Physics Circuits Determining Voltage
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Physics Circuits Determining Voltage

[From: ] [author: ] [Date: 13-09-28] [Hit: ]
Vab = 2 V - IR1 2 R = 2 V - (-0.222A) * 2Ω = 2.......
http://i213.photobucket.com/albums/cc116…

Here is a symmetrical circuit. If e pictured is 6 V and R = 8 ohms, what is the potential from a to b. This seems like a simple problem, but I can't seem to get the answer.

Thanks.

-
Group resistors in right and left branches together. We'll call branches 1 (left), 2 (middle) & 3 (right).

R1 = R3 = 1Ω + 1Ω = 2Ω

KCL
+ IR1 + IR2 + IR3 = 0 (1)

Picking all currents into junction a. Incorrect currents will be negative.

KVL (left loop - ClockWise direction)
2V - 2Ω IR1 - 6V + 8Ω IR2 = 0 (2)
-4 + 8 IR2 = 2 IR1
IR1 = -2 + 4 IR2 (2A)

KVL (right loop - ClockWise direction)
-8Ω IR2 + 6V + 2Ω IR3 - 2V = 0 (3)
2 IR3 = -4 + 8 IR2
IR3 = -2 + 4 IR2 (3A)

Substitute 2A and 3A into 1.

+ IR1 + IR2 + IR3 = 0
( -2 + 4 IR2 ) + IR2 + ( -2 + 4 IR2 ) = 0
9 IR2 = 4
IR2 = 0.444A

Solve 2A and 3A for other currents.

IR1 = -2 + 4 IR2 = -2 + 4 * 0.444 = -0.222A
IR3 = -2 + 4 IR2 = -2 + 4 * 0.444 = -0.222A

Vab = 2 V - IR1 2 R = 2 V - (-0.222A) * 2Ω = 2.444V
1
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