Water boils in an electric kettle in 15,min after switching on. If the length of the heating wire is decreased to 2/3 of its initial

Q: Water boils in an electric kettle in $15\,\min$ 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 ............. $min$

c $H = \frac{{{V^2}}}{R}t$ Since supply voltage is same and equal amount of heat will produce, therefore $\frac{{{R_1}}}{{{t_1}}} = \frac{{{R_2}}}{{{t_2}}}$ or $\frac{{{R_1}}}{{{R_2}}} = \frac{{{t_1}}}{{{t_2}}}$ ..... $(i)$ But $R \propto l$ $ \Rightarrow $ $\frac{{{R_1}}}{{{R_2}}} = \frac{{{l_1}}}{{{l_2}}}$..... $(ii)$ By $(i)$ and $(ii)$, $\frac{{{l_1}}}{{{l_2}}} = \frac{{{t_1}}}{{{t_2}}}$..... $(iii)$ Now ${l_2} = \frac{2}{3}\,\,{l_1}$ $ \Rightarrow $ $\frac{{{l_1}}}{{{l_2}}} = \frac{3}{2}$ By equation $(iii)$, $\frac{3}{2} = \frac{{15}}{{{t_2}}}$ $ \Rightarrow $ ${t_2} = 10\,\min$

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

Water boils in an electric kettle in $15\,\min$ 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 ............. $min$

A$15$
B$12$
C$10$
D$8$

Diffcult

STD 11 Science
NEET
STD 12 - 3. current electricity
Physics

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