Question

A circuit has a coil of resistance $50\Omega$ and inductance $\frac{3}{\pi }H$ . It is connected in series with a condenser of $\frac{40}{\pi }\mu F$ and AC supply of 200 V and 50 cycles/s. Which of the following is/are correct?

• A. The impedence of the circuit is $50\sqrt{2}$ Ω
• B. The impedence of the circuit is $50\sqrt{3}$ Ω
• C. The potential drop across inductance coil is $600\sqrt{2}V$
• D. The potential drop across condenser is $500\sqrt{2}V$

Answer 1

Answer: (A), (C), (D)

The correct options are
A The impedence of the circuit is $50\sqrt{2}$ Ω
C The potential drop across inductance coil is $600\sqrt{2}V$
D The potential drop across condenser is $500\sqrt{2}V$

Impedence,
$$\begin{array}{c}Z=\sqrt{R^2+{(\omega L-\frac{1}{\omega c})}^2}\\ Z=50\sqrt{2}\text{ohm}\end{array}$$
$i_0=\frac{V_0}{z}=\frac{200}{50\sqrt{2}}=2\sqrt{2}A$

let potential drop across inductance coil and condenser are $V_{OL}and{V}_{OC}$

$V_{OL}=i_0{x}_L=i_0\omega L$

$=2\sqrt{2}\times 2\pi \times \frac{3}{\pi }\times 50$

$V_{OL}=600\sqrt{2}volt$

$V_{OC}=i_0{X}_C=2\sqrt{2}\times \frac{1}{2\pi \times 50\times \frac{40}{\pi }\times {10}^{-6}}$

$=\sqrt{2}\times \frac{1000}{2}\times {10}^3$

$=\sqrt{2}\times 500=500\sqrt{2}V$