Water in an electric kettle connected to a 220 V supply took 5 minutes to reach its boiling point. How long would it have taken if the supply had been of 200 V?
Water absorbs heat in the electric kettle and increases in temperature. It soon reaches the boiling point once enough heat has been absorbed.
The heat produced in the electric kettle is due to the current passing through the resistors that make up a large part of the kettle. Let the resistance of the resistors be R.
The power when a voltage V is applied across a resistor with resistance R is given by V^2/R.
Here, the water took 5 minutes to boil when the voltage applied was 220. The energy required was (220^2/R)*5*60
It the time taken for the water to boil when the voltage is decreased to 200 V is T, we have (200^2/R)*T = (220^2/R)*300
=> T = (220^2/200^2)*300
=> T = 363 seconds.
The water would boil after 363 seconds if the voltage applied to the kettle were reduced from 220 V to 200 V.