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Question

In a charging circuit, after how many time constant will the energy stored in the capacitor reach one-half of its equilibrium value?[Take,ln221=1.23]

A
1.23 τ
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B
1 τ
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C
2.23 τ
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D
3 τ
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Solution

The correct option is A 1.23 τ
At steady state, let charge on the capcitor be q0, then the energy stored on the capacitor is,Ui=q202C
And after time t, let charge on the capacitor be q, then the energy be,

Uf=q22C

According to problem after time t,

Uf=Ui2

q22C=12×q202C

q=q02

In the case of charging capacitor, charge at any time t,

q=q0[1et/τ]

q02=q0[1et/τ]

12=1etτ

etτ=221

Taking ln on both sides,

tτ=ln221

t=τln221=1.23 τ

Hence, option (a) is correct.

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