Question

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?

Answer 1

The resistance in the circuit is `0.5` `Omega`

Explanation:

Data:

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

We know that:

`P=I^2R`

Where `I` is the current.

Also we know that: `I=Q/t=24/6=4` `A`

`P=I^2R implies 8=4^2*R`

Rearranging:

`R=8/16=0.5` `Omega`

Hence, the resistance in the circuit is `0.5` `Omega`.

Answer 2

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*V = 8` `W`

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

`I = Q/t = (24C)/(6s) = 4` `A`

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

`V = (8W)/(4A) = 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*R`

Rearranging to find the resistance:

`R = V/I = (2V)/(4A) = 0.5` `Omega`