Question

A light bulb is rated $150W$ for $220V$ AC supply of $60Hz$ . Calculate the resistance of the bulb and the RMS current through the bulb?

Answer 1

Hint : In this question, we need to find out the resistance of the bulb and also the RMS value of the current flowing through the bulb. For this we are going to use the formula establishing the relation between power, voltage and electric current in AC (alternating current) supply.

Complete Step By Step Answer:
Here, the square of the RMS value of the voltage across the element will be divided by the resistance of the element which will give you the power consumed (passive elements) or delivered ( active elements) by the element.
Mathematically the formula we have,
$p = \dfrac{{{V^2}_{rms}}}{R}$ Where ${V^2}_{rms}$ stands for RMS value of the voltage and R stands for the resistance of the element.
According to the question, we are given the power rating of the bulb as 150 watts, and the RMS value of the voltage across the bulb is given as 220 volts.
Therefore substituting the value of P=150 watts and ${V_{rms}}$ =220 volts in the formula $p = \dfrac{{{V^2}_{rms}}}{R}$ to determine the resistance of the bulb.
We have,
$p = \dfrac{{{V^2}_{rms}}}{R}$
$\Rightarrow 150 = {\dfrac{{\left( {220} \right)}}{R}^2}$
$\Rightarrow R = \dfrac{{220 \times 220}}{{150}}$
$\Rightarrow R = 322.6\Omega$
Hence, the resistance of the bulb is 322.6 ohm.

Note :
The point to be noted here is that the value of the voltage given in the question for the AC (alternating current) source should only be taken as RMS value. RMS value is the measure of transfer of heat between the elements also it is the root mean square value of source voltage or current.