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Which of the following conditions are to be satisfied in the figure shown, so that the common variable shaft of resistance R1 and R2 can be graduated in frequency to measure the frequency of E under balanced condition?
1. R1 = R3
2. C1 = C3
3. R2 = 2R4
4. R2 = R4
Select the correct answer using the codes given below:
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- 1 and 4
- 1 and 2
- 2 and 4
- 1, 2 and 3
Correct Option: D
Writing the bridge balance equations:
 | R1 + |  | R4 = R2 | | | |||
| jC1ω | R3 + (1/jC3ω) |
| R1 + | | R4 = R2 | |||
| jC1ω | jR3C3ω + 1 |
| or |  | R1 + |  | (1 + jR3C3ω) = | |||
| jC1ω | R4 |
| It gives; R1 + R3 | = | , | ||
| C1 | R4 |
| and R1 + R3C3ω = | |
| C1ω |
| or ω = | |
| √R1R3C1C3 |
If C1 = C3, then first equation becomes
| R1 + R3 = | |
| R4 |
Again if R1 = R3 and the common variable short of resistance R1 and R2 can be graduated in frequency to measure the frequency ω. Thus conditions to be satisfied are
C1 = C3, R2 = 2R4, and R1 = R3
