Schering Bridge for Capacitance Measurement

Schering Bridge is one of the very important a.c bridges to measure capacitance, dielectric loss, dissipation factor and relative permittivity of a capacitor.  The Schering Bridge circuit is shown below.

Here,

C₂=imperfect capacitor whose capacitance is to be determined

 r= resistance representing loss component of  C₂

C₁=loss free standard capacitor

C₄=variable capacitor

R₄=non-inductive resistance connected in parallel with C₄

R₃=pure (non-inductive ) resistor

Balanced is obtained by varying capacitors and resistors. At balance, current through galvanometer is zero. So that

e₁=e₂  and 

e₃=e₄

combining  the above equations    

                    e₁× e₃=e₂ × e₄

             Z₁× Z₃= Z₂× Z₄

         (R₃)×(1/jwc₁) = (r+(1/jwc₂)) × (R₄/(1+jw c₄R₄))

Simplifying and equating real and imaginary parts, we get

r=c₄R₃/c₁

c₂=c₁R₄/R₃

Schering Bridge phasor diagram can be drawn as shown.

The quality of a capacitor is usually expressed in terms of its dielectric loss angle which is defined as the angle by which current departs from its position if it were an ideal (no loss component) capacitor. The angle δ in above phasor diagram is the  dielectric loss angle for the given capacitor C₂.

tan δ is usually called dissipation factor.

As, 

sin θ = θ and tan θ = θ                ....when  θ is small

Therefore,

tan δ = δ = sin δ

but from triangle    ,

Φ + δ = 90⁰

or

δ = 90⁰- Φ

so that,

tan δ = sin δ = sin (90⁰- Φ) = cos Φ

dissipation factor = power factor = tan δ = r/x_c = wrc₂

putting value of rc₂

dissipation factor = power factor = wR₄c₄

Advantages of Schering Bridge :-

   1.The balance equations are free from frequency.

   2.It is used for measuring the insulating properties of electrical              cables and equipments.

   3.It is a low cost bridge as compared to other bridges.


Related articles :-
(1) Hay's Bridge
(2) Maxwell’s Inductance bridge 
(3) Anderson bridge
(4) AC Bridge Basic Theory

(5) Owen Bridge