Given below are two statements: Statement I: A uniform wire of… | JEE Main 2022 (28 Jul, Shift 2)

Q39JEE Main 2022 · 28 JUL · SHIFT 2Medium

Combination of Resistors

Given below are two statements:

Statement I: A uniform wire of resistance $80\ \Omega$ is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be $5\ \Omega$ .

Statement II: Two resistances 2R and 3R are connected in parallel in an electric circuit. The value of thermal energy developed in 3R and 2R will be in the ratio $3 : 2$ .

In the light of the above statements, choose the most appropriate answer from the option given below

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Answer: (c)

Statement I: each part is $20\ \Omega$ ; four in parallel give $\dfrac{20}{4} = 5\ \Omega$ . True.
Statement II: in parallel $V$ is the same, so $H = \dfrac{V^2 t}{R} \propto \dfrac{1}{R}$ .
$H_{3R} : H_{2R} = \dfrac{1}{3} : \dfrac{1}{2} = 2 : 3$ , not $3 : 2$ . False.
So the answer is (c).

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