# A charge of 35 C passes through a circuit every 5 s. If the circuit can generate 21 W of power, what is the circuit's resistance?

May 3, 2018

$\frac{3}{7} \approx 0.43$ ohms

#### Explanation:

We first find the current produced in five seconds. Current is given by the equation,

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

• $Q$ is the charge in coulombs

• $t$ is the time in seconds

So, we get:

$I = \left(35 \setminus \text{C")/(5 \ "s}\right)$

$= 7 \setminus \text{A}$

Now, power is related by the equation,

$P = {I}^{2} R$, since $P = I V$ and $V = I R$ (Ohm's law)

• $I$ is the current in amperes

• $R$ is the resistance in ohms

• $P$ is the power in watts

Rearranging for resistance, we get:

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

Plugging in our given values, we get:

R=(21 \ "W")/((7 \ "A")^2)

$= \left(21 \setminus {\text{W")/(49 \ "A}}^{2}\right)$

$= \frac{3}{7} \setminus \Omega$