Question

An 18 Ω, 9 Ω, and 6 Ω resistor are connected in parallel to an emf source. A current of 4 A is the 9 Ω resistor. How do you calculate the resistance of the circuit? What is the potential difference across the source?

How do you calculate the current in each resistor?

Answer 1

Since they are parallel, the voltage is the same for all resistors.

Explanation:

Second question:
`U=I_2xxR_2=4Axx9Omega=36V`

First question:
You could use `1/R=1/(R_1)+1/(R_2)+1/(R_3)=1/18+1/9+1/6=1/3->R=3Omega`

Or:
You can calculate the currents through the other resistors, add them all up and recalculate the total resistance (voltage already calculated):
`I_1=U/(R_1)=(36V)/(18Omega)=2A`

`I_2=4A` (as given)

`I_3=U/(R_3)=(36V)/(6Omega)=6A`

Now `R=U/I=(36V)/(2A+4A+6A)=(36V)/(12A)=3Omega`