Question

If the voltage across a circuit of constant resistance is doubled, the power dissipated by that circuit will

A) decrease to one-fourth the original power.

B) be two times as large.

C) decrease to one-half the original power.

D) be four times as large.

Answer 1

D) be four times as large.

Step-by-step explanation:

The power dissipated is the product of the potential difference between the terminals and the current intensity that passes through the device:

`P=VI`

In this case, the device is a resistor. Therefore, from ohm's law:

`V=IR\\I=(V)/(R)`

Finally, we obtain the relation between power and voltage:

`P=(V^2)/(R)`

We have
`V'=2V`:

`P'=(V'^2)/(R)\\P'=((2V)^2)/(R)\\P'=4(V^2)/(R)\\P'=4P`

So, the power dissipated by that circuit will be four times as large.