A bulb is rated at `100V`, `100W`. It can be treated as a resistor. Find out the inductance of an inductor (called choke coil) that should be connected in series with the bulb at its rated power with the help of an ac source of `200V` and `50Hz`.

Options

A. `(pi)/(sqrt(3))H`
B. `100H`
C. `sqrt(2)/(pi)H`
D. `sqrt(3)/(pi)H`

Answer

D

Explanation

From the rating of the bulb, the resistance of the bulb can be calculated.
`R=(V_(rms)^(2))/(P) =100 Omega`

For the full to be operated at its rated value the rms current throught it should be 1A
Also,
`rms = (V_(rms))/(Z) :. 1= (200)/sqrt(100^(2)+(2pi50l)^(2))rArr L = sqrt(3)/(pi) H`