. . . 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,   $(r_1+\frac{1}{jwC_1})(\frac{R_4}{jwC_4R_4+1})=\frac{R_3}{jwC_2}.....(1)\\$ $(r_1+\frac{1}{jwC_1})R_4=\frac{R_3}{jwC_2}(1+jwC_4R_4)\\ Or, r_1R_4-\frac{jR_4}{wC_1} =-j\frac{R_3}{wC_2}+\frac{R_3R_4C_4}{C_2}-----(2)\\$ Equating the real and imaginary terms in equ. (2), we obtain $r_1= \frac{R_3C_4}{C_2}.....(3)$ and, $C_1= \frac{R_4C_2}{R_3}.....(4)$ 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,  $\varepsilon _r=\frac{C_1d}{\varepsilon_0A }---------(6)$   Cite this Simulator:iitkgp.vlab.co.in,. (2015). Measurement of Relative permittivity by Schering Bridge. Retrieved 23 January 2018, from iitkgp.vlab.co.in/index.php?sub=39&brch=124&sim=1787&cnt=1 ..... ..... .....
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