Schering Bridge

It is used for the accurate measurement of small capacitance. The unknown capacitor C is connected in arm AB along with the associated resistance R₁ in series. The arm AD contains a standard capacitor C₃ having negligible resistance. The two remaining arms BC and CD contain non-conductive R₂ and R₄. A variable calibrated air capacitor C₄ is put in parallel with R₄. The bridge is balanced by varying R₄ and C₄.

Theory. The general balance condition of an a.c. bridge is
            Z₁/Z₂ = Z₁/Z₄
        Z₁ = R₁ + 1/jωC, Z₂ = R₂, Z₃ = 1/jωC₃ and 1/Z₄ = 1/R₄ + 1/1/ jωC₄

R1 + 1/ jωC/R₂ = 1jωC₃(1/R₄ + jωC₄)

Or        R₁ + 1/ jωC = R₂/ jωC₃ R₄ + R₂C₄/C₃

    Equating the real and imaginary parts, we get
        R₁ = R₂ C₄/C₃                                    … (1)
And        1/C = R₂/C₃R₄
Or        C = R₄/R₂C₃                                     … (2)

C can be calculated using Eq. (2)
Advantages. This bridge is used for the measurement of dielectric constants, particularly of liquids. It provides the accurate determination of very small capacitances. In industries it is widely used in testing of cables and insulators at high voltages.