Question

The four arms of a bridge are:
arm ab : an imperfect capacitor $C_1$ with an equivalent series resistance of $r_1$
arm bc : a non-inductive resistance $R_3$
arm cd : a non-inductive resistance $R_4$
arm da : an imperfect capacitor $C_2$ with an equivalent resistance of $r_2$ in series with $R_2$.

A supply of 450 Hz is given between terminal a and c and the detector is connected between b and d. At balance

$R_2=4.8\Omega R_3=2000\Omega R_4=2850\Omega$
and $C_2=0.5\mu F$ and $r_2=0.4\Omega$



The dissipating factor of capacitor $C_1$ is ______ $\times {10}^{-3}$.

• A. 7.34

Answer 1

The correct option is A 7.34
The bridge is shown below,



At balance $(r_1+\frac{1}{j\omega C_1})R_4=(r_2+R_2+\frac{1}{j\omega C_2})R_3$

Separating the real and imaginary terms,

$r_1=(r_2+R_2)\frac{R_3}{R_4}=(0.4\times 4.8)\times \frac{2000}{2850}=3.65\Omega$

$C_1=C_2.\frac{R_4}{R_3}=(0.05\times {10}^{-6})\times \frac{2850}{2000}=0.712\mu F$

Dissipating factor, $D_1=tan{\delta }_1=\omega C_1{r}_1$

$=2\pi \times 450\times 0.712\times {10}^{-6}\times 3.65=0.00734=7.34\times {10}^{-3}$