In lab we investigated the circuit below known as the Wheatstone Bridge. In this

Question

In lab we investigated the circuit below known as the Wheatstone Bridge. In this part of the assignment do not use numerical values. In lab we assigned variables for currents through the battery and each resistor. Then we wrote equations based on Kirchhoff's Rules. There were three equations for the "junction rule" and three for the "loop rule". Using the the method of simultaneous equations, prove that the current through resistor R5 is zero if R1/R3 = R2/R4. Do not show every step in the algebra, just explain and show the main steps of reducing the equations to an equation that allows you to conclude that the current through R5 is zero.

Explanation / Answer

From Kirchhoff's first rule,

I2 - I4 + I5 = 0

I1 - I3 - I5 = 0

from second rule

(I2 R2) - (I5 R5) - (I1 R1) = 0

(I4 R4) - (I3 R3) + (I5 F5) = 0

When the bridge is balanced, I5 = 0

I2 R2 = I1 R1 (1)

I4 R4 = I3 R3 (2)

from first law, I2 = I4 ; I1 = I3

dividing (1)/(2)

R2/R4 = R1/R3

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