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Question

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


A

403.5ohm

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B

404.5ohm

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C

401.5ohm

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D

402.5ohm

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Solution

The correct option is D

402.5ohm


Step 1: Given

Initial resistance, R1=400ohm

Final resistance, R2=405ohm

Step 2: Balance the bridge with initial resistance

We can calculate the unknown resistance in a Wheatstone bridge by balancing the two legs of the bridge circuit.

Therefore,

PQ=R1X-(1)

Step 3: Balance the bridge with the final resistance

After interchanging P and Q,

QP=R2X-(2)

Step 4: Solve the equations

Dividing equations (1) by (2)

PQQP=R1XR2X1=R1R2X2

Step 5: Solve for X.

X2=R1R2X=400×405=402.5ohm

Therefore, option D is the correct option.


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