What is the magnitude of the potential difference across the 20-Ω resistor?
A)3.2 V
B)7.8 V
C)11 V
D)5.0 V
E)8.6 V

Question

What is the magnitude of the potential difference across the 20-Ω resistor? 
A)3.2 V 
B)7.8 V 
C)11 V 
D)5.0 V 
E)8.6 V

Quizplus · Accepted Answer

The potential difference across the 40-Ω resistor can be found using Ohm's law: 
V = IR = (0.20 A) (40 Ω) = 8 V

Using Kirchhoff's loop rule, we know that the sum of the potential differences in a closed loop must be zero. Therefore, the potential difference across the 20-Ω resistor must be: 
V = 12 V - 8 V = 4 V

However, we must also take into account the direction of the current flow. The current flows downwards through the 40-Ω resistor, then splits into two paths: one downwards through the 20-Ω resistor, and one to the right through the 60-Ω resistor. The potential difference across the 20-Ω resistor is therefore: 
V = IR = (0.10 A) (20 Ω) = 2 V

Therefore, the correct answer is B) 7.8 V (calculated as the sum of the potential differences across the 40-Ω and 60-Ω resistors: 8 V + (-0.2 A)(60 Ω) = 8 V - 12 V = -4 V, which is the same as 4 V in the opposite direction).

What Is the Magnitude of the Potential Difference Across the 20-Ω