Consider the circuit shown below. The switch has been in position a for a long time. The capacitor is uncharged. (a) What energy is currently stored in the magnetic field of the inductor? (b) At time t = 0, the switch S is thrown to position b. By applying Faraday's Law to the bottom loop of the above circuit, obtain a differential equation for the behavior of charge Q on the capacitor with time. (c) Write down an explicit solution for Q(t) that satisfies your differential equation above and the initial conditions of this problem.

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Consider the circuit shown below. The switch has been in position a for a
long time. The capacitor is uncharged.
(a) What energy is currently stored in the magnetic field of the
inductor?
(b) At time t = 0, the switch S is thrown to position b. By applying
Faraday's Law to the bottom loop of the above circuit, obtain a
differential equation for the behavior of charge Q on the
capacitor with time.
(c) Write down an explicit solution for Q(t) that satisfies your
differential equation above and the initial conditions of this
problem.
(d) How long after t = 0 does it take for the electrical energy stored
in the capacitor to reach its first maximum, in terms of the
quantities given?
(e) At that time, what is the energy stored in the inductor? In the
capacitor?
R
Transcribed Image Text:Consider the circuit shown below. The switch has been in position a for a long time. The capacitor is uncharged. (a) What energy is currently stored in the magnetic field of the inductor? (b) At time t = 0, the switch S is thrown to position b. By applying Faraday's Law to the bottom loop of the above circuit, obtain a differential equation for the behavior of charge Q on the capacitor with time. (c) Write down an explicit solution for Q(t) that satisfies your differential equation above and the initial conditions of this problem. (d) How long after t = 0 does it take for the electrical energy stored in the capacitor to reach its first maximum, in terms of the quantities given? (e) At that time, what is the energy stored in the inductor? In the capacitor? R
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