### Combination of Resistors- Series

The current through a single resistor ** R** across which there is a potential difference

**is given by Ohm’s law**

*V***. Resistors are sometimes joined together and there are simple rules for calculation of equivalent resistance of such combination.**

*I = V/R*Two resistors are said to be in series if only one of their end points is joined.

Consider two resistors ** R_{1}** and

**in series. The charge which leaves**

*R*_{2}**must be entering**

*R*_{1}**. Since current measures the rate of flow of charge, this means that the same current I flows through R**

*R*_{2}_{1}and R

^{2}. By Ohm’s law:

Potential difference across ** R_{1} = V_{1} = I R_{1}**, and Potential difference across

*R*_{2}= V_{2}= I R_{2}.The potential difference ** V** across the combination is

**Hence,**

*V*_{1}+V_{2}.

*V = V*_{1}+ V_{2}= I (R_{1}+ R_{2}).This is as if the combination had an equivalent resistance ** R_{eq},** which by Ohm’s law is

### Combination of Resistors- Parallel

In parallel combination of two resistors, the charge that flows in at A from the left flows out partly through R_{1} and partly through R_{2}. The currents I, I_{1}, I_{2} shown in the figure are the rates of flow of

Charge at the points indicated. Hence,

The potential difference between A and B is given by the Ohm’s law applied to ** R_{1,} V = I_{1} R_{1}**. Also, Ohm’s law applied to

**gives**

*R*_{2}

*V = I*_{2 }R_{2 }If the combination was replaced by an equivalent resistance ** R_{eq}**, by Ohm’s law