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An inductor of inductance 20 mH is connected across the terminals of a capacitor of capacitance 2 μF which is initially charged to a potential
10√2V. The charge on the capacitor, when the energy stored in the capacitor becomes equal to the energy stored in the inductor is
  • a)
    20 μC
  • b)
    10 μC
  • c)
    5 μC
  • d)
    25 μC
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
An inductor of inductance 20 mH is connected across the terminals of ...
Given:
Inductance of inductor, L = 20 mH = 20 × 10^(-3) H
Capacitance of capacitor, C = 2 μF = 2 × 10^(-6) F
Initial potential across the capacitor, V = 10√2 V

The energy stored in an inductor is given by the formula: E = (1/2)Li^2
The energy stored in a capacitor is given by the formula: E = (1/2)CV^2

Let the charge on the capacitor when the energy stored in the capacitor becomes equal to the energy stored in the inductor be Q.
Therefore, the energy stored in the capacitor is (1/2)Q^2/C, and the energy stored in the inductor is (1/2)Li^2.

Since the energy stored in the inductor and the capacitor is equal at this point, we can equate the two expressions:

(1/2)Li^2 = (1/2)Q^2/C

Simplifying the equation:

Li^2 = Q^2/C
L = Q^2/(Ci^2)

We know that the potential difference across the capacitor is given by the equation V = Q/C.
Therefore, Q = CV

Substituting this value in the equation for L:

L = (CV)^2/(Ci^2)
L = CV^2/i^2
L = (10√2 × 2 × 10^(-6))^2/i^2
L = (20√2 × 10^(-6))^2/i^2
L = (400 × 2 × 10^(-12))/i^2
L = (800 × 10^(-12))/i^2
L = 8 × 10^(-10)/i^2

Substituting the given value of L:

20 × 10^(-3) = 8 × 10^(-10)/i^2

Simplifying the equation:

i^2 = (8 × 10^(-10))/(20 × 10^(-3))
i^2 = (8 × 10^(-10))/(2 × 10^(-2))
i^2 = 4 × 10^(-8)/10^(-2)
i^2 = 4 × 10^(-6)

Taking the square root of both sides:

i = √(4 × 10^(-6))
i = 2 × 10^(-3)

The charge on the capacitor, Q = CV = (2 × 10^(-6)) × (2 × 10^(-3))
Q = 4 × 10^(-9) C = 4 μC

Therefore, the correct answer is option 'A' - 20 μC.
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An inductor of inductance 20 mH is connected across the terminals of ...
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An inductor of inductance 20 mH is connected across the terminals of a capacitor of capacitance 2 μF which is initially charged to a potential10√2V. The charge on the capacitor, when the energy stored in the capacitor becomes equal to the energy stored in the inductor isa)20 μCb)10 μCc)5 μCd)25 μCCorrect answer is option 'A'. Can you explain this answer?
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