Question

In the AC bridge, shown in the figure, $R={10}^3\Omega \text{and}C={10}^{-7}F.$ If the bridge is balanced at a frequency ${\omega }_0,$ the value of ${\omega }_0$ in rad/s is

• A. 10000

Answer 1

The correct option is A 10000
Redraw the bridge:

At balance condition,

$z_1{z}_3=z_2{z}_4$

$R[R+\frac{1}{j\omega C}]=2R\left[\frac{R}{1+j\omega RC}\right]$

$[R+\frac{1}{j\omega C}](1+j\omega RC)=2R$

On comparing Real and Imaginary part

R + R = 2R ...(i)

and,
$\frac{1}{j\omega C}+j\omega R^{2}C=0$

$\frac{1}{j\omega C}=-j\omega R^{2}C$

$\omega =\frac{1}{RC}=\frac{1}{{10}^3\times {10}^{-7}}$

= 10000 rad/sec.