KVPY 2019 SB SX Exam Previous Papers

Question : 97 of 120

Marks: +1, -0

A circuit constants of a coil with inductance L and an uncharged capacitor of capacitance C. the coil is in aconstant uniform magnetic field such that the flux through the coil is Φ. At time t = 0, the magnetic field isabruptly switched off. Let

ω_0 =1/√{LC}

and ignore the resistance of the circuit. Then,

Current in the circuit is $I(t) = (Φ/L) \cos ω_0t$
magnitude of the charge on the capacitor is $|Q(t)| = 2Cω_0|\sin ω_0t|$
initial current in the circuit is infinite
initial charge on the capacitor is $Cω_0Φ.$

Validate

Solution:

{-q}/c=L{di}/{dt}

….. (i) from KVL
antiquely

L i_0 -0 = ϕ

i_0 =ϕ/L

from (1)

{-q}/c=L{d^2q}/{dt^2}

⇒

q = q_0 \sin (ω_0 t)

⇒

I = q_0 ω\cos (ω_0 t) = i_0 \cos (ω_0 t)

i=ϕ/L\cos (ω_0 t)

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