Initially the open switch leaves a series capacitor-resistor-inductor circuit driven by the battery. After a long time the electric current is zero and the capacitor voltage is . Closing the switch bypasses and, under the stated idealization, instantaneously discharges the capacitor. The inductor current remains continuous at zero.
The remaining RL circuit obeys , so
(1)
The capacitor's impulsive discharge through the ideal short is distinct from the finite electric current through the coil. A finite switch resistance would resolve that separate fast transient.

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