Combination of Resistors
Before you go through this article, make sure that you have gone through the previous article on Series 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 parallel combination of resistors.
Parallel Combination of Resistors
Two or more resistors are said to be connected in parallel combination when

Expression For Equivalent Resistance
Consider
 Two resistors of resistances R_{1} and R_{2} are connected in parallel combination across a battery.
 The battery maintains a potential difference V across the combination.
Using Kirchoff’s Voltage Law in the loop ACDBEFA, we have
I_{1}R_{1} + V = 0
V = I_{1}R_{1}
I_{1} = V / R_{1} ………..(1)
Using Kirchoff’s Voltage Law in the loop AGHBEFA, we have
I_{2}R_{2} + V = 0
V = I_{2}R_{2}
I_{2} = V / R_{2} ………..(2)
Also Read How to Apply Kirchhoff’s Laws?
Adding Equations01 & 02, we get
(Equation03)
Now, we wish to replace the above parallel 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 parallel 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}
I = V / R_{eq} ………..(4)
On comparing equations (3) and (4), we get
This is the required expression for equivalent resistance of a parallel combination of two resistors.
The formula can be extended for n resistors in the same way.
In parallel combination,
the reciprocal of equivalent resistance is equal to the sum of reciprocals of the individual resistances. 
Important Notes
Note01:
In parallel combination,
 The potential difference across each resistor is same but current divides among the individual resistors.
 The total current drawn from the battery is equal to the sum of currents flowing through the individual resistors.
Note02:
If two resistors having resistances R_{1} and R_{2} are combined in parallel combination, then their equivalent resistance is given by
(Not Recommended to Use)
Taking LCM and then reciprocal, this formula for two resistors can be rewritten as
(Recommended to Use)
Trick To LearnEquivalent Resistance = Product of two resistors / Sum of two resistors 
If the resistance of one resistor is n times the resistance of the other resistor i.e. R_{2} = nR_{1} (say), then substituting in the above formula and solving, the formula can be rewritten as
(Recommended to Use)
Trick To LearnEquivalent Resistance = Big One / (n+1) 
Note03:
If n resistors each of resistance R are combined in parallel combination, then their equivalent resistance is given by
Note04:
In parallel combination, the equivalent resistance is smaller than the smallest individual resistance.
Note05:
The smallest value of equivalent resistance that can be obtained with the given resistances is by combining them in parallel combination.
Test Your Concepts
Quiz on Parallel Combination of Resistors
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