Question

A piece of wire of resistance 'R' is cut into three equal parts. These parts are then connected in parallel. If the equivalent resistance of this parallel combination is 'R1', what is the value of the ratio R1 : R?

(a) 1 : 3
(b) 1 : 6
(c) 1 : 9
(d) 1 : 12

Answer 1

The equivalent resistance 'R1' of three equal wires cut from a wire with resistance 'R' and connected in parallel is one-third of 'R'. Therefore, the ratio R1:R is 1:3.

Step-by-step explanation:

When a piece of wire with resistance 'R' is cut into three equal parts, each part will have a resistance of 3R since resistance is proportional to the length of the conductor. When these parts are connected in parallel, the equivalent resistance 'R1' can be calculated using the parallel resistance formula:

• 1/R1 = 1/(3R) + 1/(3R) + 1/(3R)
• 1/R1 = 3/(3R)
• 1/R1 = 1/R
• R1 = R

Since there are three resistors in parallel, the total equivalent resistance will be one-third of the resistance of each piece, meaning R1 = R/3. Thus, the ratio of R1 to R is 1:3. Therefore, the correct answer is (a) 1 : 3.