Combination of Resistors
Sometimes, a number of resistors are connected in a circuit in order to get a desired value of current in the circuit.
Resistors may be combined in a circuit in the following ways
 Series Combination
 Parallel Combination
 Mixed Combination
In this article, we will learn about series combination of resistors.
Series Combination of Resistors
Two or more resistors are said to be connected in series combination if

Expression For Equivalent Resistance
Consider
 Two resistors of resistances R_{1} and R_{2} are connected in series combination across a battery.
 The battery maintains a potential difference V across the combination.
Using Kirchoff’s Voltage Law in the above circuit, we have
IR_{1} – IR_{2} + V = 0
I (R_{1} + R_{2}) + V = 0
V = I(R_{1} + R_{2}) ………..(1)
Also Read How to Apply Kirchhoff’s Laws?
Now, we wish to replace the above series combination of resistors with a single equivalent resistor of resistance R_{eq}.
An equivalent resistor is one which draws the same current from the battery as drawn by the individual resistors together. 
Replacing the above series combination of resistors with an equivalent resistor, we have
Using Kirchoff’s Voltage Law in the above circuit, we have
IR_{eq} + V = 0
V = IR_{eq} ………..(2)
On comparing equations (1) and (2), we get
This is the required expression for equivalent resistance of a series combination of two resistors.
The formula can be extended for n resistors in the same way.
In series combination,
the equivalent resistance is equal to the sum of the individual resistances. 
Important Notes
Note01:
In series combination,
 The current flowing through each resistor is same but potential difference divides among the individual resistors.
 The potential difference across the combination is equal to the sum of potential difference across the individual resistors.
Note02:
The equivalent resistance of a series combination of resistors is equal to the sum of their individual resistances.
Note03:
If n resistors each of resistance R are combined in series combination, then their equivalent resistance is given by
R_{eq} = R + R + ……. n times
Thus,
Note04:
In series combination, the equivalent resistance is larger than the largest individual resistance.
Note05:
The largest value of equivalent resistance that can be obtained with the given resistances is by combining them in series combination.
Test Your Concepts
Quiz on Series Combination of Resistors
Next Article
Parallel Combination of Resistors
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