A coil of inductance is connected across an alternating voltage source of angular…
PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A coil of inductance L is connected across an alternating voltage source of angular frequency ω and peak value Vm. The resistance of the coil may be neglected.
(i) Starting from the relation v=Ldtdi, derive the expression for the instantaneous current i(t) through the coil and establish the phase relation between the voltage across the inductor and the current through it.
(ii) Hence obtain the expression for the inductive reactance XL in terms of ω and L.
(iii) Using the expressions obtained, show that the average power consumed by the inductor over a complete cycle of the alternating voltage is zero.
(iv) The inductor in part (i) has L=0.10H and is connected to a 220V (rms), 50Hz mains supply. Calculate the rms current in the circuit.