Given below are two statements : Statement I : A uniform wire of resistance 80   Ω is cut into…

Given below are two statements :
Statement I : A uniform wire of resistance 80 Ω is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be 5 Ω.

Statement II : Two resistance 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 options given below

  1. Both statement I and statement II are correct
  2. Both statement I and statement II are incorrect
  3. Statement I is correct but statement II is incorrect
  4. Statement I is incorrect but statement II is correct.

Solution

Statement 1- R=80 Ω

When it is cut into 4 equal parts, the resistance of each part will be,

R1=R2=R3=R4=20 Ω

When these resistances are connected in parallel,

Req =204=5 Ω

Hence, the statement I is correct.

Statement 2 -

When the resistances are connected in parallel, the potential difference between them is same. Therefore, the power consumed can be written as,

P=V2R

P1P2=R2R1=23

Hence, statement II is incorrect.

Asked in: JEE Main 2022 (28 Jul Shift 2)

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