Q. A virtual current of $4A$ and $50\ Hz$ flows in an ac circuit containing a coil. The power consumed in the coil is $240\ W$. If the virtual voltage across the coil is $100\ V$ its inductance will be
A) $\frac{1}{3\pi}H$
B) $\frac{1}{5\pi}H$
C) $\frac{1}{7\pi}H$
D) $\frac{1}{9\pi}H$
Explanation
(b) $R = \frac{P}{i_{rms}^{2}} = \frac{240}{16} = 15\Omega;Z = \frac{V}{i} = \frac{100}{4} = 25\Omega$
Now $X_{L} = \sqrt{Z^{2} - R^{2}} = \sqrt{(25)^{2} - (15)^{2}} = 20\Omega$
$\therefore 2\pi vL = 20 \Rightarrow L = \frac{20}{2\pi \times 50} = \frac{1}{5\pi}Hz$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.