Short Answer:

A Maxwell bridge is used to measure unknown inductance by comparing it with a known standard capacitor and resistors in an AC bridge circuit. It operates by balancing the bridge using known values so that no current flows through the detector, indicating that the impedance in both branches is equal.

This bridge is especially useful for measuring inductance of coils with moderate quality factor (Q) by converting the problem of inductance measurement into one of balancing against capacitance and resistance.

Detailed Explanation:

Maxwell bridge for inductance measurement

The Maxwell bridge, also known as the Maxwell-Wien bridge, is a precision AC bridge that measures an unknown self-inductance (L) by comparing it with a standard known capacitance (C) and resistances. It is based on the principle of an AC bridge, where the balance condition is achieved by adjusting resistive and reactive components so that the bridge detector shows zero output.

This bridge is most suitable for measuring the inductance of coils, transformers, or chokes, especially when the inductance is moderate and the quality factor is not too high.

Construction and Working:

A typical Maxwell bridge has four arms:

• Arm 1: Unknown inductor with internal resistance (Lx and Rx)
• Arm 2: Known resistor R1
• Arm 3: Variable resistor R2 (used for balancing)
• Arm 4: A known standard capacitor C in series with a resistor R3

AC supply is connected across one diagonal of the bridge, and a detector (like headphones or a null detector) is connected across the other diagonal.

Working Principle:

1. Balance Condition:
   • The bridge is said to be balanced when the voltage across the detector becomes zero, i.e., no current flows through it.
   • At balance, the impedance in both branches are equal in both magnitude and phase.
2. Mathematical Condition:
   • When the bridge is balanced:

Lx=R2⋅R3⋅CL_x = R_2 \cdot R_3 \cdot CLx​=R2​⋅R3​⋅C Rx=R2R1⋅R3R_x = \frac{R_2}{R_1} \cdot R_3Rx​=R1​R2​​⋅R3​

1. Where:
   • LxL_xLx​ = unknown inductance
   • RxR_xRx​ = internal resistance of the inductor
   • R1,R2,R3R_1, R_2, R_3R1​,R2​,R3​ = known resistors
   • CCC = standard capacitor
2. Balancing Process:
   • The values of R2 and R3 are adjusted until the detector shows no deflection (null point).
   • The inductance and resistance of the unknown coil are then calculated using the balance formulas.

Advantages:

• Uses a standard capacitor, which can be made very accurate.
• Accurate for measuring moderate inductance values.
• Simple circuit with easy balancing.
• Works well with low-frequency AC sources.

Limitations:

• Not suitable for very low or very high Q inductors.
• Accuracy depends on the precision of the capacitor and frequency stability.
• Cannot be used for high-frequency measurements due to reactance variations.

Applications:

• Measurement of inductance of coils and windings
• Testing choke coils or relay coils
• Calibration of inductors in research and laboratories
• Educational demonstrations of AC bridge methods

Conclusion:

The Maxwell bridge is a reliable and widely used AC bridge method for measuring unknown inductance using a standard capacitor and known resistors. By achieving balance in the bridge, the unknown inductance is calculated precisely. It is simple, cost-effective, and suitable for laboratory and educational use, especially for components with moderate inductance and quality factor.