Question

Chapter 27, Problem 035 In the figure ε = 8.32 v, R1 = 1400 Ω, R2 = 2220 Ω, and R3-4100 Ω. What are the potential differences (in V) (a) VA·Va (b) ve-Ve, (c) Ve·Vo, and (d) ¼·VC? Rg Ri Rg te Ri (a) Number (b) Number (c) Number (d) Number Click if you would like to Show Work for this question: Units Units Units Units Open Show Work

Answer 1

Because of the symmetry of the problem, we can presume that the current i1 is the same current flowing through both 2k resistors; i2 flows through both 3k resistors and i3 is the current through R3. If we apply the junction rule,

E − i1R1 − i2R2 = 0

E − i1R1 − (i1 − i2)R3 − i1R1 = 0

8.32 V − i2(2220Ω) − i1(1400Ω) = 0

8.32V − 2i1(1400Ω) − (i1 − i2) (4100Ω) = 0

by solving the above two equations we get

i1=0.00249 A and i2 = 0.00217A and i3 = i1 − i2 = 0.00032 A

VA − VB = i1R1 = 3.486 V

VB − VC = i3R3 = 1.312V

VC − VD = i1R1 = 3.486 V

VA − VC = i2R2 = 4.81 V