Question

A virtual current of $4A$ and $50Hz$ flows in an AC circuit containing a coil. The power consumed in the coil is $240W$. if the virtual voltage across the coil is $100V$. its resistance will be:

• A. $\frac{1}{5\pi }H$
• B. $\frac{1}{3\pi }H$
• C. $15H$
• D. $\frac{1}{\pi }H$

Answer 1

The correct option is A $\frac{1}{5\pi }H$

Power consumption only occurs in resistor.

$R=\frac{P}{i_{rms}^2}=\frac{240}{16}=15\Omega$

Impedance in AC circuit.

$Z=\frac{V}{i}=\frac{100}{4}=25\Omega$

$X_L=\sqrt{Z^2-R^2}=\sqrt{{\left(25\right)}^2-{\left(15\right)}^2}=20\Omega$

$X_L=20\Omega$

$\Rightarrow 2\pi \nu L=20$

$\Rightarrow L=\frac{20}{2\pi \times 50}=\frac{1}{5\pi }Hz$

Hence, inductance of coil is $\frac{1}{5\pi }H$