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Answer to Question #33261 in Electric Circuits for Frank Loyld

Question #33261
A Wheatstone bridge ABCD (labeled in clockwise direction) with a galvanometer G joined to the junctions B and D. A cell E is connected across AC. Resistances of 15, 10, 4 and X ohms are inserted into the arms AB, BC, CD and DA respectively. The value of X is _________ ohms.

A. 2.67
B. 1.34
C. 3.22
D. 2.13
Expert's answer
R1=15 ohms
R2= 10 ohms
R3= 4 ohms
First, Kirchhoff's first rule is used to find the currents in junctions B and D:


B) I1 - I2 - Ig = 0 ( Ig - current through the galvanometer)
D) Ix - I3 - Ig = 0 ( Ix - current trough Rx)


Then, Kirchhoff's second rule is used for finding the voltage in the loops ABD and BCD:
ABD) I1*R1 + Ix*Rx + Ig*Rg = 0
BCD) I2*R2 + I3*R3+ Ig*Rg = 0


When the bridge is balanced, then Ig = 0, so the second set of equations can be rewritten as:
I1*R1 = - Ix*Rx
I2*R2 = - I3*R3
and
I1=I2
Ix=I3
From the first rule and the second rule we get:


Rx=(R3*R2)/R1


Answer: A, 2,67 ohms

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