Maxwell Bridge

The circuit of Maxwell’s L – C bridge for the determination of self-inductance. The coil whose inductance L is to be determined is placed in the arm CD in series with a variable non-inductive resistance R4. Arms AB, BC and AD contain non-inductive resistances R1, R2 and R3 respectively. A standard variable capacitor C1 is connected is parallel with resistance R1, R2 and R3 respectively. A standard variable capacitor C1 is connected in parallel with resistance R1 in the arm AB.

Let Z1, Z2, Z3 and Z4 be the impedances of branches AB, BC, AD and DC respectively.

Here, 1/Z1 = 1/R1 + 1/1/jωC1 = R1 + jωC1 or Z1 = R1/1 + jωC1 R1
    Z2 = R2, Z3 = R3 and Z4 = R4 + jωL

According to the condition of balance,
        Z1/Z2 = Z3/Z4

    R/ (1 + jωC1R1) R2 = R3/ (R4 + jωL)
Or        R4R1 + jωLR1 = R2R3 + R2R3R1 jωC1
Equating real and imaginary parts, we get
        R4R1 = R2R3
Or        R1/R2 = R3/R4
And        L = R2R3C1
Eqs. (1) and (2) are the two balance conditions which are independent of one another.
When using the bridge, R1/R2 is kept a simple ratio. R4 is varied until the head phone give minimum sound. Now the potentials at B and D are the headphone reduces to a further minimum. The experiment may be repeated varying the values of the resistances.

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