Since the kettle is connected to a fixed voltage V, the amount of heat given off by its heating element in time t is expressed by the formula (from the Joule-Lenz law):
Q = 0⋅24 RV2 t,
where R is the resistance of the heating element. Since we are neglecting loss of heat to the surrounding atmosphere, we must consider that the same quantity of heat Q is needed in both cases to bring the water in the kettle to boiling-point. If the kettle is to boil, not after 15 min, but after 10, then 15/R₁ = 10/R₂, i.e., the resistance of the heating element must be reduced 1⋅5 times. Since a wire's resistance is proportional to its length, the wire of the heating element should be shortened 1⋅5 times.
But this may raise the strength of current in the heating element above the permissible level and the element may burn out.
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