kept at the ends

Step-4 :

• Observe and connect the numbers to the respective potentials (a –> 4 ; x–> 3,5,2,7 ; b–>6,1,8 )
• On completing this, you will get a clear view of what the circuit actually was !!

          Now, it is just simple Series-Parallel problem !

Final Answer : The equivalent resistance of the circuit between a and b is 4r/3

8. Dealing with Wheatstone Bridge

• The below wheatstone configuration is often seen while solving problems based on equivalent resistance.

(I am just adding this so that you don’t feel stuck at any problem just because you were not aware of this !!)

9. Kirchhoff method for Req

When nothing works at all, there is always Kirchhoff method to the rescue !!

• We have already discussed it in the article : Tackle circuits using Kirchhoff’s Laws

10. Assignment & Conclusion :

• So now on completion of both the parts : 1st – Dealing with Resistors and this 2nd- Combining Resistors, We have a good foundation set to understand electric circuits in a much better way.

• This second part was mainly to go into much more depth for understanding circuits based on resistors. later on, we will add capacitors, inductors as well to expand our applications !!

Based on this article, some problems have been shortlisted from popular books, so that you can have a practice kind of thing as well. Solution to this assignment can be asked through email.

For solutions or doubts,

email at : physicsandelectronics079@gmail.com

DOWNLOAD 

Combining Resistors - Assignment

All the Best !!

Keep Learning !!

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Consider 2 situations. For the first case, suppose that you are running freely on an open ground and for the second case, consider yourself running on Mumbai local station (that too, at the peak working time). Immediately, you will notice that you can’t run that freely in the second case. What’s the reason ? 

Resistance. The crowd on the railway station acts like an obstruction for you while you try to run. Similar obstruction is felt by those tiny electrons while moving from the conductor. We term this difficulty for the electrons to flow due to object’s opposition as ‘Resistance‘

Topics Covered :

• What factors affect Resistance ?
• Use of Resistors in circuit (*Imp)
• Types of Resistors and Resistor colour coding 
• Power Ratings

1. What factors affect Resistance ?

Material :

• Materials which are good conductors allow easy flow of electrons through them since the nucleus in the atoms don’t influence the valence electrons much due to which they get easily detached from the atoms and contribute to the current. (Imagine atoms of conductors as not-so-strict parents).
• On the other hand, we have insulators which don’t allow the electrons to flow freely. This is due to very strong influence of the nucleus on the valence electrons and because of this, the electrons are tightly bounded to atoms. (Imagine atoms of insulators as very strict parents)

We refer to this property of material as ‘Resistivity‘.It is basically a characteristic of the material. So, conductors have lower resistivity as compared to insulators since they offer lesser resistance to electron flow for a given volume.

Cross-sectional Area :

• From our daily life experiences, we know that driving on a broad highway feels much more free as compared to driving on a narrow road. Because of which, the first thing we try to do on highway is to speed up our vehicle. On similar basis, when the area of cross section of a wire is more , lesser is the resistance, hence, making electron flow easier.

Length :

• More the length of wire/object implies that more atoms/molecules will interact with the electrons, hence increasing the obstruction. So, Resistance is high in this case

Taking into account all the above 3 factors (Material, Cross-sectional Area and length), we can compress it into a formula as : 

Question : We have a quick question over here now. Have a look at it !! 

Solution :

Important to Note :

In the formula of R, rho is the resistivity, L is the length (along the current direction) and A is the area of cross-section (current passes through this section of area while passing)

CASE-1 :

CASE-2 :

CASE-3 :

Temperature :

Usually in normal cases, as the temperature increases, the resistance is seen to be increased. There is also a relationship between the resistance and the temperature. 

Cross-sectional Area :

2. Use of Resistors in Circuits :

Ok, so now coming to the main portion : what is the actual use of resistor in any electronic circuit !? Answering this question, there are 2 main uses of resistor :

• Limiting the current 
• Controlling the voltage

Limiting the current :

Resistors are commonly used to make sure that only the current required by the device goes into it, nothing more ! Getting excess current than required can damage the devices very badly (i.e. it might even make them burned off. This happens mostly with sensitive elements like LEDs, ICs, transistors, etc.)

Let’s consider a problem

Suppose that you need to make an red LED glow with the help of a 9V battery. So, shall we just directly connect the 9V battery to LED ? What happens if we do that !? 

                         Before Simulation (for connections)                          Fig.1                                       After Simulating (LED burns)

Basically, if we directly connect battery to the LED, there is a lot of current flowing through the LED which causes it to ‘burn’. Excessive current to the sensitive components fries them up !! So, what’s the solution for this ?

