Question

An electric bulb has a rated power of $50W$ at $100V$. If it is used on an AC source $200V$, $50Hz$, a choke has to be used in series with it. This choke should have an inductance of

• A. $0.01mH$
  
• B. $1mH$
  
• C. $0.1H$
  
• D. $1.1H$
  

Answer 1

Answer: (D)

$1.1H$

Resistance of the bulb $=\frac{V^2}{P}=200\Omega$

Let inductance of choke be $L$.

Then the impendence of inductor $=2\pi \times 50\times L$

Both the voltages will be perpendicular in the phasor diagram. Net voltage is vector addition of both.

The total is $200V$. For $100V$ to be on resistor, $100\sqrt{3}$ will be on inductor.

$\Rightarrow \frac{2\pi \times 50\times L}{200}=\sqrt{3}$

$\Rightarrow L=1.1H$