# A charge of 12 C passes through a circuit every 4 s. If the circuit can generate 8 W of power, what is the circuit's resistance?

Sep 27, 2016

I got: $0.9 \Omega$

#### Explanation:

Here we have a current $I$ of charge passing through the circuit in a given time, or:
$I = \text{charge"/"time} = \frac{12}{4} = 3 A$
The power is energy delivered by our charges (passing in the circuit) at each second.
We can write power in general as:
$P = V I$ But here we take advantage of Ohm's Law, $V = R I$, to rearrange our expression of Power to include resistance as:
$P = {I}^{2} R$
so that:
$R = \frac{P}{I} ^ 2 = \frac{8}{9} = 0.89 = 0.9 \Omega$