Current Electricity and Electrical InstrumentHard

Question

ABCD is a square where each side is a uniform wire of resistance 1Ω. A point E lies on CD such that if a uniform wire of resistance 1Ω is connected across AE and constant potential difference is applied across A and C then B and E are equipotential. Then -

Options

A. = 1
B. = 2
C.
D. = √2

Solution


Assume DE  R1Ω
EC ⇒ R2Ω
R1 + R2 = 1Ω
VB = VE
Means balance wheat stone bridge


R2 = = 1 - R1
R1 + 1 = R1 + 2 - R12 - 2R
R12 + 2R1 - 1 = 0 ⇒ R1 = - 1 + √2 ⇒ R2 = 2 - √2
= √2

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