# A charge of 40 C passes through a circuit every 8 s. If the circuit can generate 16 W of power, what is the circuit's resistance?

Sep 11, 2016

$R = 0.64$ Ω

#### Explanation:

One of the formulas for electric power is $P = {I}^{2} R$.

Also, electric current is defined as the flow of charge.

Mathematically, this is expressed as $I = \frac{Q}{t}$.

Let's substitute this expression of $I$ into the equation for electric power:

$\implies P = {\left(\frac{Q}{t}\right)}^{2} R$

$\implies P = \frac{{Q}^{2}}{{t}^{2}} R$

Then, let's rearrange the equation to express it in terms of $R$:

$\implies R = \left(\frac{P {t}^{2}}{{Q}^{2}}\right)$ Ω

Now, let's substitute the values for electric charge, time and electric power:

$\implies R = \left(\frac{16 \cdot {8}^{2}}{{40}^{2}}\right)$ Ω

$\implies R = \left(\frac{16 \cdot 64}{1600}\right)$ Ω

$\implies R = \left(\frac{1024}{1600}\right)$ Ω

$\implies R = 0.64$ Ω