Resistors in series

Current

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.

So in the circuit above \(I_{S}=I_{1}=I_{2}=I_{3}\)

Potential difference

When resistors are connected in series, the total of all the potential differences (sometimes referred to simply as voltage) around the circuit is equal to the potential difference (p.d.) of the supply:

\[V_{S} = V_{1}+V_{2}+V_{3}\]

This relationship expresses the law of conservation of energy.

The supply voltage is a measure of the energy supplied to each electron. The p.d. across each component is the energy converted by each component. Therefore the energy supplied equals the energy converted – energy has been neither created nor destroyed in the circuit.

Resistance

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

\[{R_S} = {R_1} + {R_2} + {R_3}\]