JEE Mains · Physics · STD 12 - 3. current electricity
Water boils in an electric kettle in \(20\) minutes after being switched on. Using the same main supply, the length of the heating element should be _______ to _______ times of its initial length if the water is to be boiled in \(15\) minutes.
- A increased, \(\frac{3}{4}\)
- B increased, \(\frac{4}{3}\)
- C decreased, \(\frac{3}{4}\)
- D decreased, \(\frac{4}{3}\)
Answer & Solution
Correct Answer
(C) decreased, \(\frac{3}{4}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{P}=\frac{\mathrm{v}^2}{\mathrm{R}}, \mathrm{R}=\frac{\rho \ell}{\mathrm{A}}\) \(\mathrm{P} \propto \frac{1}{\ell}\) \(\frac{\mathrm{P}_1}{\mathrm{P}_2}=\frac{\mathrm{t}_2}{\mathrm{t}_1}=\frac{15}{20}=\frac{\ell_2}{\ell_1}\) \(\ell_2=\frac{3}{4} \ell_1\)
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