• Just add the appropriate resistor with the LED. This resistor will take care that only the sufficient amount of current is made to be passed from LED

How to decide the resistance value ?

For the problem, we have :

• A 9V battery
• Red LED (maximum safe current – 20mA & forward voltage drop of 2V)

Note :

Every component does a voltage drop when current passes through them. For LED, we call it as ‘forward voltage drop’. The word ‘forward’ comes due to the reason that the diode only allows current to flow in one direction due to which the voltage drop will also happen in forward direction only. 

Now, for the analysis part :

Our main aim is to find the value of ‘R’. We are considering 20mA current to be flowing in the circuit because it’s the maximum current which can pass safely from LED and give max. brightness. 

Consider the loop ABCDA,

(To know more about Kirchhoff Laws and how to use them from basics, refer this article) – Tackle Circuits using Kirchhoff’s laws

Note :

The voltage drop across different colour LED is different . This is because, they emit different colours as well. The following table gives the data about the voltage drops across different colour LEDs :

So, this is how we limit the current using the resistor hence protecting our sensitive components from getting damaged !!

Controlling the Voltage :

Another very important use of Resistors is to control the voltage at a region/point in the circuit. 

Let’s take an example

Suppose that you have a mini-circuit designed which needs 5V supply to work/operate. And again you are having my 9V battery itself. So it’s obvious that you can’t directly give the 9V supply to the mini-circuit. It would blow-up !! 

Solution : To tackle this problem, we can design a voltage-divider circuit. 

Consider the loop ABCDA

• In the circuit below, our main aim is to get 5V at ‘H’ 
• So, we need a resistor which can make a voltage drop of 4V. But this alone resistor won’t serve the purpose as for a complete loop, sum of potential  differences should be zero. (KVL)
• Basically we need one more resistor which can do the voltage drop of  remaining 5V

Analysis of Circuit :

Let current in the circuit be ‘i’

• With this circuit, we have created an outlet pin from where 5V can be used as the power source for the mini-circuit !!

                                                                                            Fig. Actual Connections in reality 

3. Types of Resistors :

Fixed Value Resistor :

These resistors have their values fixed from the manufacturers itself. But there can be a slight deflection from the value. We call this deflection as ‘tolerance’. 

                                                                                                 Fig. Fixed Value resistor

How to Calculate total Value of Resistor ? – (Colour Coding)

• The first band gives first digit
• The second band gives second digit
• Third band gives the multiplier (the power raised to base 10)
• Fourth band gives you the tolerance value

So, for the above example, the colour coding will be like :

• First band – Orange
• Second band – Green
• Third band – Red
• Fourth band – Silver

                                                                                        Fig. Colour Coding for Fixed Resistors

Variable Resistors : 

• Resistors, whose value can be altered are known as Variable Resistors. The manufacturer just prints the maximum value which the device can go up to. (For example, if 10K is printed on a potentiometer, it implies that you can adjust it’s resistance at any value from 0 to 10K ohms). 
• The way you can vary the resistance changes from component to component  

4. Power Rating of Resistors :

We have learnt about choosing the value of Resistance but whenever current passes through resistors, there is some heat generated as well. Now, we need to take care that this heat doesn’t damage the resistor. For this, we have power ratings assigned to resistors. Power is basically heat generated per second and is measured in Watts (W)

• There is a relation of power with Voltage and Current ,

                                                                                                        P = V x I

Here, P is the Power (in W)

           V is the potential difference across the resistor

           I is the current flowing through the resistor

• There are resistors available of 1/8 watt, 1/4 watt, 1/2 watt, 1 watt, etc. More the size of resistor, the more power rating it has !

Example :

From the above example, we can infer that resistor of 1/8 W is ‘just’ sufficient. But to ensure even more safety, we can go with 1/4 W resistor as well !!

Conclusion :

Through this article, we tried to learn about Resistor and how do the basic analysis of the  circuits involving resistors. According to me, understanding electronics right from the root will be really beneficial.

Learning to deal with Resistors, Capacitors, Inductors, IC’s help us to build the reasoning behind circuit design. 

In the coming articles, Combination of Resistors and various techniques to solve them will also be discussed (like symmetry, etc) – UPLOADED

Till then, Keep Learning !!

All the Best !!

For Best Experience, View on Desktop/Laptop !

In this Article, we are going to discuss one of the very important and most discussed method in the chapter of Electric Circuits. It’s used mainly in order to analyze the circuits.

