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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 = 2 R4
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
- 1 and 4
Correct Option: D
Under the balanced condition.
From above figure
 | R1 + |  | / 2 = R3 | × | |||
| 1/jωC1 | R1 +(1/jωC3) | R3 | |||||
or
| R4 | | R1 + | | = | | | ||
| jωC1 | jR3ωC3+1 |
or R4 [jR1ωC1+1] [1 + jωC3R3]=jωC1R2R3
on comparing real and imaginary part, we get,
| R1R3C2ω = | |
| c1ω |
or
| ω2 = | |
| C1C3R1R3 |
or
| ω = | |
| √C1C3R1R3 |
If C1 = C3
and R1 = R3
then given R2 = 2R4
Thus condition to be satisfied are
C1 = C3, R1 = R3
and R2 = 2R4
