# A charge of 8 C passes through a circuit every 2 s. If the circuit can generate 3 W of power, what is the circuit's resistance?

Dec 19, 2016

I found: $0.2 \Omega$

#### Explanation:

You know that current $I$ is the rate of passing of charge $Q$ through a section of a conductor with time $t$ or:

$I = \frac{Q}{t}$

$I = \frac{8}{2} = 4 A$
Power $P$ is the rate of transformation of energy with time that, in case of electrical circuits, can be written (using also Ohm's Law: $V = R I$):
$P = V I = {V}^{2} / R = {I}^{2} R$
$P = {I}^{2} R$ and rearranging:
$R = \frac{P}{I} ^ 2 = \frac{3}{4} ^ 2 = \frac{3}{16} = 0.1875 \approx 0.2 \Omega$