A charge of $35 C$ $35 C$ passes through a circuit every $5 s$ $5 s$ . If the circuit can generate $12 W$ $12 W$ of power, what is the circuit's resistance?

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Answer 1 · 2016-11-04T12:43:40

$\frac{12}{49}$ $12/49$ Ohms

The relationship between power P, voltage V, and current I is

$P = I V = I^{2} R$ $P = IV = I^2 R$ as $V = I R$ $V = IR$ from Ohm's Law

So $R = \frac{P}{I^{2}}$ $R = P/I^2$

We know also that current is the rate of flow of charge, so $I = (Delta q)/(Delta t)$

This means

$R = ( P )/( (Delta q)/(Delta t))^2 = ( 12 )/( (35)/(5))^2 = 12/49 \ Omega$

A charge of 35 C35C35 C passes through a circuit every 5 s5s5 s. If the circuit can generate 12 W12W12 W of power, what is the circuit's resistance?