Two resistors of values 6.0 and 12.0 Ω are connected in parallel.This combination in turn is hooked in series with an 8.0-Ω resistor and a 24-V battery.What is the current in the 12-Ω resistor?
A) 1.3 A
B) 4.0 A
C) 12 A
D) 0.67 A

Question

Quizplus · Accepted Answer

First, we can use the formula for equivalent resistance in a parallel circuit:

1/R_total = 1/6 + 1/12

1/R_total = 3/12

R_total = 4 Ω

This means that the combination of the 6 Ω and 12 Ω resistors has an equivalent resistance of 4 Ω.

Next, we can use the formula for equivalent resistance in a series circuit:

R_total = 4 + 8 + 12

R_total = 24 Ω

Now we can use Ohm's law to find the current:

I = V/R

I = 24/24

I = 1 A

Since the 12 Ω resistor is part of the parallel combination, it has the same voltage as the other resistors in that combination. Therefore, we can use Ohm's law again to find the current in the 12 Ω resistor:

I = V/R

I = 24/12

I = 2 A

Therefore, the current in the 12 Ω resistor is 2 A, which corresponds to answer choice D (0.67 A is incorrect because it is the current in the 6 Ω resistor, not the 12 Ω resistor).

Two Resistors of Values 6