# A 100 ohm resistance and a capacitor of 100 OHM reactance are connected in series across a 220 V source. When the capacitor is 50% charged find the peak value of displacement current.

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$Netresis\mathrm{tan}ceofthecircuit=resis\mathrm{tan}ce+capacitivereac\mathrm{tan}ce\phantom{\rule{0ex}{0ex}}Z=100+100=200ohm\phantom{\rule{0ex}{0ex}}accordingtothecontinutyequation,displacementcurrentistheconductioncurrent\phantom{\rule{0ex}{0ex}}hence{I}_{D}=\frac{V}{Z}=\frac{200}{200}=1A\phantom{\rule{0ex}{0ex}}andpeakvalue={I}_{o}=\sqrt{2}{I}_{D}=1\times 1.414=1.414A$

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