Question

A piece of wire of resistance 'R' is cut lengthwise into three identical parts. These parts are then connected in parallel. If the equivalent resistance of this combination is \( R' \), then the value of \( R/R' \) is:

• A. 1/9
• B. 1/3
• C. 3
• D. 9

Hint:

In a parallel combination of identical resistors, the equivalent resistance decreases, and the overall resistance can be calculated using the formula for parallel resistances.

Answer 1

The Correct Option is D

When a wire is cut into three identical parts, each part has a resistance of \( R/3 \). When resistances are connected in parallel, the equivalent resistance \( R' \) is given by the formula: \[ \frac{1}{R'} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \] For three identical resistances \( R_1 = R_2 = R_3 = R/3 \), we have: \[ \frac{1}{R'} = \frac{1}{R/3} + \frac{1}{R/3} + \frac{1}{R/3} = \frac{3}{R/3} = \frac{9}{R} \] Thus, \( R' = \frac{R}{9} \), and the ratio \( R/R' = 9 \). Therefore, the correct answer is option (4).