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In the free oscillations of an LC circuit, the sum of energies stored in the capacitor and the inductor.
  • a)
    varies cubically with time
  • b)
    varies linearly with time
  • c)
    varies as square of time
  • d)
    is constant in time
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
In the free oscillations of an LC circuit, the sum of energies stored ...
At any time, t
energy stored in capacitor, EC=q2/2C
Total energy stored in C and L at any time t
E=EC+EL
E=(q2/2C)+(LI2/2)
If q=q0sinωt
I=dq/dt=q0cosωtω=ωq0cosωt
Put in (i), E=[(q0sinωt)2/2C] + L(ωq0cosωt)2/2
E=(q02/2C) sin2ωt+(q02/2)cos2ωt.ω2L
But ω2=12/LC
∴E=(q02/2C) sin2ωt+(q02/2) (L/LC) cos2ωt
=q02/2C(sin2ωt+cos2ωt)
=q02/2C= constant in time.
 
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Most Upvoted Answer
In the free oscillations of an LC circuit, the sum of energies stored ...
At any time, t
energy stored in capacitor, EC=q2/2C
Total energy stored in C and L at any time t
E=EC+EL
E=(q2/2C)+(LI2/2)
If q=q0sinωt
I=dq/dt=q0cosωtω=ωq0cosωt
Put in (i), E=[(q0sinωt)2/2C] + L(ωq0cosωt)2/2
E=(q02/2C) sin2ωt+(q02/2)cos2ωt.ω2L
But ω2=12/LC
∴E=(q02/2C) sin2ωt+(q02/2) (L/LC) cos2ωt
=q02/2C(sin2ωt+cos2ωt)
=q02/2C= constant in time.
 
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Community Answer
In the free oscillations of an LC circuit, the sum of energies stored ...
Energy is stored in capacitor inthe form of electric field and in inductor inthe form of magnetic field sototal energy is constant
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