Home
Class 12
PHYSICS
An LC circuit contains a 20 mH inductor ...

An LC circuit contains a 20 mH inductor and a `50 mu F` capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0.
(a) What is the total energy stored initially ? Is it conserved during the oscillalions?
(b) What is the natural frequency of the circuit?
(c ) At what time is the energy stored? (i) Completely electrical ? (ii) Completely magnetic ?
(d) At what time is the total energy shared equally between the inductor and the capacitor ?
(e) If a resistor is inserted in the circuit, how much energy is eventually dissipated as heat ?

Text Solution

Verified by Experts

(a) L = 20 mH = 20 `xx 10^(-3)` H
C = 50 `mu f = 50 xx 10^(-6)` F
`q_(0) = 10 mC = 10^(-2) ` C
Total initial energy
`U_(0) = (1)/(2) (q_(0)^(2))/(C) = (1)/(2) xx (10^(-2) xx 10^(-2))/(50 xx 10^(-6)) J` = 1.0 J
Yes , sum of energies stored in L and C is conserved If R = 0
(b) Natural frequency of the circuit is
f = `(1)/(2pi sqrt(LC))`
f = `(1)/( 2xx 3.14 sqrt(20 xx 10^(-3) xx 50 xx 10^(-6))`
(C) (i) charge on the capacitor at any instant is
q = `q_(0) ` cos `omega t `
or ` " " q = q_(0) cos (2pi)/(T)` t
The energy stored will be completely electrical when the charge will have maximum value.
when t = 0 , `(T)/(2 ) , T , (3T)/(2)` .....
(ii) Energy stored is completely magnetic when electirc energy as well as charge on the capacitor will be zero , ie.for
t `= (T)/(4), (3T)/(4) , (5T)/(4)` .....
(d) Maximum energy stored in capacitor = `(1)/(2) xx (q_(0)^(2))/(C)`
Half the total energy =`(1)/(2) ((1)/(2)) xx (q_(0^(2))/(C))`
= ` ((1)/(2)x((q_(0))/(sqrt(2)))^(2))/(C)`
energy will be half when charge becomes `(q_(0))/(sqrt(2))`
q = `q_(0) " cos " omega`t
`rArr (q_(0))/(sqrt(2)) = q_(0) cos (2pi)/(T) ` t
`cos (2 pi)/(T) t = (1)/(sqrt(2)) = cos (2n + 1) (pi)/(4)`
t = (2n + 1) `(T)/(8)`
energy will be half when
t = ` (T)/(8), (3T)/(8), (5T)/(8) `.....
here, T = `(1)/(f)` = 6.3 ms
(e) The resistance damps out the LC oscillations eventuall .
the whole of the initial energy equal to 1.0 J is eventually dissipated as heat.
Promotional Banner

Topper's Solved these Questions

  • ALTERNATING CURRENT

    MODERN PUBLICATION|Exercise NCERT FILE EXEMPLAR PROBLEMS Subjective Question (VERY SHORT ANSWER TYPE QUESTIONS)|13 Videos

  • ALTERNATING CURRENT

    MODERN PUBLICATION|Exercise HIGHER ORDER THINKING SKILLS & ADVANCED LEVEL|7 Videos

  • ALTERNATING CURRENT

    MODERN PUBLICATION|Exercise NCERT FILE (TEXTBOOK EXERCISES )|11 Videos

  • ATOMS

    MODERN PUBLICATION|Exercise Chapter Practice Test|16 Videos

Similar Questions

Explore conceptually related problems

An LC circuit contains a 20 mH inductor asn a 50 mu F capacitor with initial change of 10 mC . The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0 .

An LC circuit contains a 20 mH inductor and a 50 mu F capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant at which the circuit which is closed be t=0. At what time the energy stored is completely magnetic ?

An L–C circuit contains inductor of inductance L and capacitor of capacitance C with an initial charge q_0 . The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0. (i) What is the total energy stored initially?

An LC circuit contains a 20 mH inductor and 25 mu F capacitor with an initial charge of 5 mC. The total energy stored in the circuit initially is

An L-C circuit contains 20 mH inductor and a 50 muF capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0. what is the total energy stored initially ? At what times is the total energy shared equally between the inductor and the capacitor ?

An LC circuit contains a 20mH inductor and a 50muF capacitor with an initial charge of 10mC. The resistance of the circuit be closed at t=0. The time when the total energy shared equally between the inductor and the capacitor is, approximately.

An Lc circuit contains a 40 mH inductor and a 25 mu F capacitor. The resistance of the circuit is negligible.The time is measured from the instant the circuit is closed. The energy stored in the circuit is completely magnetic at time (in milliseconds)

What is the energy stored in a pure LC circuit ?

A circuit containing an 80 mH inductor and a 250 mu F capacitor in series is connected to 240 V, 100 rad//s supply. The resistance of the circuit is negligible. (i) Obtain rms value of current. (ii) What is the total average power consumed in the circuit ?