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## Schering Bridge | Capacitance measurement

It is one of the very important and useful methods of measuring the capacitance and dielectric loss of a capacitor. In fact, it is a device for comparing an imperfect capacitor C2 in term of a loss-free standard capacitor C1 [figure 1]. The imperfect capacitor is represented by its equivalent loss-free capacitor C2 in series with resistance r [figure 2]. For high voltage application, the voltage is applied at the junction shown in the figure. The junction between arms 3 and 4 is earthed. Since capacitor impedances at lower frequencies are much higher than resistances, most of the voltage will appear across capacitors. Grounding of the junction affords safety to the operator from the high-voltage hazards while making balancing adjustment in arm 3 and 4. For balance,

Z1Z3 = Z2Z4

Or, Separating the reals and imaginaries, we have C2 = C1(R4/R3) and r = R3.(C4/C1).

The quality of a capacitor is usually expressed in term of its phase defect angle or dielectric loss angle which is defined as the angle by which current departs from exact quadrature from the applied voltage i.e. the complement of the phase angle. If ɸ is the actual phase angle and δ the defect angle, then ɸ+δ=900. For smaller values of δ, tan δ = sin δ = cos ɸ (approximately). Tan δ is usually called the dissipation factor of the R-C circuit. For low power factors, therefore, dissipation factor is approximately equal to the power factor.

As shown in figure 3, Dissipation factor = power factor = tan δ

=r/Xc=r/(1/ωC2)= ωrC2

Putting the value of rC2 from above,

Dissipation factor = ωrC2 = ωC4R4 = power factor

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