JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Current Electricity

A uniform heating wire of resistance

36Ω

is connected across a potential difference of 240 V. The wire is then cut into half and a potential difference of 240 V is applied across each half separately. The ratio of power dissipation in first case to the total power dissipation in the second case would be 1 :

x

, where

x

is ______.

Answer: 4

Solution

The initial power is

P_{1} = \frac{V ^{2}}{R} = \frac{24 0 ^{2}}{36} = 1600 W

. Cutting the wire in half makes each piece

18 Ω

, each dissipating

\frac{24 0 ^{2}}{18} = 3200 W

, so the two together dissipate

6400 W

. The ratio of the first case to the second is

1600 : 6400 = 1 : 4

, so

x = 4

JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Integer answer

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