Question

A resistor of $100\Omega$, a pure inductance coil of L = 0.5 H and capacitor are in series in a circuit containing an a.c sources of 200 V, 50 Hz. In the circuit, current is added is ahead of the voltage by ${30}^0$.Find the value of the capacitance

• A. 1.46
• B. 3
• C. 4
• D. 5

Answer 1

The correct option is A 1.46

In the circuits

Inductive Reactance $X_2=2\pi vL=2\pi \left(50\right)\times \left(0.5\right)=50\pi \Omega$

Let capacitance be C so, $x_c=\frac{1}{2\pi vc}=\frac{1}{100\pi c}$

an current leads voltage (circuit is more capacitive) by ${30}^o,=\varphi$

$\tan \varphi =\frac{X_C-X_L}{R}\Rightarrow \tan {30}^o=\frac{\frac{1}{100\pi c}B-50\pi }{100}$

that gives $C=1.46F$