Alternating current and voltage

Question

A pure resistive circuit element X when connected to an AC supply of peak voltage 200V gives a peak current of 5A which is in phase with the voltage. A second circuit element Y, when connected to the same AC supply also gives the same value of peak current but the current lags behind by 900. If the series combination of X and Y is connected to the same supply, the rms value of current is

Moderate

Solution

for the first case $\frac{200}{5}=40\mathrm{\Omega}=\mathrm{R}$

If current lags by ${90}^{o}$ it is an inductive circuit: $\frac{200}{5}=40\mathrm{\Omega}={\mathrm{X}}_{\mathrm{L}}$

For series impedance = $\mathrm{Z}=\sqrt{{\mathrm{X}}_{\mathrm{L}}^{2}+{\mathrm{R}}^{2}}=40\sqrt{2}$

${\mathrm{i}}_{\mathrm{rms}}=\frac{200}{\sqrt{2}.40\sqrt{2}}=\frac{5}{2}\mathrm{A}$

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