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Measurement of Relative permittivity by Schering Bridge

Objective: To determine the relative permittivity of an unknown capacitor.

       Fig. 1. Relative Permittivity measurement by Schering Bridge circuit.


The circuit diagram is shown in Fig.1.

Let, C1=capacitor whose capacitance is to be measured.

r1= a series resistance representing the loss in the capacitor C1.

C2= a standard capacitor.

R3= a non-inductive resistance.

C4= a variable capacitor.

R4= a variable non-inductive resistance. 

d= Spacing between electrodes,

A= effective area of electrodes,

\varepsilon _0 = permittivity of free space.

At balance, 


(r_1+\frac{1}{jwC_1})R_4=\frac{R_3}{jwC_2}(1+jwC_4R_4)\\ Or, r_1R_4-\frac{jR_4}{wC_1} =-j\frac{R_3}{wC_2}+\frac{R_3R_4C_4}{C_2}-----(2)\\

Equating the real and imaginary terms in equ. (2), we obtain

r_1= \frac{R_3C_4}{C_2}.....(3)


C_1= \frac{R_4C_2}{R_3}.....(4)

Two independent balance equations (3) and (4) are obtained if C4 and R4 are chosen as the variable elements.

Dissipation factor , D_1= wC_4R_4.....(5) .

For, a parallel plate arrangement , relative permittivity,

 \varepsilon _r=\frac{C_1d}{\varepsilon_0A }---------(6)


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