the complete guide to resistors - part 3

Combining Resistors: Series, Parallel & Equivalent Resistance – Part 3

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Till now, we have learnt about the Resistor, basically how it works, what its applications are, how to use it in a circuit, etc. But we come across the circuits that involve some combinations of resistors. Our aim in this article is to simplify this network and obtain the equivalent resistance of the network.

Table Of Contents
  1. 1. What is meant by finding equivalent resistance ?
  2. 2. Resistors in Series
  3. 3. Resistors in Parallel
  4. 4. Example on Series & Parallel Combinations

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 Combinations

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

3
4


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

5
6


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

The Complete Guide on Resistors:

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