Three resistors with resistances of 2.0 Ω, 6.0 Ω, and 12 Ω are connected across an ideal dc voltage source V, as shown in the figure. If the total current in the circuit is I = 5.0 A, what is the current through the 12-Ω resistor?
A) 1.7 A
B) 2.5 A
C) 0.56 A
D) 5.0 A
E) 0.75 A

Question

Three resistors with resistances of 2.0 Ω, 6.0 Ω, and 12 Ω are connected across an ideal dc voltage source V, as shown in the figure. If the total current in the circuit is I = 5.0 A, what is the current through the 12-Ω resistor? 
A) 1.7 A 
B) 2.5 A 
C) 0.56 A 
D) 5.0 A 
E) 0.75 A

Quizplus · Accepted Answer

Using Ohm's Law $V = IR$, we can find the voltage drop across each resistor:
$V_{2\Omega} = (2.0 \Omega)(5.0 A) = 10 V$
$V_{6\Omega} = (6.0 \Omega)(5.0 A) = 30 V$
$V_{12\Omega} = (12 \Omega)(5.0 A) = 60 V$
The total voltage drop across the circuit is the voltage of the power source:
$V_{total} = V_{2\Omega} + V_{6\Omega} + V_{12\Omega} = 100 V$
Now we can find the current through the 12-Ω resistor using Ohm's Law:
$I_{12\Omega} = \frac{V_{12\Omega}}{R_{12\Omega}} = \frac{60 V}{12 \Omega} = 5.0 A 	imes \frac{1}{5} = 1.0 A$
Therefore, the answer is C, 0.56 A.

Three Resistors with Resistances of 2