Question 6
A copper wire having resistance R is cut into four equal parts. (i) Find the resistance of each part in terms of the original resistance of the wire and (ii) find the resistance of the combination if these four parts are joined to parallel.
Answer
(i) When a copper wire of resistance R is cut into four equal parts, each part will have a resistance of R/4. This is because the resistance of a wire is directly proportional to its length, and when the wire is cut into four equal parts, each part will have one-fourth of the length and therefore one-fourth of the resistance.
(ii) When the four parts are joined in parallel, the equivalent resistance of the combination can be calculated using the formula for resistors in parallel:
1/Req = 1/R1 + 1/R2 + 1/R3 + 1/R4
1/Req = 1/(R/4) + 1/(R/4) + 1/(R/4) + 1/(R/4)
1/Req = 4/R
1/Req = R/4
