Higher

When more than two resistors are connected in parallel the equation becomes:

\frac{1}{R}=\frac{1}{R}_{1} +\frac{1}{R}_{2} +\frac{1}{R}_{3} {...}

Example

The following resistor network is set up.

Resistor network - there are 3 resistors in parallel to each other, measuring 12 Ohms, 18 Ohms, and 6 Ohms

Calculate the total resistance of the network.

Answer

\frac{1}{R}=\frac{1}{R}_{1} +\frac{1}{R}_{2} +\frac{1}{R}_{3}

R1 = {12}\Omega

R2 = {18}\Omega

R3 = {6}\Omega

\frac{1}{R}=\frac{1}{12} + \frac{1}{18} + \frac{1}{6}

\frac{1}{R}=\frac{11}{36}

R = \frac{36}{11}

R = {3.27}\Omega

This means that the three individual resistors can be replaced by one resistor of {3.27}\Omega.

Resistors in parallel

Adding resistors in parallel decreases the total resistance.

The current has a choice of paths and only has to pass along one branch of the circuit.

It does not pass through each resistor and the total resistance of a parallel circuit is always smaller than the smallest resistor.