Question

An inductance of $\frac{200}{\pi }$mH,a capacitance of $\frac{{10}^{-3}}{\pi }$F and a resistance of 10$\Omega$ are connected in series with a.c. source 200V,50Hz.The phase angle of the circuit for current and voltage source is:

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Using the expression for the reactance's ,we have

$X_L$=$2\pi fL$

=$2\times \pi \times 50\times \frac{200}{\pi }\times {10}^{-3}$

=20$\Omega$
$X_C$=$\frac{1}{2\left(\pi \right)fC}$=$\frac{{10}^3}{2\times \pi \times \frac{50}{\pi }}$

=10$\Omega$

R=10$\Omega$

We have tan $\Phi$=$\frac{x_L-x_C}{R}$

$\frac{20-10}{10}$

=1

$\Rightarrow$ $\Phi$=$\frac{\pi }{4}$