By Analyzing a circuit, we mean :

• Finding current flowing in a branch of circuit
• Finding potential of a point in circuit
• Finding potential difference across the electrical components (resistors, capacitors, inductors, etc.)

There are lot of other techniques as well to simplify and solve the circuits. But When everything fails, this works !!

Topics Covered :

• What are the Kirchhoff’s Laws ? – KCL and KVL
• How to apply it in circuits ?
• Easy – Moderate Examples
• Kirchhoff to find Equivalent Resistance

1. What are Kirchhoff’s Laws ?

Kirchhoff’s Current Law (KCL) :

Statement : “The sum of all the currents entering a junction is equal to sum of all the currents leaving the junction”

Explanation :

Kirchhoff’s Voltage Law (KVL) : 

Statement : The sum of the potential differences across all the circuit elements for a closed loop is always zero

2. How to Apply in Circuits ?

Now, comes the part of where to give plus(+) and where to give minus(-)

For this, just go by the definitions and anything that opposes the definition gets the opposite sign.

Resistor : It’s a device which causes potential drop and the drop happens in the direction of current. So if we move in the direction of current (through resistor), the voltage has to drop !!

Va is potential at A, while Vb is potential at B

In this case above, the equation can be written as    Va – iR = Vb

Battery : Just look at ‘our direction’. If we are moving from positive terminal of battery to neagtive terminal of battery, the voltage is going to decrease (Obvious)

In the above case, the equation can be written as   Va – E = Vb

We focus on circuits containing batteries and resistors in this article. Getting a grip on this type of circuits would bring us in a position to easily deal with circuits containing capacitors and inductors as well

3. Easy – Moderate Examples :

Q.1 Find the current flowing in the loop and also plot a graph which keeps track of the potential across the circuit

Solution :

• We first decide the current direction in the loop ABCDA 
• Then, we decide the direction in which we are going to move and according start moving from that point (here A) around the circuit. (Here, we move in A-> B -> C -> D -> A)
• Apply kirchhoff’s law as discussed. (This example will make it a lot clear)

Starting from A ->B,

We encounter 12V battery, As discussed, only consider ‘our direction’ . Here, we move from negative terminal to positive terminal, hence we have potential rise. Hence, 

                                                                                               +12

For 2ohm resistor, we are moving in the direction of current, so potential should drop. Hence, equation till now will become 

                                                                                            +12 – 2i

For 4ohm resistor, again we are moving in the direction of current, so again potential should drop. Equation is :

                                                                                             +12 – 2i – 4i

For 9V battery, we are moving from positive terminal to negative terminal, so potential drops over here. Hence,

                                                                                          +12 – 2i – 4i – 9 

We have completed writing the sum of potential differences across all the elements in circuit (all were present in A -> B). And, according to KVL, this sum should be zero, Therefore,

                                                                                         +12 – 2i – 4i – 9 = 0

                                                                                                 i = 0.5 A

The answer is positive which implies that the assumed direction of current is correct.

We draw the graph for keeping track of the voltage rise and drops across the elements (components)

On Y-axis, we have the Voltage (in volts) and we keeping a track of potential wrt the components

– In this, we consider the negative terminal of 12V battery to be at 0V (i.e. our reference).

It’s mandatory to have a point having 0V in any electric circuit. This is because potential at a point can be defined only when the reference has been set

Note : There is no potential drop or rise in wire (it’s constant). Wire can be described as a medium to carry-forward the potential without making any changes in it. 

Question-2

Solution :

We give markings first so that it’s easier for us. For each loop, we consider a new current. Let’s do this much first

Now, if we see carefully, in the path G-> H -> A -> B, only current i1 will be flowing. But for the branch BG, we have i1 as well as i2 coming into picture since it’s a common branch to loop ABGHA and loop BCFGB.

Hence considering i1 > i2 and also i2 > i3 (you may consider it either way),  the current distribution in all the branches becomes,

(Observe that KCL is also being followed)

Let’s go loop by loop. First we take loop ABGHA (it means we start from A and end at A)

Eqn is : 

Coming to loop GBCFG, (starting from G)

Moving to loop CDEFC, (starting from C)

Substitute (1) and (3) in equation (2) for getting value of i2,

We get,                                                                                                  

So, we can conclude that there is no current flowing through any of the resistors

Question -3

Solution : 

We can clearly see two loops over here. And we consider 2 currents i1 and i2 in each of the loop. It’s completely our choice, whether to consider current in clockwise or in anticlockwise direction. Here, we consider i1 to be clockwise in loop ABDA while i2 to be anticlockwise in loop CDBC.

Refer diagram below.

