The following combination of resistors: 4.0Ω, 6.0Ω, 12.0Ω, and 7.0Ω has a total resistance of 9.0Ω. The 7Ω resistor is serial, while the 6Ω, 4Ω and 12Ω resistors are parallel. The current through the 7.0Ω resistor is 2.0 A. What is the potential difference of the battery?

Answer 1

To solve this problem, we first need to find the total resistance of the parallel combination of resistors 6Ω, 4Ω, and 12Ω.

The formula for calculating the total resistance of parallel resistors is:

1/Rtotal = 1/6Ω + 1/4Ω + 1/12Ω
1/Rtotal = 2/12 + 3/12 + 1/12
1/Rtotal = 6/12
Rtotal = 12/6
Rtotal = 2Ω

Now we can calculate the total resistance of the combination of resistors 7.0Ω and 2.0Ω in series:

Rtotal = 7Ω + 2Ω
Rtotal = 9Ω

Since the total resistance of the circuit is 9Ω and the potential difference is the same for all resistors in series, the potential difference of the battery is given by Ohm's Law:

V = I * R
V = 2.0 A * 9.0 Ω
V = 18.0 V

Therefore, the potential difference of the battery is 18.0 V.