Q21 / 142 · NTA Abhyas (JEE Main) 2020 · Physics · Electrostatics

In the given circuit, initially switch S1 is closed and S2 and S3 are open. After charging of the capacitor, at t=0, S1 is open and S2 and S3 are closed. If the relation between inductance, capacitance and resistance is L = 4CR2, then find the time (in s) after which the current passing through the capacitor and inductor will be the same. [given R=ln2 mΩ, L=2 mH]

Figure

Correct answer: 1

Solution

Charge on capacitor after complete charging=Cε

Now at t = 0 two circuits are formed,

(A)  Discharging of capacitor


∴ q=Cεe-t/τL= Cεe-t/2RC

∴ i1= ε2Re-t/2RC

(B) Growth of current in L-R circuit

i2= ε2R1-e-t/τL

now i1= i2

ε2Re-t/τC = ε2R1-e-t/τL   …1

given L = 4CR2

∴ L2R= 2RC = 1ln2

⇒ t ln2 = ln2

⇒ t = 1 s

Hence, the correct answer is 1.

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