# A charge of 12 C passes through a circuit every 9 s. If the circuit can generate 6 W of power, what is the circuit's resistance?

May 7, 2017

The resistance is $= 3.375 \Omega$

#### Explanation:

The charge is

$Q = I t$

the current is $I = \frac{Q}{t}$

The power is

$P = U I$

But

According to Ohm's Law

$U = R I$

So,

the power is $P = R I \cdot I = R {I}^{2}$

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

$= \frac{6}{\frac{12}{9}} ^ 2$

$= 6 \cdot \frac{81}{144}$

$= 3.375 \Omega$