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  4. A resistor 30 Ω , inductor of reactance 10 Ω and capacitor of reactance 10 Ω are connected in series to an AC voltage source e=300√2 sin(ω t) . The current in the circuit is

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Q. A resistor $ 30\,\Omega , $ inductor of reactance $ 10\,\Omega $ and capacitor of reactance $ 10\,\Omega $ are connected in series to an $AC$ voltage source $ e=300\sqrt{2}\,sin(\omega t) $ . The current in the circuit is

KEAMKEAM 2008Alternating Current

Solution:

$ e=300\sqrt{2}\sin \omega t $ ... (i)
$ {{I}_{0}}=\frac{{{e}_{0}}}{Z}=\frac{300\sqrt{2}}{\sqrt{{{(30)}^{2}}+{{(10-10)}^{2}}}} $
$ \{\because Z=\sqrt{{{R}^{2}}+{{X}_{L}}-{{X}_{C}}{{)}^{2}}}\} $ $ =\frac{300\sqrt{2}}{30}=10\sqrt{2}A $
$ \therefore $ Current $ I=\frac{{{I}_{0}}}{\sqrt{2}}=10\,A $