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We have another Physics problem here !
The problem is a kind of blend of physics and electronics which made this problem to fall in this section. The problem is multi-concept based. As a hint, the problem mixes up :
As a reference, you can use the attached article so that you are all covered to complete this problem : Click Here
The Problem Statement has been uploaded below in the form of PDF.
Problem 7 
Topic under the Chapter : Electrostatics
To understand this topic, we need to know about ‘free electrons’. These free electrons behave very similar to the gas atoms in a container. Both of them are under continuous random motion throughout the space given to them.
Free electrons are nothing but some loosely bonded valence electrons which come out of the atom very easily ; just as the loosely stitched button comes out of the shirt very easily : )
Note that :
When we talk of bodies, we classify them as –
Now suppose you have a metal conductor placed in a region. And you bring a positive charge ‘+q’ in that region ‘externally’.
Important Note :
These charges are ‘induced’ on the conductor due to the external charge. This phenomenon of separation of charges in a body by some external factor is called ‘Charge Induction’
As discussed, the basic difference between non-metal and metals is the absence of free electrons in case of non-metals.
Setup – Let’s consider the same condition. An non-metallic body has been placed in a region. Now, we bring a positive charge in vicinity of this body.
Important Note :
This alignment in dipoles in a non-conducting body due to an external charge is called induction in non-conducting bodies or ‘Polarization’. The separation between positive and negative charges is very very small. So, usually, we ignore it in our problem solving, etc.
Special Note :
This is why a Charged body always attracts a Neutral body. We can also conclude that :
“Attractive force on neutral conducting body will be more due to any external charge”
In presence of an external electric field set up by an charge placed outside a body; charge separation happens within the body. This phenomenon is called charge induction.
What is Polarization in Electrostatics ?
The formation of dipoles within the atoms of non-metal due to the external electric field set up by the charge placed outside the body is called Polarization
Galvanometer is a deflection type meter which is used to measure the current value. The needle present in the Galvanometer gets deflected when a current passes through it and the amount of deflection produced is proportional to the current passing through the device.
There are two types of Galvanometers :
So, the basic difference between the two is that, Unidirectional can give information only about magnitude while Bi-directional can tell direction as well as magnitude.
The inner setup of Galvanometer has something known as Coil Resistance ‘G‘ and at maximum deflection, the safe current which flows through the galvanometer is ‘ig‘ . The symbol for Galvanometer is :
The purpose of an Ammeter is also to measure current but the range for current measurement is much higher.
The Voltmeter is used specifically to measure the potential difference across the given terminals.
(Question from Arihant – Electricity and Magnetism)
(Question from Arihant – Electricity and Magnetism)
So, we have learnt about the Galvanometer and how can we use it as an Ammeter and a Voltmeter.
All the Best !
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In this Article, we will try to cover another sensor – Ultrasonic Sensor (HC-SR04).
The working of this sensor can be explained in 4 steps :
The Ultrasonic Sensor HC-SR04 has a transmitter and a receiver present in the same module
The Transmitter sends out the ultrasonic sound waves at a high frequency of about 40kHz. By 40kHz, we mean that, the sound waves travels in the medium with a frequency of 40,000 cycles per second
The transmitted wave hits the obstacle and gets reflected back
The reflected wave is then received by the on-board receiver
The time required for the sound wave to come back (transmitter to receiver) is calculated. And using this time data and velocity of sound in the medium, we calculate the distance (d) between the sensor and the obstacle.
There are 4 pins on the HC-SR04 Ultrasonic Sensor
– The VCC pin is where you provide the +5V power supply
Saying the same thing through some graphs will look like :
-GND is to as usual connected to the common ground
Pin Connections :
Let’s build a quick mini project to understand the working of this sensor :
TinkerCad Circuit Diagram :
Code for the Project : GitHub File Link –> Click Here to Access
All the Best !
Keep Learning
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There’s a very common difference between a resistor and a capacitor :
We have already learnt about Charging and Discharging of Capacitor in the article : Learning about Capacitors . According to that, if our circuit consists of only a Capacitor attached to a battery, then :
Refer to the timeline diagram below which shows how resistance to electron flow is offered by capacitor during charging
This resistance offered by a Capacitor is referred to as ‘Capacitive Reactance’
f –> represents the frequency of the source
Note that :
Case : DC Source is attached across capacitor
Result : We all know that frequency of DC Source is zero as there is no switching in polarity. Therefore, f=0 and we get reactance as infinite. Hence, we can see that the circuit almost behaves as an open circuit in case of a DC Source
And also in case of AC Source, it is quite evident from the formula that, if the frequency of the source is increased, it results in decrease of capacitive reactance. Let’s take 2 cases to understand this : Both are AC Source – One with f = 50kHz and second with f = 10Hz (Capacitance is 10uF)
Sub-Case f = 50 kHz Sub-Case f = 10 Hz
Hence, verified !
