Resistors in series and parallel

Resistors in series

When resistors are connected in series, the current through each resistor is the same. In other words, the current is the same at all points in a series circuit.

When resistors are connected in series, the total voltage (or potential difference) across all the resistors is equal to the sum of the voltages across each resistor.

In other words, the voltages around the circuit add up to the voltage of the supply.

The total resistance of a number of resistors in series is equal to the sum of all the individual resistances.

Circuit diagram with one battery and three resistors in series. The resistance is labelled R1, R2 and R3. The voltage  is labelled V1, V2 and V3 and the current is labelled I1, I2 and I3.

In this circuit the following applies.

I1 = I2 = I3

VT = V1 + V2 + V3

and, RT = R1 + R2 + R3

curriculum-key-fact
Adding components in series increases the total resistance in a circuit.

Resistors in parallel

When resistors are connected in parallel, the supply current is equal to the sum of the currents through each resistor. The currents in the branches of a parallel circuit add up to the supply current.

When resistors are connected in parallel, they have the same potential difference across them. Any components in parallel have the same potential difference across them.

In order to calculate the total resistance of two resistors connected in parallel, this equation is used.

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

To calculate the total resistance of three resistors connected in parallel, we add a third resistor to the equation (and so on).

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

curriculum-key-fact
Adding components in parallel decreases the total resistance in a circuit.
Question

Calculate the resistance of this parallel combination.

Circuit diagram with three resistors connected in parallel. The resistors are labelled 3 Ohms, 6 Ohms and 9 Ohms.

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

\frac{1}{R}=\frac{1}{3}+\frac{1}{6}+\frac{1}{9}

R = 1.64 Ω

curriculum-key-fact
The total resistance is less than the smallest resistor.