# A charge of 35 C passes through a circuit every 5 s. If the circuit can generate 82 W of power, what is the circuit's resistance?

May 15, 2018

$1.67$ ohms

#### Explanation:

We first find the current produced, 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 here, we get:

I=(35 \ "C")/(5 \ "s")=7 \ "A"

Then, power is given through the equation:

$P = {I}^{2} R \setminus \left(\because V = I R \setminus \text{and} \setminus P = I V\right)$

where:

• $P$ is the power in watts

• $R$ is the resistance in ohms

So, we get:

82 \ "W"=(7 \ "A")^2*R

$R = \left(82 \setminus {\text{W")/(49 \ "A}}^{2}\right)$

$= 1.67 \setminus \Omega$