Question

A coil has resistance of $6\Omega$ & inductance of $0.08H$. It is connected with alternating voltage of $250V,\frac{50}{\pi }Hz.$ The average power consumed in circuit

• A. $3750W$
• B. $3250W$
• C. $2500W$
• D. $1875W$

Answer 1

The correct option is A $3750W$

Given, $V_{rms}=250V$
$P_{avg=}{V}_{rms}{I}_{rms}\cos \left(\varphi \right)=V_{rms}{I}_{rms}\frac{R}{Z}={\left(\frac{V_{rms}}{Z}\right)}^{2}R(\because \cos (\varphi )=\frac{R}{Z}\&\frac{V_{rms}}{Z}=I_{rms})$
Also,
$X_L=\omega L=2\pi \nu L=2\pi \times \frac{50}{\pi }\times \left(0.08\right)=8\Omega$And,
$Z=\sqrt{R^2+{X_L}^2}=\sqrt{{\left(6\right)}^2+{\left(8\right)}^2}=10\Omega$Therefore,
$P_{avg}={\left(\frac{V_{rms}}{Z}\right)}^{2}R={\left(\frac{250}{10}\right)}^2\times 6=3750W$