Question

How should two resistors, with resistances R1 Ω, R2 Ω, be connected to a battery of

e.m.f. V volts so that the electrical power consumed is minimum?

Answer 1

The two resistors should be connected in series.

(I assume that the question is stating the electrical power consumed by the resistors)

Step-by-step explanation:

Think about the formula P = V^2 / R

For the electrical power consumed to be a minimum, we must let V be as small as possible.

For small V, between a series and a parallel connection, series is the correct connection as the combined potential difference (pd) for the two resistors is equal to the electromotive force (emf) of the battery.

However, for parallel connections, the combined pd for the two resistors is equal to twice the emf of the battery. (Each resistor will have a pd equal to the emf of the battery)

With lower total V, with the same R, power P consumed will decrease.