Question

A copper wire having resistance R is cut into four parts.(i) Find the resistance of each part in terms of original resistance of the wire and (ii) Find the resistance of the combination if these four parts are connected in parallel?

Answer 1

Original resistance of the wire is R.
(i) If it is cut in to 4 equal parts then the resistance of each part will be 1/4 of original resistance since resistance is directly proportional to the length. So resistance of each part is

R/4.

(ii) R1 = R/4, R2 = R/4, R3 = R/4, R4 = R/4 
When the wires are connected in parallel the combination would be

Req = 1 / (1/R1 + 1/R2 + 1/R3 + 1/R4)
        = 1/ (1/(R/4) + 1/(R/4) + 1/(R/4) + 1/(R/4)
        = 1/ (4/R + 4/R + 4/R + 4/R)
        = 1 / (16/R)
        = R / 16

Answer 2

Answer:

I) R/4

II) R/16

I. R1 = R2 = R3 = R4

RS = 4 R1

R1 = R1/4