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Show mathematically that in an a.c. circ...

Show mathematically that in an a.c. circuit containing only inductance, the current lags behind the e.m.f. by a phase of `pi/2`.
An a.c. voltage `E=E_0 sin omegat` is applied across an inductor L. Obtain an expression for current I.

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Show mathematically that in an a.c. circuit only containing capacitance, the current leads e.m.f by a phase angle pi/2 .

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