Current Electricity 2 Question 6

6. In a Wheatstone bridge (see figure), 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

(2019 Main, 11 Jan I)

(a) 404.5Ω

(b) 401.5Ω

(c) 402.5Ω

(d) 403.5Ω

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Solution:

  1. For a balanced Wheatstone bridge,

PR=QX

In first case when R=400Ω, the balancing equation will be

PR=QXP400Ω=QXP=400×QX

In second case, P and Q are interchanged and R=405Ω

QR=PXQ405=PX

Substituting the value of P from Eq. (i) in Eq. (ii), we get

Q405=Q×400X2

X2=400×405X=400×405=402.5

The value of X is close to 402.5Ω.



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