Physics · Current Electricity · NEET
Each part has resistance R/n. Resistance is R = rho L / A. Cutting into n equal parts keeps the area A and resistivity rho the same, but each piece now has length L/n. So each piece has resistance rho (L/n) / A = R/n. Example: a 12 ohm wire cut into 3 equal parts gives three 4 ohm pieces.
Two steps happen. First, folding a wire into n equal layers is the same as cutting it into n parts each of resistance R/n. Second, these n equal parts now sit side by side (in parallel), so the equivalent resistance is (R/n) divided by n = R/n squared. Cutting divides by n, then parallel joining divides by n again, so overall it is R/n squared.
No. Resistivity (rho) is a material property. It depends only on the material and temperature, not on the shape, length or how you cut the wire. Cutting changes the resistance R because length and area change, but rho stays the same. This is a very common NEET trap.
Start with resistance R. Cut into 2 equal halves, each half is R/2. Connect the two R/2 halves in parallel: 1/Req = 1/(R/2) + 1/(R/2) = 4/R, so Req = R/4. This matches the R/n squared rule with n = 2, giving R/4.
Cutting keeps the area the same and only shortens the length, so each of n parts is R/n. Stretching keeps the volume constant: if length becomes n times, area becomes 1/n times, and resistance becomes n squared R. So cutting reduces resistance while stretching increases it. Do not mix the two formulas.
A wire of resistance 100 ohm is divided into 10 equal parts. The first 5 are connected in series and the next 5 in parallel; the two combinations are then joined in series. The resistance of the final combination is:
A wire of resistance R is cut into 8 equal pieces. Two sets are made by joining four pieces in parallel each; the two sets are then connected in series. The net resistance is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Each piece has resistance R/n, because the length of each piece is L/n while area and resistivity stay the same.
It becomes R/n squared. Each piece is R/n, and n equal R/n resistors in parallel give (R/n)/n = R/n squared.
Yes. Folding a wire into two equal layers makes the two halves (each R/2) carry current side by side, which is a parallel connection giving R/4.
Resistivity depends only on the material and temperature. Cutting only changes physical dimensions (length and area), which change resistance R, not resistivity rho.
First find each piece as R/n. Then apply series (add) or parallel (reciprocal add) to the given arrangement. All-parallel of n pieces gives R/n squared directly.
