## 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 C_{2} in term of a loss-free standard capacitor C_{1} [figure 1]. The imperfect capacitor is represented by its equivalent loss-free capacitor C_{2} 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,

**Z _{1}Z_{3} = Z_{2}Z_{4}**

Or,

Separating the reals and imaginaries, we have **C _{2} = C_{1}(R_{4}/R_{3})** and

**r = R**.

_{3}.(C_{4}/C_{1})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=90 ^{0}**. 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/X _{c}=r/(1/ωC_{2})= ωrC_{2}**

Putting the value of rC_{2 }from above,

**Dissipation factor = ωrC _{2} = ωC_{4}R_{4} = power factor**