First slide

Power in a.c. circuit

Question

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 to operate the bulb at its rated power with the help of an ac source of 200 v and 50 Hz.

Easy

A

$\frac{π}{\sqrt{3}} H$
B

100 H
C

$\frac{\sqrt{2}}{π} H$
D

$\frac{\sqrt{3}}{π} H$

Solution

$R = \frac{V_{r m s}^{2}}{p} = \frac{(100)^{2}}{100} = 100 Ω$
For the bulb to be operated at its rated value the rms current through it should be 1A $I = \frac{200}{\sqrt{100^{2} + [2 π (50 L)]^{2}}} \Rightarrow L = \frac{\sqrt{3}}{π} H$

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