# A charge of 5 C passes through a circuit every 2 s. If the circuit can generate 15 W of power, what is the circuit's resistance?

##### 2 Answers
Nov 6, 2017

The resistance is $2.4 \Omega$

#### Explanation:

A rate of charge movement that causes 5C of charge to pass every 2 s is a current of 2.5 A

$I = \frac{Q}{t} = \frac{5 C}{2 s} = 2.5 \frac{C}{s} \mathmr{and} 2.5 A$

Next we use the relation

$P = {I}^{2} R$ to find the resistance

Write this as

$R = \frac{P}{I} ^ 2 = \frac{15 W}{2.5 A} ^ 2 = 2.4 \Omega$

Nov 6, 2017

$2.4 \Omega$

#### Explanation:

$C = I t$
charge = current * time

$I = \frac{C}{t} = \frac{5}{2} A$
current = charge/time

$P = {I}^{2} R$
power = current^2 * resistance

$15 W = {\left(\frac{5}{2}\right)}^{2} \cdot R$

$15 W = 6.25 \cdot R$

$R = \frac{15}{6.25} \Omega$

$= \frac{60}{25} = \frac{12}{5}$

$= 2.4 \Omega$