# A charge of 25 C passes through a circuit every 4 s. If the circuit can generate 25 W of power, what is the circuit's resistance?

Jun 26, 2018

$0.64$ ohms.

#### Explanation:

We first find the current passing through, which is given by the equation:

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

where:

• $I$ is the current in amperes

• $Q$ is the charge in coulombs

• $t$ is the time in seconds

So, the current is:

$I = \left(25 \setminus \text{C")/(4 \ "s}\right)$

$= 6.25 \setminus \text{A}$

Power is related through current and resistance by the equation:

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

where:

• $P$ is the power in watts

• $I$ is the current in amperes

• $R$ is the resistance in ohms

Rearranging for resistance, we get:

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

Plugging in the values, we get:

R=(25 \ "W")/((6.25 \ "A")^2)

$= \left(25 \setminus {\text{W")/(39.0625 \ "A}}^{2}\right)$

$= 0.64 \setminus \Omega$