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.


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