If two identical devices with the same power rating are used for the same time, but one is twice as efficient, what is the energy input difference?

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Multiple Choice

If two identical devices with the same power rating are used for the same time, but one is twice as efficient, what is the energy input difference?

Efficiency tells us how much of the input energy actually becomes useful energy. If you want the same amount of useful energy in the same time, the device that is more efficient needs less input energy. Let the useful power be the same for both devices. For a given time, the useful energy is fixed (useful energy = useful power × time). The input energy is this useful energy divided by the efficiency: E_in = (useful energy) / η. If one device is twice as efficient as the other (η_more = 2η_less), then its input energy is half: E_in_more = (useful energy)/ (2η_less) = 1/2 × E_in_less. So the more efficient device requires half the energy input over the same time.

Efficiency tells us how much of the input energy actually becomes useful energy. If you want the same amount of useful energy in the same time, the device that is more efficient needs less input energy.

Let the useful power be the same for both devices. For a given time, the useful energy is fixed (useful energy = useful power × time). The input energy is this useful energy divided by the efficiency: E_in = (useful energy) / η. If one device is twice as efficient as the other (η_more = 2η_less), then its input energy is half: E_in_more = (useful energy)/ (2η_less) = 1/2 × E_in_less. So the more efficient device requires half the energy input over the same time.

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