Question

Which bridge is best suited for the measurement of a high-quality factor (Q) inductor?

• A. Maxwell's Bridge
• B. Hay's Bridge
• C. Anderson's Bridge
• D. Schering Bridge

Hint:

Inductor Q-Factor Bridge classification:
Low Q (\( Q < 1 \)) \( \implies \) Anderson's Bridge.
Medium Q (\( 1 < Q < 10 \)) \( \implies \) Maxwell's Bridge.
High Q (\( Q > 10 \)) \( \implies \) Hay's Bridge.

Answer 1

The Correct Option is B

Step 1: Understanding the Problem:
The question asks to identify the specific AC bridge that is best suited for measuring the self-inductance of a coil with a high Quality Factor (\( Q > 10 \)).
AC bridges are used to measure electrical properties like inductance, capacitance, and resistance by achieving a balanced condition.

Step 2: Key Formula or Approach:
The Quality Factor (\( Q \)) of an inductor represents the ratio of its inductive reactance to its series resistance:
\[ Q = \frac{\omega L}{R} \] AC bridges for inductance measurement (like Maxwell's and Hay's) utilize standard capacitors in their arms to balance the inductive reactance of the unknown coil.
Depending on the connection layout of these standard components, the bridge equations simplify for different ranges of \( Q \).

Step 3: Detailed Explanation:
Let us compare the applicability of the different bridges listed:

• Hay's Bridge:
In Hay's Bridge, the standard capacitor is connected in series with the resistance in the adjacent arm.
The balance equation for the unknown inductance is:
\[ L = \frac{R_2 R_3 C_4}{1 + \left(\frac{1}{Q}\right)^2} \] For a high-quality factor coil (\( Q > 10 \)), the term \( \big(\frac{1}{Q}\big)^2 \) becomes extremely small (less than 0.01) and can be neglected.
The formula simplifies directly to \( L \approx R_2 R_3 C_4 \), making it independent of frequency.
This is why Hay's bridge is highly suited for high-Q measurements.

• Maxwell's Bridge (Option A):
The standard capacitor is connected in parallel with the adjacent arm resistance. It is best suited for medium-Q coils (\( 1 < Q < 10 \)). For high Q, the parallel resistance value becomes too large and impractical.

• Anderson's Bridge (Option C):
Used primarily for low-Q coils (\( Q < 1 \)).

• Schering Bridge (Option D):
Used strictly for measuring unknown capacitance and dielectric loss, not inductance.

Step 4: Final Answer:
The bridge best suited for measuring a high-quality factor (Q) inductor is Hay's Bridge.