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Measurement of Capacitance by Wien Series Bridge

Objective: To determine the capacitance of an unknown capacitor. 

                             Fig. 1. Wien Series Bridge Circuit .


C1= Capacitor whose capacitance is to be measured,

R1= a series resistance representing the loss in the capacitor C1,

C4 = a standard capacitance with series resistance of R4,

R2 and R3 = non-inductive resistances.

At balance, 

(R_1+\frac{1}{jwC_1})*R_3=(R_4+\frac{1}{jwC_4})*R_2--------(1)\\ R_1R_3+\frac{R_3}{jwC_1}=R_2R_4+\frac{R_2}{jwC_4}--------(2)\\

Equating the real and imaginary terms, we obtain

R_1R_3=R_2R_4\\ R_1=\frac{R_2R_4}{R_3}-------------------(3))\\ and, \frac{R_3}{jwC_1}=\frac{R_2}{jwC_4} \\ C_1=\frac{C_4R_3}{R_2}----------------------(4)\\

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

The dissipation factor of capacitance C1 is defined as,






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