# Water boils in an electric kettle in 15 minutes after switching on. If the length of the heating wire is decreased to 2/3 of its initial value, then the same amount of water will boil with the same supply voltage in Option 1) 15 minutes Option 2) 12 minutes Option 3) 10 minutes Option 4) 8 minutes

P Plabita

As we learnt in

Resistance formula -

$R=\rho \frac{l}{A}=\frac{m}{ne^{2}\tau}\cdot \frac{l}{A}$

- wherein

$\rho =$ resistivity of material

$n=$ Number of free electrons per unit volume.

Initial power  $P_{i}=\frac{V^{2}}{R}$

Final power $P_{f}=\frac{V^{2}}{\frac{2}{3}R}=\frac{3}{2}\cdot P_{i} \left [ \because R \propto l \right ]$

Since energy is same: Pi ti = Pf tf

$\Rightarrow t_{f}= \frac{P_{i}t_{i}}{P_{f}}=\frac{2}{3}\times 15 min = 10 min$

Option 1)

15 minutes

This solution is incorrect

Option 2)

12 minutes

This solution is incorrect

Option 3)

10 minutes

This solution is correct

Option 4)

8 minutes

This solution is incorrect

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