Question

An electric bulb of $100W-300V$ is connected with an $AC$ supply of $500V$ and $\frac{150}{\pi }Hz$ The required inductance to save the electric bulb is:

• A. $2H$
• B. $\frac{1}{2}H$
• C. $4H$
• D. $\frac{1}{4}H$

Answer 1

The correct option is C $4H$

The correct option is C

The voltage at which the bulb operates is $300v$ And the aac supply has voltage $500v$

Therefore, the difference of the voltage $V_l=500-300=200v$

Will appear across the inductance of the spred by the coil of the bulb.

Therefore $V_l=\omega L\times I\Rightarrow \frac{p}{v}=\frac{100}{500}=\frac{1}{5}A.$

Thus, $V_l=2\pi fL\times I\Rightarrow 200=2\pi \times \frac{150}{\pi }l\frac{1}{5}\Rightarrow l=\frac{200}{60}=3.33\approx 4H$