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Standard VIII

Physics

Heating Effect of Electric Current

An LC circu...

Question

An $L C$ circuit contains a $20 m H$ inductor and a $50 μ F$ capacitor with an initial charge of $10 m C$ . The resistance of the circuit is negligible. Let the instant circuit is closed be at $t = 0$
What is the total energy stored initial? Is it conserved during the $L C$ oscillations?

0.01 J

, yes

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0.1 J

, yes

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1 J

, yes

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2 J

, yes

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Solution

The correct option is C $1 J$ , yes
total energy $= \frac{1}{2} {C V}^{2} = \frac{1}{2} \frac{9^{2}}{C} = \frac{1}{2} \times \frac{100 \times 10^{- 6}}{50 \times 10^{- 6}}$
$= 1 J$
Yes, here in $L C$ oscillation no energy is losses.

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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?

Q. An LC circuit contains a 20 mH inductor and a 50

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(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
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An LC circuit contains a 20 mH inductor and a 50μF capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant circuit is closed be at t=0What is the total energy stored initial? Is it conserved during the LC oscillations?

The correct option is C 1 J, yestotal energy=12CV2=1292C=12×100×10−650×10−6 =1JYes, here in LC oscillation no energy is losses.

An $L C$ circuit contains a $20 m H$ inductor and a $50 μ F$ capacitor with an initial charge of $10 m C$ . The resistance of the circuit is negligible. Let the instant circuit is closed be at $t = 0$
What is the total energy stored initial? Is it conserved during the $L C$ oscillations?

The correct option is C $1 J$ , yes
total energy $= \frac{1}{2} {C V}^{2} = \frac{1}{2} \frac{9^{2}}{C} = \frac{1}{2} \times \frac{100 \times 10^{- 6}}{50 \times 10^{- 6}}$
$= 1 J$
Yes, here in $L C$ oscillation no energy is losses.