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The arms of a four-arm bridge abcd, supplied with sinusoidal voltage, have the following values :
Arm ab: A resistance of 200 Ω in parallel with a capacitance of 1 μF
Arm bc: 400 Ω resistance
Arm cd: 1000 Ω resistance
Arm da: A resistance R2 in series with a 2 μF capacitance
What are the values of R2 and the frequency respectively at which the bridge will balance?
- a)200 Ω, 456 Hz
- b)400 Ω, 398 Hz
- c)200 Ω, 398 Hz
- d)400 Ω, 456 Hz
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The arms of a four-arm bridge abcd, supplied with sinusoidal voltage, ...
Calculation:
The given configuration corresponds to wien bridge
Under the condition of tridge balance,
Put the relevant Values in equation
Put the relevant Values in equation
= 398 HZ
Therefore, correct Answer is option (b).
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Community Answer
The arms of a four-arm bridge abcd, supplied with sinusoidal voltage, ...
Given Data
- Arm ab: 200Ω in parallel with 1μF
- Arm bc: 400Ω
- Arm cd: 1000Ω
- Arm da: R2 in series with 2μF
Calculation
- At balance, the reactance of arm ab must be equal to the reactance of arm cd.
- The reactance of arm ab is given by Xab = 1 / (2πfC)
- The reactance of arm cd is given by Xcd = 1000Ω
- Equating the two, we get: 1 / (2πf * 1μF) = 1000Ω
- Solving for f, we get f = 398 Hz
- Now, at balance, the ratio of resistances in arm ab to arm bc must be equal to the ratio of reactances in arm cd to arm da.
- This gives us: (200 / R2) = (1000 / (1 / (2π * 398 * 2 * 10^-6)))
- Solving for R2, we get R2 = 400Ω
Conclusion
Therefore, the values of R2 and the frequency at which the bridge will balance are 400Ω and 398 Hz respectively, which matches with option 'B'.
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The arms of a four-arm bridge abcd, supplied with sinusoidal voltage, have the following values :Arm ab: A resistance of 200Ω in parallel with a capacitance of 1μFArm bc: 400Ω resistanceArm cd: 1000Ω resistanceArm da: A resistance R2in series with a 2μF capacitanceWhat are the values of R2and the frequency respectively at which the bridge will balance?a)200Ω, 456 Hzb)400Ω, 398 Hzc)200Ω, 398 Hzd)400Ω, 456 HzCorrect answer is option 'B'. Can you explain this answer?
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