Is the Current in the Middle of a Balanced Wheatstone Bridge Always Zero?

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SUMMARY

The current in the middle of a balanced Wheatstone bridge is always zero when all resistors are equal. This conclusion is derived from applying Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL) to the circuit. The equations show that the sum of currents entering and leaving a junction is zero, leading to the result that the currents through the branches are equal. Specifically, when resistors R1, R2, R3, and R4 are equal, the potentials at points A and B are identical, confirming that the current in the middle is indeed zero.

PREREQUISITES
  • Understanding of Kirchhoff's Voltage Law (KVL)
  • Familiarity with Kirchhoff's Current Law (KCL)
  • Basic knowledge of electrical circuits and resistors
  • Concept of a Wheatstone bridge configuration
NEXT STEPS
  • Study the principles of Kirchhoff's Laws in greater detail
  • Explore the Wheatstone bridge applications in measuring resistance
  • Learn about potential difference and its role in circuit analysis
  • Investigate the effects of unequal resistors in a Wheatstone bridge
USEFUL FOR

Students of electrical engineering, circuit designers, and anyone studying circuit analysis and the behavior of resistive networks.

mafra
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Homework Statement


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Show that the current in the middle is zero if all the resistors are equal


The Attempt at a Solution



KVL for left and right:
V - R*i1 - R*i2 = 0
V - R*i3 - R*i4 = 0

i1 + i2 = i3 + i4

KCL:
i1 + i3 = i2 + i4
i1 + iG = i2
i3 = iG + i4

I must prove that i1 = i2 or i3 = i4 but all I get is i1 = i4 and i2 = i3 combining KVL and KCL
 
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For the current in the middle to be zero, points A and B are at the same potential.
 

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