[Physics] What’s the relation between output voltage and time to boil water given the same kettle

electricityhomework-and-exercisespowervoltage

An electric kettle rated 220V, 2000W needed 10 minutes to boil water when it is half filled with water in Singapore where the output voltage is 220V. Estimate the amount of time needed to do the same task if the kettle was brought to the USA where the output voltage is 110V.

Options:

1. 5 minutes
2. 10 minutes
3. 20 minutes
4. 40 minutes

To be able to answer this you have to know how the output voltage is related to the power produced by the kettle. Can someone explain this relationship?

I don't quite understand what it is meant by " An electric kettle rated 220V, 2000W". I get that 2000W means the kettle uses 2000J/s and V is the work done by kettle per unit charge. But what is the difference between the 2 (power and charge of the kettle)? And how does the V of kettle differ from output voltage?

Best Answer

First, this is a poor question (the question that was asked of you, presumably). That's because it requires you to make an assumption about how the kettle works.

For instance, if the kettle's circuitry strives to maintain a constant power output (2000 W), then it will draw more current and maintain its 2000 W output when operated at 110V, which would mean no change in the time.

Since 10 minutes is not the correct answer (and if I were grading this test and someone said 10 minutes I'd say that's acceptable, because I let you assume how it operates). One assumption is to say that the heating element inside the kettle is fixed ($R$ = const) such that the power dissipated goes like $V^2 / R$. With half the voltage, you'd have 1/4 the power, and loosely speaking, it would take 4 times as long, so 40 minutes.

Your teacher should have added, "assume the kettle is nothing more than a resistor that has a voltage applied across it."

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