In the LCR circuit the ac driving voltage is v = vm sin ωt.
(i) Write down the equation of motion for q (t).
(ii) At t = t0, the voltage source stops and R is short-circuited. Now write down how much energy is stored in each of L and C.
(iii) Describe subsequent motion of charges.
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i) The equation for variation of motion of charge with respect to time is given as
L d2q(t)/dt + R dq(t)/dt + q(t)/C = Vm sin ωt
ii) The energy stored in each of L and C is given as
Uc = 1/2Cω2[Vm2/R2+(XC – Xl)2] cos2 (ωto + ϕ)
iii) For the circuit to become LC oscillator, R needs to be short-circuited. By doing so, the capacitor will continue to discharge and all the energy will be transferred to L and back and forth. This way there will be an oscillation of energy from electrostatic to magnetic.
An alternating current is a type of electric current which flows in both directions, unlike a direct current, which flows in a single direction. Alternating current is usually represented as a sine waveform and sometimes as triangular waves and square waves. The AC carrier signal is useful for carrying different media, such as sound and video, with the help of modulation.
Some of the Applications of Alternating Current
- Televisions
- Battery cells
- Radios
- Kitchen appliances
- Fans
Download the NCERT Exemplar Class 12 Physics Chapter 7 Alternating current, available in PDF format below.