Again same procedure, 

Consider one loop at a time. First, let’s go with ABDA

Coming on to next loop CDBC, 

On solving (1) and (2), 

Here, i2 is positive while i1 is negative, which implies that the sense of i2 is same as considered (anticlockwise) while for i1, its opposite to what we considered (i.e. in reality, it’s moving in anticlockwise sense)

Actual situation :

For marking the potentials, we need a reference. We choose the negative terminal of 3V (at G) to be at 0V

Part – (a)

Part – (b)

So, finding the potential difference across cell G is same as finding potential difference between points C and D

                                                                                                     while

Finding the potential difference across cell H is same as finding potential difference between points C and B

4. Kirchhoff to find Equivalent Resistance

To find equivalent resistance across 2 points given :

• Assume a battery between the 2 points (having voltage of your choice)
• Find the current passing through the battery
• From the relation R = V/I, the value of R is nothing but equivalent resistance

Example :

We have 2 points ‘a’ and ‘b’ and we need to find equivalent resistance between these points

• Step 1 – We consider a battery of 10V between ‘a’ and ‘b’

• Step 2 – We need to find current flowing through battery (Here, it’s i1)

For loop ahcba,

For loop hgdch, 

For loop gfedg,

Substitute i3 value from (3) in (2). Solve the new equation with (1) to get the value of i1

We get,

• Step 3 : Use the relation R = V/I. The value of R is nothing but the equivalent resistance between points ‘a’ and ‘b’

Therefore, the equivalent resistance between ‘a’ and ‘b’ is 6 ohms

Conclusion :

Kirchhoff’s laws can be used in general to analyze all the electric circuits. Though we have even faster techniques to solve the circuits, but incase if we are not able to use any of those, Kirchhoff’s laws will always be there for us !! 

This is what makes it important. 

Also, apart from it’s importance in just solving problems, it also gives us a very nice understanding on circuit analysis !!

All the Best !!

Keep Learning !!

For Best Experience, View on Desktop/Laptop

• As mentioned in the problem statement description, this problem is designed to connect both of these beautiful subjects : Chess and Physics. So, having a problem which needs just the basics of the subject was required.

So, from the physics side, we have Vectors  – the basic concept in high school Physics while from chess side we need to learn just the Chess Notations. 

In part 1 or (a),

We learn the procedure to calculate the displacement vector. This can be achieved by 2 methods – One is quite quick than the other. So I am just terming it as ‘Quick Method‘ while the second one is the ‘Polygon law of Vector Addition‘. 

In part-2 or (b) :

We try to answer the question by changing the position of origins. 

Overall, I see this as a ‘fun’ problem and not a very calculation intensive problem. So, just Chill and Solve the problem !!

I am attaching the solution file for the problem below

Solution :

DOWNLOAD

web final vectors on board

Enjoy Learning !! 

All the Best !!

For Best Experience, View on Desktop/Laptop

💎This problem is mainly designed to act as a ‘bridge’ 🌉 between physics students and chess players !!

What I mean by this is that , Physics people need to learn basic chess to solve this, while Chess players need to learn little physics to solve this problem.

Problem Statement :

Two friends decide to play an friendly match. Both of them sit for the match. The following game (given below) has been played on the chessboard by them. The square shaped chessboard has the length of ‘8L’.

Game Notations :

Getting frustrated from the piece loss, player with the Black pieces decides to resign the game and the result of the game is 1-0

Question Parts :

1. With reference to the game played, find out the displacement vector of the white’s g1 knight after the 7^th move from white side has been completed. (Take the origin as the centre of the chessboard)

       2. Does the position of origin matter in the answer of part 1 ?

Assumptions :

Assume the pieces to be point masses and are located at the center of respective squares

(Chess Notations can be observed from figure below)

Solution has been uploaded – SOLUTION

Enjoy Solving !!

(For Best Experience, View on Desktop/Laptop)

Author – Saurabh Salvi

#RC Airplane Series – 5

In this article, we are going to learn about the correct battery selection for our RC Airplane Project. This step is very crucial as the battery is going to be serving as the powerhouse for the entire set of electronic components on the plane. 

I will be covering some examples as well for your clarity. Let’s directly dive into the topic !

Why choose LiPo Battery?

Among so many batteries, when it comes to the electronic projects (especially RC aircrafts), we directly choose Lipo over others. 

LiPo stands for Lithium Polymer batteries. These are known for their ‘High Energy Density‘. 

By comparing the definitions, we can see that, if more mass is accumulated in lesser volume, we term that substance as highly dense substance. Similarly, if given energy can be stored in a lesser volume, we term the substance as the one having ‘high energy density’ !

