KVPY2019PhysicsAlternating Current
A circuit consists of a coil with inductance L and an uncharged capacitor of capacitance C . The coil is in a constant uniform magnetic field such that the flux through the coil is ϕ . At time t = 0   min , the magnetic field is abruptly switched OFF. Let ω 0 = 1 / L C and ignore the resistance of the circuit. Then,
Options
- Acurrent in the circuit is I t = ϕ / L cos ω 0 t
- Bmagnitude of the charge on the capacitor is | Q t | = 2 C ω 0 sin ω 0 t
- Cinitial current in the circuit is infinite
- Dinitial charge on the capacitor is C ω 0 ϕ
Correct answer
A. current in the circuit is I t = ϕ / L cos ω 0 t
Step-by-step solution
At t = 0 capacitor is uncharged and flux of inductor is ϕ . Now, using ϕ = L I , at t = 0 current in circuit is I 0 = ϕ L Instantaneous current in circuit is d q d t . where, q is solution of L d 2 q d t 2 + q C = 0 or d 2 q d t 2 + q L C = 0 At t = 0 , current in circuit is non-zero, so instantaneous current is given by = I 0 cos ω t = ϕ L · cos ω t