Electrostatics : Electron in electric field

Question :

An circuit consists of a series combination of a 50mH inductor and a 20μF capacitor. The circuit is connected to AC supply of 220V and 50hz .

The circuit has the value of R=0

1) Which of the following is correct for the circuit?

a) I₀=2.17 A ,I_rms= 1.53 A

b) I₀=5.1 A ,I_rms= 3.6 A

c) V₀=311 V ,V_rms=200 V

\) None of these

2) which of the following is false

a) Voltage drop across inductor is 23.1 V

b) Voltage drop across capacitor is 243 V

c) Voltage drop across inductor is 243 V

d) Voltage drop across capacitor is 23.1 V

3) which of the following is true

a) Average power transferred to inductor is zero

b) Average power transferred to capacitor is zero

c) Average power absorbed by the circuit is zero

d) None of the above

Solution:

The following quantities are given in the question

L=50mH=50X10^-3 H

C=20μF=20X10^-6F

V_rms=220V

f=50hz or ω=2πf=100π rad/sec

Now

$V_0=\sqrt{2}{V}_{\mathrm{rms}}=311V$

The peak current is given by the below equation in LC circuit

$I_0=\frac{V_0}{Z{}_{}}$

Where

$Z=\frac{1}{\mathrm{\omega L}-\frac{1}{\mathrm{\omega C}}}$

Substituting the values from above

I₀=-2.17 A

So magnitude is

I₀=2.17 A

I_rms=I₀/$\sqrt{2}$=1.53 A

Voltage drop across inductor is given by

V_L=I_rmsωL=23.1 V

Voltage drop across capacitor is given by

V_C=$\frac{I_{\mathrm{rms}}}{\mathrm{\omega C}}$=243 V

Since in both inductor and capacitor,voltage and current are at right angle,no power will be transferred to them

Hence total power absorbed is also zero