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 resistance 2 R and 3 R are connected in parallel in a electric circuit. The value of thermal energy developed in \(3 R\) and \(2 R\) will be in the ratio \(3: 2\). In the light of the above statements, choose the most appropriate answer from the options given below

(A) Both statement I and statement II are correct

(B) Both statement I and statement II are incorrect

(D) Statement I is incorrect but statement II is correct.

JEE Main · 2022 · 28 Jul 2022 · Shift 2 · Current Electricity

Given below are two statements :

Statement I : A uniform wire of resistance

80Ω

is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be

5Ω

.

Statement II : Two resistance 2 R and 3 R are connected in parallel in a electric circuit. The value of thermal energy developed in

3 R

and

2 R

will be in the ratio

3 : 2

.

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

Answer: (C)

Statement I: Each part has resistance

80/4 = 20Ω

. Four such resistors in parallel give

R_{e q} = 20/4 = 5Ω

. Statement I is correct.

Statement II: For resistors in parallel, power dissipated

P = V^{2} / R

, so

P_{1} / P_{2} = R_{2} / R_{1} = 3 R / (2 R) = 3/2

, not

3 : 2

as claimed (the ratio is inverted). Statement II is incorrect.

Therefore, Statement I is correct but Statement II is incorrect.

JEE Main · 2022 · 28 Jul 2022 · Shift 2 · Single correct option