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I need help with 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

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)
939 Views

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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