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Question #42748
The Question
An AC Wheatstone bridge ABCD is connected to an ideal AC voltage source across nodes A and C. The arms of the bridge contain the following components: Arm AB consists of a resistor in series with a capacitor . Arm BC consists of a resistor in parallel with a capacitor . Arm AD is a pure resistor , and Arm DC is a pure resistor . An ideal AC voltmeter is connected between nodes B and D. It is observed that the RMS reading of the voltmeter remains strictly constant and non-zero for all possible values of the source angular frequency . What is the ratio ?
Options
- A.
2
- B.
3
- C.
5
- D.
6
Check Your Answer
Correct Answer
Step-by-Step Solution
Explanation
How the Examiner Thinks
Multi-Concept_Bridge
Master problems that require linking physics and math concepts to solve complex competitive questions.
Concepts Behind This Question
Wheatstone Bridge Sensitivity|Frequency Sensitivity of Z|Complex Algebra
Why This Question Is Tricky
Common Mistakes
This question tests the misconception that AC bridge analysis is synonymous with finding a single resonant 'balance' frequency where the imaginary impedance vanishes.
Students commonly fall into the trap of assuming the bridge must be balanced at resonance (), which would incorrectly yield .
By demanding a frequency-independent RMS voltage, the problem forces the application of complex phasor magnitudes across the entire frequency spectrum.
It reveals that a Wien bridge topology can act as an all-pass filter (constant amplitude, varying phase) only when the specific real-part attenuation ratio is satisfied, requiring rigorous algebraic manipulation of complex impedances rather than rote application of DC balance conditions.
Quick Facts About This Question
Question Information
| Subject | Physics |
| Chapter | Current Electricity - Class 12 |
| Concept | Wheatstone Bridge Sensitivity |
| Difficulty | 8 |
| Cognitive Load | 7 |
| Target Solve Time | 160 sec |
| Access | Free |