A Maxwell Bridge , also known as the Maxwell-Wien Bridge, is an AC bridge circuit used for measuring an unknown inductance by balancing the loads of its four arms, one of which contains the unknown inductance. Figure 1 below shows a diagram of the Maxwell Bridge.  

Figure 1.  The Maxwell Bridge

As shown in Figure 1, one arm of the Maxwell bridge consists of a capacitor in parallel with a resistor (C1 and R2) and another arm consists of an inductor L1 in series with a resistor (L1 and R4).  The other two arms just consist of a resistor each (R1 and R3).  The values of R1 and R3 are known, and R2 and C1 are both adjustable. The unknown values are those of L1 and R4.

Like other bridge circuits, the measuring ability of a Maxwell Bridge depends on 'balancing' the circuit. Balancing the circuit in Figure 1 means adjusting C1 and R2 until the current through the bridge between points A and B becomes zero.  This happens when the voltages at points A and B are equal.  When the Maxwell Bridge is balanced, it follows that Z1/R1 = R3/Z2 wherein Z1 is the impedance of C2 in parallel with R2, and Z2 is the impedance of L1 in series with R4.  Mathematically, Z1 = R2 + 1/(2πfC1); while Z2 = R4 + 2πfL1.

Thus, when the bridge is balanced,

(R2 + 1/(2πfC1)) / R1 = R3 / [R4 + 2πfL1]; or

R1R3 = [R2 + 1/(2πfC1)] [R4 + 2πfL1];

When the bridge is balanced, the negative and positive reactive components cancel out, so R1R3 = R2R4, or

R4 = R1R3/R2.

Note that the balancing of a Maxwell Bridge is independent of the source frequency.

See Also:   Bridge Circuits;  More Articles