The water in an electric kettle begins to boil in ten minutes after being switched on. The wire used as the heating element is modified so that the water begins to boil in 7 minutes. How can this be achieved?

By increasing the length of the wire.

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By decreasing the length of the wire.

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By connecting another another identical wire in series.

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By connecting another identical wire in parallel.

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Solution

The correct option is C By decreasing the length of the wire.
Heat produced $H = \frac{V^{2} t}{R}$ where $R = ρ \frac{L}{A}$
$∴$ $H = \frac{V^{2} A t}{ρ L}$ $⟹ H \propto \frac{t}{L}$
Hence length of the wire must be reduced so that water starts to boil in 7 minutes instead of 10 minutes.

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The water in an electric kettle begins to boil in ten minutes after being switched on. The wire used as the heating element is modified so that the water begins to boil in 7 minutes. How can this be achieved?

The correct option is C By decreasing the length of the wire.Heat produced H=V2tR where R=ρLA∴ H=V2AtρL ⟹H∝tLHence length of the wire must be reduced so that water starts to boil in 7 minutes instead of 10 minutes.

The correct option is C By decreasing the length of the wire.
Heat produced $H = \frac{V^{2} t}{R}$ where $R = ρ \frac{L}{A}$
$∴$ $H = \frac{V^{2} A t}{ρ L}$ $⟹ H \propto \frac{t}{L}$
Hence length of the wire must be reduced so that water starts to boil in 7 minutes instead of 10 minutes.