wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

In LC oscillation circuit if the frequency of oscillation of charge is f, then the frequency of oscillation of magnetic energy is

A
f
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
2f
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
f2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
4f
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 2f
We know that charge on the capacitor at any moment is given by

q=q0sinωt [Here, ω=2πf]

The current in the circuit is

i=dqdt=q0ωcosωt

Therefore, energy stored in the inductor at any instant is

E=12Li2

=12L×(q0ωcosωt)2

=12Lq20ω2[cos2ωt]

Let, E0=12Lq20ω2

E=E0 cos2ωt


E=E0[1+cos2ωt]2 [ cos2θ=2cos2θ1]

=E02(1+cos2ωt)

=E02(1+cos(2×2πf×t)

=E02(1+cos(2πf×t)

f=2f

So, the frequency of oscillation of magnetic energy is 2f.

Hence, (B) is the correct answer.
Alternate solution:
We can use spring block analogy for this problem.
In this analogy, we compare charge with mass and magnetic energy with kinetic energy block.

As we know that if a particle executes simple harmonic motion with a frequency f, then 2f will be the frequency of kinetic energy.
Similarly, frequency of oscillation of magnetic energy will be 2f.

flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
LC Oscillator
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon