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

A wire cut into three equal parts results in each part having a resistance of \( R/3 \). For parallel resistances, the equivalent resistance \( R' \) is found using:\[\frac{1}{R'} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}\]With three identical resistances \( R_1 = R_2 = R_3 = R/3 \), this becomes:\[\frac{1}{R'} = \frac{1}{R/3} + \frac{1}{R/3} + \frac{1}{R/3} = \frac{3}{R/3} = \frac{9}{R}\]Therefore, \( R' = \frac{R}{9} \), and the ratio \( R/R' = 9 \).Thus, the correct answer is option (4).