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Wein’s Bridge

This bridge is used for measurement of capacitances of capacitors as well as the power factor of the capacitors. The arm AB contains the unknown capacitor C1 in series with a resistance R1. The arm AD contains standard variable capacitor C3 and a non-inductive variable resistance R3. The arm BC and CD contain non-inductive resistances R2 and R4.

When the bridge is balanced, we have
        Z1/Z2 = Z3/Z4
        Z1 = R1 + I/jωC1, Z2 = R2, Z3 = R3 + 1/jωC3, Z4 = R4
        R/ + 1/ jωC1/R2 = R3 + 1/ jωC3 /R4

Cross multiplying, R1 R4 + R4/jωC1 = R2R3 + R2/jωC3

Equating the real parts, R1R4 = R2R3
Or            R1/R2 = R3/R4

Equating the imaginary parts, we get
            R4/C1 = R2/C3
            C1 = C2.R4/R2

Thus C1 can be calculated.
The power factor of capacitor C1 the given by
    Cos θ = R1/√R1 + (1/ω2C12)

But R1 << 1/ωC1
. : cos θ = ωC1R1                                            … (4)
By knowing the values of R1, ω and C1, the power factor of the unknown capacitor can be determined.

Wein Bridge

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