Question

You have the following appliances each of $500{\text{ W}}$ running on $220{\text{ V}}$ a.c :
(1) Electric iron
(2) Electric lamp
(3) Electric room heater
The electric resistance is
A. Maximum for the heater
B. Maximum for the heater
C. Maximum for the electric iron
D. Same in all three cases

Answer 1

Hint: in order to solve the question, we will derive the relation between power, resistance and potential difference from the original relation between power potential difference and current after then we use the value of power and potential difference to find the resistance of appliances.

Formula used:
$P = V \times I$
Here, $P$ refers to power of the appliances, $V$ refers to potential difference and $I$ refers to current flowing through appliances.
Ohm’s law
$V = I \times R$
Here, $I$ refers to current, $V$ refers to potential difference and $R$ refers to resistance.

Complete step by step answer:
In the question we are given the power that is $500{\text{ W}}$ and potential difference of $220{\text{ V}}$ . Each of the appliances include Electric iron ,Electric lamp, Electric room heater. The original formula of the power;
$P = V \times I$
But we will derive the formula which includes the physical quantities given in question that is potential difference and resistance. We will derive it with the help of ohm’s law
$V = I \times R$
We will find I and then will replace it the power formula
$I = \dfrac{V}{R}$

Now replace
$P = V \times I$
$\Rightarrow P = V \times \dfrac{V}{R}$
Squaring the potential difference
$P = \dfrac{{{V^2}}}{R}$
Now we will take R on other as we have to find the resistance
$R = \dfrac{{{V^2}}}{P} \\
\Rightarrow P = 500{\text{ W}} \\
\Rightarrow V =220{\text{ V}}$
Inserting the values
$R = \dfrac{{{{220}^2}}}{{500}}\Omega $
$\therefore R = 96.8{\text{ }}\Omega $
As we know the power of all appliances are the same so the resistance will also be the same.

Hence, the correct option is D.

Note: Many of the people will make the mistake by not using the derived formula instead of that they will use the original formula but for that they have find which is not given in the question hence it will increase the complexity of the question therefore it is wise to use the derived formula which have both resistance and the potential difference.