Question

The bridge used for the measurement of an unknown capacitance is:

• A. Wheatstone Bridge
• B. Wien Bridge
• C. Schering Bridge
• D. Kelvin Double Bridge

Hint:

Schering Bridge \( \implies \) Capacitance and Dissipation Factor (\( \tan\delta \)).
Kelvin Double Bridge \( \implies \) Very low resistance.
Maxwell Hay's Anderson \( \implies \) Inductance.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks to identify the specific AC bridge used for measuring unknown electrical capacitance from the given list of options.
Different bridge circuits are optimized for measuring resistance, capacitance, inductance, or frequency based on their balance equations.

Step 2: Key Formula or Approach:
The Schering bridge is an AC bridge that balances an unknown capacitor (represented as a series combination of capacitance \( C_1 \) and resistance \( r_1 \)) against a standard loss-free capacitor \( C_2 \).
The balance equations for a Schering bridge are:
\[ C_1 = C_2 \left(\frac{R_4}{R_3}\right) \] \[ r_1 = R_3 \left(\frac{C_4}{C_2}\right) \] Where \( R_3, R_4 \) are non-inductive resistors, and \( C_4 \) is a variable capacitor connected in parallel with \( R_4 \).

Step 3: Detailed Explanation:
Let us review the functions of all the bridges listed in the options:

• Schering Bridge (Option C):
- It is primarily used to measure capacitance, dissipation factor, and relative permittivity of insulating materials at high voltages.
- The dissipation factor (\( D \)) is calculated directly as:
\[ D = \omega C_4 R_4 \]
• Wheatstone Bridge (Option A):
- This is a DC bridge used exclusively to measure medium resistance (typically in the range of \( 1\ \Omega \) to \( 100\ \text{k}\Omega \)).

• Wien Bridge (Option B):
- Primarily used for measuring frequency of AC signals, although it can also be used to measure capacitance in some applications.

• Kelvin Double Bridge (Option D):
- This is a highly specialized DC bridge designed for measuring very low resistances (less than \( 1\ \Omega \)) with high accuracy by eliminating lead contact resistances.

Step 4: Final Answer:
The bridge used for the measurement of an unknown capacitance is the Schering Bridge.