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 through the circuit is I = 2.0 A, what is the applied voltage V?
A) 6.0 V
B) 3.0 V
C) 2.0 V
D) 2.7 V
E) 1.5 V

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 through the circuit is I = 2.0 A, what is the applied voltage V? 
A) 6.0 V 
B) 3.0 V 
C) 2.0 V 
D) 2.7 V 
E) 1.5 V

Quizplus · Accepted Answer

We can use Ohm's law to find the voltage drop across each resistor:

V1 = IR1 = (2.0 A)(2.0 Ω) = 4.0 V 
V2 = IR2 = (2.0 A)(6.0 Ω) = 12.0 V 
V3 = IR3 = (2.0 A)(12 Ω) = 24.0 V

The total voltage applied across the circuit is the sum of the voltage drops across all three resistors:

V = V1 + V2 + V3 = 4.0 V + 12.0 V + 24.0 V = 40.0 V

Therefore, the applied voltage V is 40.0 V.

Three Resistors with Resistances of 2