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A bridge circuit is shown in the figure given below. Which one of the sequences given below is most suitable for balancing the bridge?
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- First adjust R4 and then adjust R1
- First adjust R2 and then adjust R3
- First adjust R2 and then adjust R4
- First adjust R4 and then adjust R2
Correct Option: A
X1 ωL1, X4 =1/ωC4, Z1 = R1 + jX1, Z4 = R4 - jX4
| At balance, | = | ||
| Z2 | Z4 |
⇒ Z1Z4 = Z3Z2
| ⇒ (R1 + jωL1) |  | R4 - j |  | = R2R3 | |
| ωL4 |
Equating Real and Imaginary terms, we get,
| ⇒ L1 = | , R1 = | ||
| 1 + (ωC4R4)² | 1 + (ωC4R4)² |
| Quality factor, Q = | = | ||
| R1 | ωC4R4 |
| Then L1 = | R1 = | ||
| 1 + (1/Q²) | 1 + (1/Q²) |
For Q > 10 , L1 ≈ R2R3C4,R1 = ω²R2R3C4²R4
As R2 is common in both the expressions of L1 and R1, then R2 would have to be adjusted first and then R4 should be adjusted.
