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Question:

In a Wheatstone bridge (see fig.), resistances P and Q are approximately equal. When R = 400Ω, the bridge is balanced. On interchanging P and Q, the value of R, for balance, is 405Ω. The value of X is close to:

402.5ohm

403ohm

404.5ohm

401.5ohm

Solution:

Initially
PQ = RX____(1)
After interchanging P and Q
QP = R2X_____(2)
From (1) and (2)
PX/Q = 400
QX/P = 405
Multiplying these two equations:
(PX/Q)(QX/P) = 400 * 405
X² = 400 * 405
X = √(400 * 405)
X = √162000
X = 402.5Ω