Let’s calculate the peak current achieved in the circuits in the 2 examples considered in previous section-1 . Circuit has all the parameters same, just the peak voltage of AC Source is now given to be 5V
This frequency dependent behaviour of capacitors makes them suitable to build some special type of circuits called Low Pass and High Pass Circuits.
Just remember this analogy :
To understand this circuits, lets take 2 cases : one at low frequency (f=0) and another at very high frequency.
We can find the relation,
Case 1 : Low Frequency (f = 0) of Source
This implies that the source behaves like a DC. And we know that, in steady state, Vc = Vout = Vin i.e. the whole source voltage comes across the capacitor
Case 2: Very High Frequency of Source
At high frequency, the capacitive reactance is low –> This makes the capacitor to behave as short circuit–> This implies, there is no voltage drop across capacitor –> Therefore, Vc = Vout = 0
As discussed earlier,
If we get a voltage at Vout –> It implies that we have the signal of that frequency over there. So, in case of above circuit, we are getting voltage at Vout in case of low frequency
To understand this circuit, Again lets take the same 2 cases : one at low frequency (f=0) and another at very high frequency.
Case 1 : Low Frequency (f = 0) of Source
This implies that the source behaves like a DC. And we know that, in steady state, Vc = Vin i.e. the whole source voltage comes across the capacitor. But Vout = 0 in this case, as Vout is now the voltage across the resistor (Therefore, Vout = VR = 0)
Case 2: Very High Frequency of Source
At high frequency, the capacitive reactance is low –> This makes the capacitor to behave as short circuit–> This implies, there is no voltage drop across capacitor –> Therefore, Vc = 0 . But, because of this, the whole source voltage shifts to the resistor.
This makes VR= Vout = Vin
If we get a voltage at Vout –> It implies that we have the signal of that frequency at output. So, in case of above circuit, we are getting voltage at Vout in case of high frequency
We have discussed the basics of the High and Low Pass Filter Circuits. The most fundamental difference between the two is the position of output voltage.
Keep Learning !
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Click the photo to watch the associated video about this Project
RGB, as we all know, stands for :
They are one of the primary colours which can mixed in different proportions to result in various colours.
*Hint for the Solution : For this project, we will be showing ‘143’ with the help of RGB LED
The best analogy is the painting palette which we normally use in our drawing classes. Consider having the smaller version of the paints. So how you used to obtain different colours ? –> By mixing those available colours in different ratios !
Also different shades of the colours can be obtained by varying the intensity of RGB colours
The RGB LED has 4 pins –
Always check the pin name associated with the pin. The pin order might change from manufacturer to manufacturer !
Important :
Treat each of the colour pin as a separate LED. Since only then you can control each colour on the LED individually.
So, as discussed in our Problem Statement, we are going to code our LED such that it somehow conveys the message ‘143’ (A modern way to say ” I love You “). This is how it can be done :
Table for Code
We know that Digital Pins have only 2 signals – ‘1’ and ‘0’ –> i.e. It’s either ON or it’s OFF respectively. This case is like a switch which we use to turn ON and turn OFF the fan.
Fig. For Digital Pins without PWM
BUT Now, PWM is like adding a Regulator besides the switch (it’s just an addition to what we had before). This will allow us to vary and control the speed of the fan as well
Fig. For Digital Pins with PWM
The code to the Main Project Can be Found in the below attached GitHub File. The comments will guide you to understand the reasoning for that particular section of code.
GitHub Folder Link (Arduino Code for the Project) : Click Here
So, through this Mini Arduino Project-2, we learnt to interface RGB LED with Arduino and also learnt some basic working of the same. As discussed, we will be looking into PWM signals in a lot more detail in upcoming articles.
Keep Learning !
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Combining what we have learnt in previous articles, opens up a whole new set of ideas to explore. The combination of Resistor and Capacitors results in an RC Circuit. One of the very important type of electronic circuits to be studied due to their wide range of applications.
Previous articles Alert !
Let’s consider a circuit with a battery of emf ‘E’ and a capacitor (capacitance ‘C’) connected in series to it via a switch ‘S’. Note that Capacitor is uncharged initially.
We know, charging will start as soon as the Switch ‘S’ is closed and also it is seen that the capacitor gets charged very quickly. This is shown in Fig.2 where we plot the charge v/s time graph in order to keep a track of the charge appearing on capacitor plates w.r.t time
Now, we add a resistor with resistance R in series with the capacitor. Capacitor is uncharged initially. We have the most basic RC Circuit possible for analysis.
