Resistors may be used to represent various electrical components used in practice. One such example is a light bulb that behaves like a resistor. It is therefore important to understand how current and voltages vary when resistors are in series or in parallel.

## Resistors in Series

Resistors are combined in series as shown in Figure 1.

The formula for calculating the effective resistance \(R_{eff}\) is

\(R_{eff} = R_1 + R_2 \)

The above diagram can then be simplified with only one resistor with resistance \(R_{eff}\) instead of two.

For a circuit with more than two resistors in series, the same addition principle applies. Say the circuit has n resistors, effective resistance becomes

\(R_{eff} = R_1 + R_2 + R_3 + \dots + R_n \)

## Resistors in Parallel

Resistors can also be combined in parallel circuits as shown in Figure 2.

The effective resistance \(R_{eff}\) is given by

\(\large{\frac{1}{R_{eff}} = \frac{1}{R_1} + \frac{1}{R_2}}\)

The above equation is can be rewritten as

\(R_{eff} = \frac{R_1 R_2}{R_1 + R_2}\)

In the case of circuits with more than two resistors, the general equation is

\(\large{\frac{1}{R_{eff}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \ldots + \frac{1}{R_n}}\)

## Example

Consider the circuit shown in Figure 3 below.

Resistors \(R_1\) and \(R_2\) are in parallel and can be combined using the above equation

\(R_{1,2} = \frac{R_1 R_2}{R_1 + R_2}\)

Next, the overall effective resistance can be found by combining \(R_{1,2}\) with \(R_3\). Since they are in series, the resistances are added.

\(R_{eff} = R_{1,2} + R_3 \)