Home
Class 12
PHYSICS
Show that the sum of electrostatic energ...

Show that the sum of electrostatic energy and magnetic energy in an LC oscillator equals `(q_(0)^(2))/(2C)`.

Text Solution

Verified by Experts

Total energy = `=U_(E)+U_(m)`
`=(1)/(2)(q_(0)^(2))/(C)cos^(2)omegat+(1)/(2)Lq_(0)^(2)omega^(2)sin^(2)omegat`
`=(1)/(2)(q_(0)^(2))/(C)cos^(2)omegat+(1)/(2)q_(0)^(2)L((1)/(sqrt(LC)))^(2)sin^(2)omegat`
`=(1)/(2)(q_(0)^(2))/(C)cos^(2)omegat+(1)/(2)(q_(0)^(2))/(C)sin^(2)omegat`
`=(1)/(2)(q_(0)^(2))/(C)[cos^(2)omegat+sin^(2)omegat]`
`=(1)/(2)(q_(0)^(2))/(C)`
`q_(0)` and C are time independent constants.
Note :
Maximum energy of a capacitor = maximum energy of an inductor = `(1)/(2)(q_(0)^(2))/(C)=(1)/(2)Li_(m)^(2)`
At any given instant, the total energy, in an LC oscillator is the sum of energy in each of them.
Promotional Banner

Topper's Solved these Questions

  • ALTERNATING CURRENT

    SUBHASH PUBLICATION|Exercise FIVE MARKS QUESTIONS WITH ANSWERS|12 Videos

  • ALTERNATING CURRENT

    SUBHASH PUBLICATION|Exercise NUMERICALS WITH SOLUTIONS|34 Videos

  • ALTERNATING CURRENT

    SUBHASH PUBLICATION|Exercise TWO MARKS QUESTIONS WITH ANSWERS|12 Videos

  • ANNUAL EXAM QUESTION PAPER -MARCH -2017

    SUBHASH PUBLICATION|Exercise PART -D|12 Videos

Similar Questions

Explore conceptually related problems

The plates of a parallel plate capacitor have an area of 100 cm^(2) each and are separated by 3mm. The capacitor is charged by connecting it to a 400 V supply. (a) Calculate the electrostatic energy stored in the capacitor. (b) If a dielectric of dielectric constant 2.5 is introduced between the plates of the capacitor then find the electrostatic energy stored and also change in the energy stored.

Obtain the expression for the energy stored in a charged parallel plate capacitro and express it in its three equivalent forms, in terms of capacitance C, charge Q on the plate and potential difference V between the plates. Use this result to show that the energy density, of the electric field E, in a capacitor equals 1/2varepsilon_0E^2 .

Show that kinetic energy of rotating body is 1/2 I sigma^2

The sum of the roots of the quadratic equations ax^(2) + bx + c=0 is