Show that voltage in an inductor leads the current by `pi//2` rad for a pure inductor

Show that in an inductane, the voltage leads the current by pi//2 .

(a) Prove that the current flowing through an ideal inductor connected across a.c. source, lags the voltage in phase by pi/2 . (b) An inductor of self inductance 100 mH, and a bulb are connected in series with a.c. sources of rms voltage 10 V, 50 z. It is found that effective voltage of the circuit leads the current in phase by pi/4 . Calculate the inductance of the inductor used and average power dissipated in the circuit, if a current of 1 A flows in the circuit.

When a 60 mH inductor and a resistor are connected in series with an AC voltage source, the voltage leads the current by 60°. If the inductor is replaced by a 0.5 uF capacitor, the voltage lags behind the current by 30°. What is the frequency of the AC supply ?

S.T. the voltage across a pure capacitor lags the current by 90^(@) or (pi)/(2) rad.

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