If a wire of 1Ω resistance is stretched to four times its length then resistancewill become ( )c) !" Ω c) !# Ωd) 2 Ω d) 4 Ω

The resistance (R) of a wire is directly proportional to its length (L) and inversely proportional to its cross-sectional area (A). This relationship is given by the formula:

R = ρ * (L / A)

where ρ (rho) is the resistivity of the material from which the wire is made.

When the wire is stretched to four times its original length, its cross-sectional area will decrease (since the volume of the wire remains constant), and its length will increase.

If we denote the original length of the wire as L1 and the new length as L2 = 4 * L1, and the original area as A1 and the new area as A2, then the new resistance R2 can be found from the formula:

R2 = ρ * (L2 / A2)

Since the volume of the wire remains constant, we have L1 * A1 = L2 * A2, or A2 = A1 * (L1 / L2) = A1 / 4.

Substituting this into the formula for R2, we get:

R2 = ρ * (L2 / (A1 / 4)) = 4 * ρ * (L2 / A1) = 4 * R1

So, the resistance of the wire will become four times its original value. Therefore, the answer is d) 4 Ω.