Question

An electric iron rated \(2.2\,\text{kW},\,220\,\text{V}\) is operated at \(110\,\text{V}\) supply. Find: (i) its resistance, and (ii) heat produced by it in \(10\) minutes.

Hint:

For electrical appliances, \[ P=\frac{V^2}{R} \] is usually the quickest formula to find resistance from the rating. Once resistance is known, use the same formula again for any new operating voltage.

Answer 1

Concept: The rating of an electrical appliance gives the voltage at which it is designed to operate and the power consumed at that voltage. For a resistive appliance such as an electric iron, the resistance can be determined using the power relation \[ P=\frac{V^2}{R}. \] Once the resistance is known, the power consumed at any other voltage can be calculated using \[ P=\frac{V^2}{R}. \] The heat energy produced in a time interval \(t\) is given by Joule's law of heating: \[ H=Pt. \]

Step 1: Calculate the resistance of the electric iron from its rated values. Given, \[ P=2.2\,\text{kW}=2200\,\text{W} \] and \[ V=220\,\text{V}. \] Using \[ P=\frac{V^2}{R}, \] we get \[ R=\frac{V^2}{P}. \] Substituting the given values, \[ R=\frac{(220)^2}{2200}. \] \[ R=\frac{48400}{2200}. \] \[ R=22\,\Omega. \] Therefore, the resistance of the iron is \[ \boxed{R=22\,\Omega}. \]

Step 2: Calculate the power consumed when connected to \(110\) V supply. The resistance of the iron remains unchanged because it is a physical property of the heating element. Now, \[ V=110\,\text{V} \] and \[ R=22\,\Omega. \] Using \[ P=\frac{V^2}{R}, \] \[ P=\frac{(110)^2}{22}. \] \[ P=\frac{12100}{22}. \] \[ P=550\,\text{W}. \] Thus, the power consumed at \(110\) V is \[ \boxed{550\,\text{W}}. \]

Step 3: Calculate the heat produced in \(10\) minutes. Time, \[ t=10\,\text{min} =10\times60 =600\,\text{s}. \] Using Joule's law, \[ H=Pt. \] Substituting the values, \[ H=550\times600. \] \[ H=330000\,\text{J}. \] \[ H=3.3\times10^5\,\text{J}. \] Therefore, the heat produced in \(10\) minutes is \[ \boxed{3.3\times10^5\,\text{J}}. \] Final Answers: \[ \boxed{(i)\;R=22\,\Omega} \] \[ \boxed{(ii)\;H=3.3\times10^5\,\text{J}} \]