# A charge of 18 C passes through a circuit every 4 s. If the circuit can generate 36  W of power, what is the circuit's resistance?

Jun 24, 2017

$R = \frac{P}{I} ^ 2 = 1.78$ $\setminus \Omega$

#### Explanation:

We know that the current $I$ in a circuit where a charge $Q$ passes every $t$ seconds is given by:

$I = \frac{Q}{t} = \frac{18}{4} = 4.5$ $A$

We also know power in a circuit in which a current $I$ is flowing through a resistance $R$ is given by:

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

Rearranging:

$R = \frac{P}{I} ^ 2 = \frac{36}{{4.5}^{2}} = 1.78$ $\setminus \Omega$