# A charge of 25 C passes through a circuit every 4 s. If the circuit can generate 1 W of power, what is the circuit's resistance?

May 28, 2017

The circuit resistance is $= 25.6 m \Omega$

#### Explanation:

We apply the equation

$Q = I t$

The charge is $Q = 25 C$

The time is $t = 4 s$

The current is $I = \frac{Q}{t} = \frac{25}{4} A$

The power

$P = U I$

But according to Ohm's Law

$U = R I$

So,

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

So,

the resistance is $R = \frac{P}{I} ^ 2$

$= \frac{1}{\frac{25}{4}} ^ 2 = 0.0256 \Omega$