Unknown capacitance value is obtained by

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Comparison with standard

Explanation: An unknown capacitance is determined by comparing it against a known standard capacitor within a bridge circuit, such as a De Sauty bridge or a Schering bridge. The balance condition of the bridge occurs when the ratio of impedances of the arms results in a null detector reading, allowing the unknown value to be calculated relative to the standard.

Working Principle: In an AC bridge, four arms are connected in a loop with an AC excitation source. When the bridge is balanced, the product of impedances of opposite arms is equal: $Z_1 Z_4 = Z_2 Z_3$. By using a standard calibrated capacitor in one arm, the bridge is adjusted by varying resistive elements until the detector shows zero deflection, satisfying the equilibrium condition related to the unknown capacitance.

Key Formulas: $C_x = C_s \cdot \frac{R_2}{R_1}$ — General balance equation for a simple comparison bridge where $C_s$ is the standard capacitor.; $Z = \frac{1}{j\omega C}$ — Complex impedance representation of a capacitor.

Key Points: AC bridges are the primary instruments for measuring passive components like C, L, and R.; A standard capacitor is required because capacitance measurements are inherently relative rather than absolute.; Null detectors are used to indicate the bridge balance state, ensuring high sensitivity.

Advantages: High precision and sensitivity.; Independent of supply voltage fluctuations when null-balance is achieved.

Disadvantages: Requires a known standard capacitor (which may drift over time).; Measurement is sensitive to frequency and stray capacitance.

Applications: Precision capacitance standards calibration.; Measurement of dielectric loss (dissipation factor) using Schering bridges.

Additional Info: Option B (Tuned detector) is an instrument used to detect the null point, not the reference for measurement.. Option D (Vibration galvanometer) is a type of null detector used at low frequencies.

Answer: A is correct — Unknown capacitance is determined by null-balance comparison against a known standard capacitor in an AC bridge.

Exam Tip: Always verify if the bridge circuit is balanced for both resistive and reactive components, as capacitor leakage requires a parallel or series resistance balance.

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