The resistance of a wire is R. If the length of the wire is doubled and the radius gets halved by stretching, then the new resistance will be

CONCEPT:

• Resistance: The obstruction offered to the flow of current is known as the resistance.
• Mathematically it can be written as

\(R = \frac{{\rho l}}{A}\)

Where R = resistance, l = length, A = area of cross-section and ρ = resistivity

EXPLANATION:

Given – length of wire before stretching = l and radius of wire before stretching = r, length of wire after stretching (l₁) = 2l and radius of wire after stretching (r₁) = r/2

• The resistance of wire before stretching is

\(R = \frac{{\rho l}}{A} = \frac{{\rho l}}{{\pi {r^2}}}\)

• The resistance of wire after stretching is

\({R_1} = \frac{{\rho \left( {2l} \right)}}{{\pi {{\left( {\frac{r}{2}} \right)}^2}}} = \frac{{8\rho l}}{{\pi {r^2}}} = 8R{\rm{\;}}\left[ {As,\;R = \frac{{\rho l}}{{\pi {r^2}}}} \right]\)

• The resistance of wire after stretching will be eight times that of resistance of wire before stretching.