Question

An electric bulb is rated 200 V – 100 W. Find the resistance of the bulb.

Answer 1

The power rating of the electric bulb gives the value of voltage and the power consumption of the electric bulb. By using the expressions for power and the Ohm’s law, we shall be able to obtain the required value of resistance of the bulb.
Formula used:
The Ohm’s law is given as
$V = IR$ …(i)
Here V stands for the potential difference or voltage; “I” stands for current while R stands for resistance.
The power of an electrical circuit is given in terms of voltage and current by the following expression:
$P = VI$ …(ii)

Complete step-by-step solution:
We are given an electric bulb which has power rating of 200 V – 100 W. It means that the values of the voltage and the power for the electric bulb is given as
$\begin{aligned} &V; = 200V \\\ & P = 100W \\\ \end{aligned}$
Now we can use the expression for power given in equation (ii) in the following way to obtain the value of current through the bulb. It can be done in the following way.
$\begin{aligned} & P = VI \\\ &\Rightarrow I = \dfrac{P}{V} \\\ \end{aligned}$
Now substituting the known values we get
$I = \dfrac{{100}}{{200}} = 0.5A$
Now finally we can use the expression for the Ohm’s law given in the equation (i), to obtain the value of resistance.
$\begin{aligned} &V; = IR \\\ & \Rightarrow R = \dfrac{V}{I} \\\ \end{aligned}$
Now substituting the known values we get
$R = \dfrac{{200}}{{0.5}} = 400\Omega$
This the required value of resistance asked in the question.

Note: 1. We can also solve in another way, by directly substituting the Ohm’s law into the expression for power. By doing so, we get the expression of power to be $P = \dfrac{{{V^2}}}{R}$. This can directly give the value for resistance of the electric bulb.
2. The power rating of a device signifies the value of voltage that it can operate and the maximum power output that it can generate.