# Derive equivalent resistance of a series connection and the parallel connectionâ€‹ of three resistors

Resistors in series

The potential difference V=V1+V2+V3

Since current flowing is the same

$\\V=IR_1+IR_2+IR_3$

If the total resistance of the circuit is R then V=IR, therefore

$\\IR=IR_1+IR_2+IR_3\\or\ R=R_1+R_2+R_3$

The net resistance in series combination is the sum of the resistors.

Resistance in parallel

In a parallel circuit, the voltage across the resistors remains the same but the current get distributed. That is

$\\I=I_1+I_2+I_3$

If R is the total resistance of the circuit then

$\\I=\frac{V}{R}$

Therefore

$\\\frac{V}{R}=\frac{V}{R_1}+\frac{V}{R_2}+\frac{V}{R_3}\\or\ \frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$

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