# A charge of 6 C passes through a circuit every 3 s. If the circuit can generate 18 W of power, what is the circuit's resistance?

$4.5 \setminus \setminus \Omega$

#### Explanation:

The electric current $I$ is the rate of flow of charge w.r.t. time which given as

$I = \frac{\mathrm{dQ}}{\mathrm{dt}}$

$= \setminus \frac{6}{3}$

$= 2 \setminus A$

If $R \setminus \setminus \Omega$ is the electric resistance then the electric power or rate of heat generation is given by Joule's Law as follows

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

$18 = {2}^{2} R \setminus \quad \left(\setminus \because \setminus H = 18 \setminus W\right)$

$R = \frac{18}{4}$

$R = 4.5$

Hence the electric resistance is $R = 4.5 \setminus \setminus \Omega$