Question

The AC bridge is supplied with a source of frequency 1 kHz as shown in the below figure. If $R_2=3R_{1}and{C}_3=150pF,$ then at balanced condition the value of unknown capacitor $C_x$ is _______ pF.

• A. 5
• B. 50
• C. 0.5
• D. 500

Answer 1

The correct option is B 50

$\text{At balanced condition,}$

$R_2\times \frac{1}{j\omega C_3}=[R_x+\frac{1}{j\omega C_x}]\left[\frac{R_1}{1+j\omega R_1{C}_1}\right]$

$(1+j\omega R_1{C}_1)\left[\frac{R_2}{j\omega C_3}\right]=[R_x+\frac{1}{j\omega C_x}]\left(R_1\right)$

$\frac{R_2}{j\omega C_3}+\frac{R_1{R}_2{C}_1}{C_3}=R_x{R}_1+\frac{R_1}{j\omega C_x}$

$\text{On comparing imaginary part,}$

$\frac{R_2}{j\omega C_3}=\frac{R_1}{j\omega C_x}$

$C_x=\frac{R_1}{R_2}\times C_3$

$=\frac{1}{3}\times 150=50pF$