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

 

Answers (1)
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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