R2 R4 Ri (14 points) In the figure above, 1, 12, and Is are the currents flowing
ID: 3308749 • Letter: R
Question
R2 R4 Ri (14 points) In the figure above, 1, 12, and Is are the currents flowing through the resistors labeled R, R2, and Rs, respectively. To help the graders out, use the directions of the currents shown in the figure. (a) (6 points) Deduce three independent equations for the three unknown currents. Use the symbolic notation for resistances and voltages. (b) (5 points) Take Vi-20V, ½ 10V: R2-106 , and Ri = Rs = R4-10 . Calculate 1, 12, and Is. You can use equations above, or if you can see a simpler path to a very good estimate of the exact answer, use it, explaining whatever approximation you make in one sentence. (Hint: Wou! R2 is a very big resistance!). (c) (3 points) What is the potential diference between points A and B: Vs-Va?Explanation / Answer
(a)Appling KVL in left side loop,
V1 - I2 R2 - I1 R2 = 0
10 I1 + 10^6 I2 = 20 ...... (i)
in right side loop,
V2 + I3 R3 - I2 R2 + I3 R4 = 0
10^6 I2 - 20I3 = 10 ......... (ii)
Applying KCL , I1 = I2 + I3
I1- I2 - I3 = 0 ........(iii)
(b) I1 = 0.333344 A
I2 = 5/300002 =1.667 x 10^-5 A
I3 = 0.33328 A
(C) Vab = I2 R2 = (1.667 x 10^-5) (10^6)
= 16.7 Volt
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