# A charge of 35 C passes through a circuit every 5 s. If the circuit can generate 7 W of power, what is the circuit's resistance?

Feb 15, 2016

Convert the flow of charge into current, then use and rearrange $P = {I}^{2} R$ to find that the resistance is $\frac{1}{7}$ $\Omega$.

#### Explanation:

Current is defined as the rate of flow of charge:

$I = \frac{Q}{t} = \frac{35}{5} = 7$ $A$

The power in a circuit can be expressed as:

$P = {I}^{2} R$

(Combining the equation $P = V I$ with Ohm's Law, $V = I R$ will yield this.)

Rearranging:

$R = \frac{P}{I} ^ 2 = \frac{7}{7} ^ 2 = \frac{1}{7}$ $\Omega$