JEE Main · 2024 · 08 Apr 2024 · Shift 2 · Current Electricity

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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, $\frac{3}{4}$ ✓ Correct
(D)decreased, $\frac{4}{3}$

Answer: (C)

Solution

P = V^{2} / R

and

R \propto L

(length of element), so

P \propto 1/ L

. Energy delivered to boil the water is fixed:

P t = const ⟹ t \propto 1/ P \propto L

.
To reduce boiling time from 20 to 15 minutes,

L

must decrease:

\frac{L _{2}}{L _{1}} = \frac{t _{2}}{t _{1}} = \frac{15}{20} = \frac{3}{4}

So the length must be decreased to

\frac{3}{4}

of its initial value.

JEE Main · 2024 · 08 Apr 2024 · Shift 2 · Single correct option

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