In case of Charging, you can imagine Resistor as an cunning friend who doesn’t want you(capacitor) to grow in his/her life. This friend somehow tries to delay the work which you would have achieved very easily earlier.
Consider we have a capacitor, fully charged with the help of battery of emf ‘E’ and we need to discharge it.
Discharging still happens, but at a slower rate. This can be observed from the plot between q (charge on capacitor plate) v/s time ‘t’ as shown below.
So we can clearly see from Fig.8 that it takes time to reach 0 charge (for practical purpose). But how much time it takes, is decided by the R and C values
We see some non-linear curves in case of RC charging (Fig. 4) and in case of RC discharging (Fig. 8). But what is the nature of these graphs. How do we plot them exactly ? What is the equation. Let’s answer all of these through our Analysis
We represent ‘Time Constant’ by the greek letter ‘Tau’
Now that we know, how it is formulated, replace R X C with time constant.
We can keep on inserting such time values and keep a track of the charge on capacitor.
Important : Note that q is the charge on the capacitor plates at time instant ‘t’
So based on our previous articles knowledge (Resistors and Capacitors), we have learnt about the basics of RC Circuits. There will be another article to go into further depth in case of RC Circuits
Keep Learning !
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This project mainly aims to cover a part of Basics regarding Arduino IDE and Interfacing of Arduino with other components. Let’s get straight into building this project !
Problem Statement :
Our main objective for the project is to make a Arrow Keypad like thing in order to control the LEDs. The LEDs indicates the direction corresponding to the button which we pressed on the keypad
Reference Article Alert !!
How to check Resistance value of your resistor? – Refer this Article : Dealing with Resistors
Note that, there are no connections among the LEDs.
We will see how to connect each component with Arduino
*Code for the Blinking of LED can be found in our GitHub Repository – Click Here
*Code for the usage of Push Button is also added in our GitHub Repository – Click Here
*Code for the ‘controlling LED with Push Button’ is also added in the GitHub Repository – Click Here
After Being Comfortable with the above three mini-projects, the main project is very easy to do as we have do the same thing, but now, it has to be done multiple times.
We need the LED matrix type setup to be in a square shape (diamond shape). So accordingly we arrange setting up the LEDs and corresponding resistors to protect those LEDs
Reference Article Alert :
How to choose correct Resistor for a specific coloured LED ? – Refer the Article : Dealing with Resistors
You will learn that –> It is safe to use a higher resistance resistor than the required value. So we go for 220 ohms.
Connect the LEDs as learnt in Section 3.1
Overall Diagram in TinkerCad can be shown as :
The same thing in Reality looks something like :
The Complete Code for this Project can be found in the GitHub Repository by name ‘Main Project Code’ – Click Here
Below is the attached file for Code Explanation. This will exactly give you an idea of the flow that the project code has in it.
Code Explanation - Main Arduino Project 
So, with this, we have learnt to do the basic interfacing of the components with Arduino. There’s a still lot to learn about Arduino. There are also many sensors that can be used in order for different projects.
This Article was all about keeping it as basic as possible so that it is much interesting for people/students to read and see
Keep Learning !
https://www.youtube.com/watch?v=rxL8DkdYCTw
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Calculation of charge-to-mass ratio is of great importance when it comes to the subject of Modern Physics. Understanding the procedure behind this experiment is equivalent to revising the following topics as well :
Ok, so you have a value called e/m ratio ! But why is it important to caluculate this value? Is there any applications of it ?
We can see it’s application in :
Electron Microscopes :
Particle Accelerometers :
The Setup mainly consists of the following things :
Fig. Setup for the Experiement
– The plate attached to the positive terminal is used as anode to attract the electron cloud. This is done to make the electrons accelerate.
– Each electron has different energies when they come out from atoms. And when they are accelerated due to potential difference of V, then they all end having different set of velocities.
Note that : The E and B vectors are perpendicular to each other
As discussed, the anode attracts the electron cloud which makes them to accelerate towards the screen S. But well before they reach the screen, the electrons are made to pass through a region R where, for now, only Electric field is applied (B is turned off).
The current setup for Step-1 looks like :
As the electrons pass through ‘Region R‘ , they undergo deflection ‘y’ due to the electric field and follow a trajectory as shown (green) . We zoom into the Region R to get a better understanding of what’s happening
We need the expression for deflection ‘y’.
Important : Note that the deflection is going to be measured from axis
Some of the Projectile comes into picture now !
Now, our aim is to find the velocity ‘v’ of the electron. Recall that the ‘y’ is the deflection –> BUT Deflection from which path ? The answer is ‘the axis’ . We need to find the deflection caused in electron’s trajectory due to the electric field E because otherwise in the absence of E, it would just follow the straight path along axis.
