JEE Main · 2022 · 29 Jun 2022 · Shift 1 · Current Electricity

WhatsApp Email

Two coils require 20 minutes and 60 minutes respectively to produce same amount of heat energy when connected separately to the same source. If they are connected in parallel arrangement to the same source; the time required to produce same amount of heat by the combination of coils, will be ______ min.

Answer: 15

Solution

Heat produced:

Q = \frac{V ^{2}}{R} t

for constant voltage source.

For same heat

Q_{0}

Q_{0} = \frac{V ^{2}}{R _{1}} \times 20 = \frac{V ^{2}}{R _{2}} \times 60

This gives

R_{2} = 3 R_{1}

.

When connected in parallel:

R_{e q} = \frac{R _{1} R _{2}}{R _{1} + R _{2}} = \frac{R _{1} \cdot 3 R _{1}}{R _{1} + 3 R _{1}} = \frac{3 R _{1}}{4}

For same heat:

Q_{0} = \frac{V ^{2}}{R _{1}} \times 20 = \frac{V ^{2}}{3 R _{1} /4} \times t

t = 20 \times \frac{3}{4} = 15

min

JEE Main · 2022 · 29 Jun 2022 · Shift 1 · Integer answer

Practise more: all JEE Main PYQs on Current Electricity →

JEE Main · 2022 · 29 Jun 2022 · Shift 1 · Current Electricity

Solution

More JEE Main questions on Current Electricity