A charge of $15 C$ passes through a circuit every $12 s$ . If the circuit can generate $18 W$ of power, what is the circuit's resistance?

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Answer 1 · 2016-03-03T12:35:55

The resistance is $11.52$ $Omega$

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:

$P=I*V = 18$ $W$

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

$I = Q/t = (15C)/(12s) = 1.25$ $A$

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

$V = (18W)/(1.25A) = 14.4$ $V$

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

$V=I*R$

Rearranging to find the resistance:

$R = V/I = (14.4V)/(1.25A) = 11.52$ $Omega$

A charge of 15 C15 C passes through a circuit every 12 s12 s. If the circuit can generate 18 W18 W of power, what is the circuit's resistance?