# A charge of 24 C passes through a circuit every 6 s. If the circuit can generate 8 W of power, what is the circuit's resistance?

Feb 19, 2016

The resistance in the circuit is $0.5$ $\Omega$

#### Explanation:

Data:

Charge$= Q = 2 C$
Time$= t = 6 s$
Power$= P = 8 W$
Resistance=R=??

We know that:

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

Where $I$ is the current.

Also we know that: $I = \frac{Q}{t} = \frac{24}{6} = 4$ $A$

$P = {I}^{2} R \implies 8 = {4}^{2} \cdot R$

Rearranging:

$R = \frac{8}{16} = 0.5$ $\Omega$

Hence, the resistance in the circuit is $0.5$ $\Omega$.

Feb 19, 2016

The circuit's resistance is $0.5$ $\Omega$

#### Explanation:

First, let's think about what we are trying to calculate. We know the power generated from the circuit which is given by Joule's law:

$P = I \cdot V = 8$ $W$

We have also been given the rate of charge flow, which is a current:

$I = \frac{Q}{t} = \frac{24 C}{6 s} = 4$ $A$

We can substitute this current into the first equation and solve for the voltage:

$V = \frac{8 W}{4 A} = 2$ $V$

Now we have a current and a voltage and want to find a resistance. We know Ohm's Law relates all three of these:

$V = I \cdot R$

Rearranging to find the resistance:

$R = \frac{V}{I} = \frac{2 V}{4 A} = 0.5$ $\Omega$