A15-Ω resistor is connected in parallel with a 30-Ω resistor.If this combination is now connected in series with an ideal 9.0-V battery and a 20-Ω resistor,what is the current through the 15-Ω resistor?
A)0.10 A
B)0.13 A
C)0.20 A
D)0.26 A

Question

Quizplus · Accepted Answer

First, we need to calculate the equivalent resistance of the parallel combination of the 15-Ω and 30-Ω resistors:
1/Req = 1/15 + 1/30
1/Req = 1/10
Req = 10 Ω
Adding the 20-Ω resistor in series gives us a total resistance of:
Rtotal = Req + 20 Ω + 30 Ω
Rtotal = 60 Ω
Using Ohm's Law, we can find the total current:
I = V/Rtotal
I = 9.0 V / 60 Ω
I = 0.15 A
Now, we can use the current divider rule to find the current through the 15-Ω resistor:
I15 = I * (30 Ω / (15 Ω + 30 Ω))
I15 = 0.15 A * (30/45)
I15 = 0.10 A

Therefore, the answer is C) 0.20 A.

A15-Ω Resistor Is Connected in Parallel with a 30-Ω Resistor