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  • When an alternating voltage of 220 V is applied across a device P, a current of 0.25 A flows through the circuit and it leads the applied voltage by an angle <img alt="\frac{\pi}{2}" src="https://e

When an alternating voltage of 220 V is applied across a device P, a current of 0.25 A flows through the circuit and it leads the applied voltage by an angle \frac{\pi}{2} radian. When the same voltage source is connected across another device Q, the same current is observed in the circuit but in phase with the applied voltage. What is the current when the same source is connected across a series combination of P and Q?

Option: 1

\frac{1}{4 \sqrt{2}} \text { A lagging in phase by } \frac{\pi}{6} \text { with voltage }


Option: 2

\frac{1}{4 \sqrt{2}} \text { A leading in phase by } \frac{\pi}{4} \text { with voltage }


Option: 3

\frac{1}{\sqrt{2}} \text { A leading in phase by } \frac{\pi}{4} \text { with voltage }


Option: 4

\frac{1}{\sqrt{2}} \text { A leading in phase by } \frac{\pi}{6} \text { with voltage }


Answers (1)

best_answer

P is a capacitor, X_C=\frac{220}{0.25}=880 \Omega
Q is resistance, \mathrm{R}=\frac{220}{0.25}=880 \Omega
When \mathrm{\mathrm{P} \, \, and \,\, \mathrm{Q}} are in series.
\mathrm{\begin{aligned} & \mathrm{Z}=\sqrt{\mathrm{R}^2+\mathrm{X}_{\mathrm{C}}^2}=880 \sqrt{2} \Omega \\ & \phi=\tan ^{-1}\left(\frac{\mathrm{X}_{\mathrm{C}}}{\mathrm{R}}\right)=45^{\circ} \text { (current leading) } \\ & \Rightarrow \mathrm{I}=\frac{\mathrm{V}}{\mathrm{Z}}=\frac{1}{4 \sqrt{2}} \mathrm{~A} \end{aligned} }

Posted by

Pankaj Sanodiya

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