Question

A charge of `54 C` passes through a circuit every `6 s`. If the circuit can generate `162 W` of power, what is the circuit's resistance?

Answer 1

`R=2" "Omega`

Explanation:

`I=(Delta Q)/(Delta t)" Current of circuit"`

`Delta Q=54C" ; "Delta t=6 s`

`I=54/6=9 " "A`

`P:"Power"`

`R:"Resistance"`

`P=I^2*R`

`162=9^2*R`

`R=162/81`

`R=2" "Omega`

Answer 2

I found `2Omega`

Explanation:

You know that current `I` is the charge passing a section of conductor each second.
In your case you have:
`I=Q/t=54/6=9A`
Power is the rate of transformation (work) energy with time:
`P=E/t=V*I`
Using Ohm's Law we get:
`P=I^2R`
rearranging:
`R=P/I^2=162/(9^2)=2Omega`