Question

Vani’s hair dryer has a resistance of $50\Omega $ when it is first turned on.
1. How much current does the hair dryer draw from the $230V$- line in Vani’s house?
2. What happens to the resistance of the hair dryer when it runs for a long time?

Answer 1

Hint: The current that is flowing through the hair dryer can be found using the Ohm’s law and substituting the values of the resistance and voltage we get the current in the dryer. When a long time goes by the temperature increases so resistance also increases.

Formula Used
In the solution we will be using the following formula,
$V = IR$
where $V$ is the voltage, $I$ is the current and $R$ is the resistance.

Complete step by step answer:
 In the problem, we are given the resistance of the hair dryer as $50\Omega $. It is connected to the $230V$ line in Vani’s house. Now from Ohm’s law, we can find the current that is drawn by the hair dryer from the $230V$ line.
The Ohm’s law is given as,
$V = IR$
Therefore, $V = 230V$ and the resistance is given as, $R = 50\Omega $
So substituting we get,
$230 = I \times 50$
Therefore, we can find the current by dividing both the sides by 50 and get,
$I = \dfrac{{230}}{{50}}A$
On calculating we get,
$I = 4.6A$
So the current drawn by the hair dryer is $4.6A$.
The hair dryer is made of metal. So as the time goes by the metal gets heated up. The resistance is directly proportional to the temperature. So as the temperature increases, the resistance also increases.
So after some time, the fuse that is installed in the hair dryer cuts out the current that is flowing in the hair dryer.

Note Ohm's law says that for the resistance remaining constant, the current increases with the voltage. This relation between the current and voltage is not linear in some materials. They are called non-ohmic.