Question

A virtual current of $4\, A$ 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. $\frac{1}{9 \pi} H$

Answer 1

Answer: (B)

$R=\frac{P}{i_{r m s}^{2}}=\frac{240}{16}=15 \,\Omega$
$Z=\frac{V}{i}=\frac{100}{4}=25 \,\Omega$
Now, $X_{L}=\sqrt{Z^{2}-R^{2}}$
$=\sqrt{(25)^{2}-(15)^{2}}=20\, \Omega$
$\therefore 2 \pi v L=20$
$ \Rightarrow L=\frac{20}{2 \pi \times 50}=\frac{1}{5 \pi} H$