We have to balance the forces (to get zero deflection). Remember it’s a negative charge.
We then adjust the values of E and B until the magnitudes of forces are same. This allows us to build a ‘velocity selector‘
As discussed in Section 2 of this article, all the electrons come with different set of velocities. But, for continuing our experiment, we need only the electrons of specific velocity to be focused on. So, how to exactly distinguish those electrons ?
We can clearly see the relation of E and B with velocity. This means that controlling the values of E and B allows us to select the electrons which have their velocities as E/B. The electrons possessing this specific velocity will go through the region undeflected and hence we can separate them.
Calculating the e/m ratio with the expressions and equations we got till now :
Substituting v = E/B in the expression of y obtained in step-1, we get :
Keep Learning !
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In the Part-1 : Learning about Capacitors, We already got an idea about the functioning of the capacitors. But now, with that understanding, how to make use of them in electric circuits !?
This is what we focus in this article. Getting inclined towards the numerical aspect of the capacitors is our goal for this article !!
Topics to be Covered :
As discussed in part-1, more the charge separation happens (+Q on one plate and -Q on other), more will be the potential difference across the plates of capacitor(V). So basically we can say,
Now we introduce the ‘constant’ of proportionality –> Capacitance (C). The relation becomes :
Note that :
There are many configurations possible to make a capacitor, but the most simplest one to analyze is the Parallel plate Capacitor. This setup basically consists of :
The capacitance of the parallel plate capacitor is given by :
We can clearly verify from the above expression that, the capacitance just depends upon the geometrical factors and the dielectric constant.
*Interested readers can have a look at the derivation of the above expression in document attached at the end of the article or can download the file directly
Click here to download the file – DOWNLOAD
“In simple words, Dielectric are a type of insulating materials which allow Electric field but don’t allow electric current to pass through them”
They are majorly used to serve 3 purpose:
It is necessary to maintain the gap (even though small) between the metal plates. Because, the capacitor would loose all of it’s storing capacity if the metal plates come in contact with each other; since in that case, it would just behave as a simple conductor.
Dielectric Breakdown :
Better the dielectric material, more will be the dielectric breakdown voltage. Let’s consider 2 situations :
Situation-1 (Air between plates)
Situation – 2 (Dielectric material D2 inserted between plates)
The dielectric breakdown voltage of material (say D2) is more than that of air. This implies that more voltage across capacitor plates is required in case of D2 for breakdown to happen. This proves our point that, the insertion of dielectric allows us to apply more voltage across capacitor plates without causing any dielectric breakdown.
Suppose we have a capacitor with just air between the plates. Now we insert a dielectric material of dielectric constant ‘k’ between the plates completely. Have at the look at the flowchart below to just get an quick overview of what happens !
Flowchart – Summary of how Dielectrics help to increase Capacitance
“Like the way we have current in case of resistors, in the same way, for capacitors, we have charge”
Consider 3 capacitors C1, C2 and C3 in series combination and V1, V2 and V3 are the potential differences across them respectively.
Since we need to find the ‘equivalent’ capacitance :
So, we can observe that, by keeping capacitors in series, we get the value of equivalent or resultant capacitance which is even lesser than the one which has least capacitance among the three. Suppose, C2 < C1 < C3, then Ceq < C2
Again : “Like the way we have current in case of resistors, in the same way, for capacitors, we have charge”
Consider 3 Capacitors C1, C2 and C3 in parallel combination and the charges passing through them are q1, q2 and q3 respectively.
We know the relation from KCL :
The equivalent capacitance incase of parallel combination will be greater than the greatest among the three (here)
Now, there are again some types of network circuits in which we are expected to find the equivalent Capacitance.
There are several methods to simplify and solve such type of circuits like :
We have already looked at the above methods with context to resistors in Part-2 : Combining Resistors
Though the article is for Resistors, the approach of simplifying the circuit/network still remains the same !
Example :
Step-1 :
Distribute the voltages across all plates. In this example we consider the voltage/potential at A to be ‘a’ and at B, to be ‘b’. Still we are not able to cover all the plates. So we introduce another unknown potential ‘x’
Remember that : Potential always remains constant on a conductor
Step-2 :
Assign the numbers to each face of the plates
Step-3 :
Keep points ‘a’ and ‘b’ at the ends and all the unknowns which we introduced should come in between.
Step-4 :
To make a capacitor, we need 2 plates and separate them by a distance
So, now, we just look at the numbers assigned to their faces and make a simlified circuit
Step-5 :
Solve by normal Series- Parallel concepts
The equivalent capacitance of the simplified circuit is 5C/3, where C is :
Till then, Keep Learning !
Attached Document : Reference for Derivation of Capacitance for Parallel Plate Capacitors
Reference - Capacitor Derivation