Battery Specifications :

When it comes to LiPo batteries, we have 3 main parameters which we need to check in order to select the right LiPo for our project. Those are :

• Number of cells (Voltage of the battery (in volts))
• Capacity (in mAh)
• ‘C’ rating/discharge rate

Voltage of LiPo battery :

A battery is a combination of cells. So basically to calculate the total voltage of the battery, we need to know the voltage of a single cell. 

Thumbrule :

• The volatge of the cell in Lipo battery should not go below 3.3V and also should not cross 4V as in both cases it might damage the cell and hence the battery
• So, we decide a term called ‘Nominal Voltage‘. This is basically an approx. average value of the max and min voltages. In case of LiPo, we take it as 3.7 V. For batteries, we always consider the nominal voltage

‘S’ represents the number of cells

Based on the S number, we calculate the total voltage of battery.

For example, the above battery is ‘3S’ which implies that it has 3 cells in it. Therefore,

Suppose, we select a model for our BLDC motor : DYS D2826-10 1400KV Outrunner Brushless Motor

Now, we need to correctly choose our motor based on the motor suggested specifications or check datasheet

Now, selecting 2s LiPo or 3s LiPo depends on your model and requirements. The more voltage you apply, the more RPM you will get for the same given motor by the relation :

Capacity of Battery :

The Capacity of Battery gives you an idea of the time in which the battery will get drained off. The unit of Capacity for LiPo is ‘mAh’. It stands for milli-Amp hours.

We try to understand the same with an example. Suppose I have a battery of 4200 mAh. 

• It implies that my battery will get drained off completely if I keep drawing 4.2 A from the battery continuously for 1hr.
• Now, from the same battery, if I draw only 2.1 A (less than 4.2 A), then the battery will drain off after 2 hrs ; giving me more usage time. 
• Pretty Obvious that if you draw lesser current, the battery will allow more usage time !!

For RC Airplanes, Capacity plays an important role for determining the flight time (time for which the plane will fly).

We will discuss about Flight time in coming section below

‘C’ Rating / Discharge Rate :

This thing is nothing but a simple multiplier. It is used to know the actual strength of our battery. This value helps us to calculate the maximum current (continuous and burst) which the battery can provide safely !! 

Formulation : 

Some times, we need some more current than the maximum continuous current value as well. So in that case, the burst continuous current comes into picture. It shows that the battery can provide some extra amount of current as well if required though only for a short interval of time.  

Usually, on batteries, only continuous discharge rate is given. For burst rate, we need to check the battery specifications on websites

For example, 

My battery has specifications 2200 mAh, 11.1V and  I want to decide the appropriate C rating to be chosen. I also know that the maximum current requirement for all my electronic components (majorly motor) is 20 A.

Solution :

So, I need a battery which must have the strength/ability to continuously providing 20A (though its not always needed). By the above formula,

We get,                                                                          20 = 2.2 * (C rating)     

                                                                                         C rating = 9.1 C

So now, anything more than 9.1 C (like 10C, 15C, etc) is absolutely fine BUT less than 9.1 C is NOT OK !!

Flight Time Calculations :

A very important concept and is crucial especially for competitions were time constraints are there. As discussed in Capacity sub-section above, this concept is a lot dependent on the Capacity of battery. 

Note the step-by-step procedure :

After completing all the steps, we get a flight time value. But once this flight time is completed for an RC plane, the battery will be completely drained off !! And WE DON’T WANT THIS !!

• It is always advisable for LiPo batteries to keep atleast 25 % remaining (i.e. use only 75 % of the battery). So if only 75 % of the battery is to be used, then we will obviously get only 75 % of our calculated flight time. This will be our min. actual flight time. It can be more than this but not less, since we calculated this value based on the ‘Max.’ current from motor.

Detailed Example

The below document is a short example designed to get you more clarity on the theory part. Do go through the document once you go through the article completely. Keep both, this article and the example side-by-side and then learn and analyze how it’s done !!

RC Airplane Series – All Articles  (You are at Part – 5 !)

• Part-6 (Next) : ESC Calculations and Electronics Connection
• Part-4 (Previous): Motor and Propeller Selection
• Part-3 : Designing your Airplane !!
• Part-2 : Understanding the control surfaces !
• Part-1 : What’s in the Wings ?

Conclusion

From this article, we got to learn about the procedure to select the correct LiPo battery for our project. In the next upcoming articles, we will cover the ESC calculations and also learn about the thrust test. Till then, Enjoy Learning !!

All the Best !!