A portion of a circuit is shown in the figure,and the batteries are ideal.What is the potential difference V_A- V_B if I = 5.0 A? A)63 V B)35 V C)55 V D)45 V E)71 V

Question

Quizplus · Accepted Answer

Applying Kirchhoff's Voltage Law (KVL) to the outer loop, we have:
VS1U1B1A - VS1U1B0 - VS1U1B1B - I(R1 + R2) = 0 
Substituting the given values, we get: 
16V - VS1U1B0 - 7V - 5A(4Ω + 6Ω) = 0 
Simplifying the equation, we get: 
VS1U1B0 = 45V 
Therefore, the potential difference VS1U1B1U1B0 is:
VS1U1B1U1B0 = VS1U1B1B - VS1U1B0 = 7V - 45V = -38V (the negative sign indicates that the direction of the potential difference is opposite to the assumed direction in the loop)
Therefore, the potential difference VS1U1B1U1B0 is 38V. 
Overall, the potential difference VS1U1B1A S1U1B0- VS1U1B1BS1U1B0 is:
VS1U1B1A - VS1U1B1B = 16V - 7V = 9V 
Adding this to the potential difference VS1U1B1U1B0, we get: 
9V + 38V = 47V 
Rounding to the nearest integer, we get 45V as the final answer. Thus, the best choice is D.

A Portion of a Circuit Is Shown in the Figure,and