Question

A piece of wire of resistance 10 ohm is drawn out so that its length is increased to three times its original length. Calculate the new resistance.

Answer 1

Specific resistance (ρ) = \(\frac{\mathrm{RA}}{l}\)
\(\mathrm{R}=\frac{\rho l}{\mathrm{A}}\)
When the length is increased by three and then the area of cross-section is reduced by three,

Resistance of wire R = 10Ω

New resistance R = `("p"(3"l"))/[("A"/3)]`

= p(3l) x `3/"A"`

= `(9"p""l")/"A"`

= 9 x R

= 9 x 10

R = 90Ω