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Standard XII

Physics

Electrical Oscillations

Compute the t...

Question

Compute the total energy in the circuit at $t = 2.00 m s$

2.5625 μ J

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4.5625 μ J

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6.5625 μ J

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8.5625 μ J

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Solution

The correct option is D $6.5625 μ J$
Energy stored in capacitor at $t = 2 m s$ , $U_{C} = 6.5531 μ J$ (solved earlier)
Energy stored in an inductor at $t = 2 m s$ , $U_{L} = 0.0094 μ J$ (solved earlier)
Total energy stored at that instant $U_{T o t a l} = U_{C} + U_{L}$
$⟹ U_{t o t a l} = 6.5531 + 0.0094 = 6.5625 μ J$

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An LC circuit contains a 20 mH inductor and a 50 μF capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0.

(a) What is the total energy stored initially? Is it conserved during LC oscillations?

(b) What is the natural frequency of the circuit?

(i) completely electrical (i.e., stored in the capacitor)? (ii) completely magnetic (i.e., stored in the inductor)?

(d) At what times is the total energy shared equally between the inductor and the capacitor?

(e) If a resistor is inserted in the circuit, how much energy is eventually dissipated as heat?

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Compute the total energy in the circuit at t=2.00ms

The correct option is D 6.5625μJEnergy stored in capacitor at t=2 ms, UC=6.5531μJ (solved earlier)Energy stored in an inductor at t=2 ms, UL=0.0094μJ (solved earlier)Total energy stored at that instant UTotal=UC+UL⟹ Utotal=6.5531+0.0094=6.5625μJ

Compute the total energy in the circuit at $t = 2.00 m s$