A wire of resistance R is cut into four equal parts These parts are then connected in parallel If th...........

Everyday Science Physics

A wire of resistance R is cut into four equal parts. These parts are then connected in parallel. If the equivalent resistance of this

combination is R', then the ratio R/R is :

This questions was previously asked in

CAPF 2023 Paper-1

1/16

1/4

- Let’s break down the problem:

- The original wire has resistance \( R \).

- Cutting it into four equal pieces means each piece has length \( l/4 \).

- Resistance of each new piece \( r = R/4 \) (since resistance is directly proportional to length).

- These four pieces are then connected in parallel.

- Equivalent resistance for n equal resistors (each \( r \)) in parallel: \( R' = r/n = (R/4)/4 = R/16 \).

- So, the required ratio \( R/R' = R/(R/16) = 16 \).

- Option 4 (16) is the correct answer.

Option explanations:

- Option 1 (1/16): This would be if you did R'/R, not R/R'.

- Option 2 (1/4): Not relevant for parallel combination of four.

- Option 3 (4): Happens for series combination.

- Option 4 (16): Correct for parallel combination after cutting.

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