A student connects a battery to two lamps. The student first connects the lamps in series, then reconnects them in parallel. Explain how the brightness of each lamp changes when the circuit is changed from series to parallel, and why this happens.

In a series circuit the two lamps share the battery voltage, so each lamp receives only half the battery voltage. In a parallel circuit each lamp is connected directly across the battery and therefore each receives the full battery voltage.

Because the voltage across each lamp is higher in the parallel arrangement, the current through each lamp is higher (I=V/R). The power dissipated by each lamp is P=VI, so with a higher voltage and higher current the power – and therefore the energy per second – is greater.

Thus each lamp is brighter in the parallel circuit than in the series circuit.

In a series circuit the current is the same through both lamps but is smaller than in the parallel circuit because the total resistance of the series combination is higher, limiting the current from the battery.