A metal wire of 1 ~cm length and 1 ~mm radius has a resistance of 3 10⁻³ . If a wire of the same metal of length 3 ~cm and radius 0.5 ~mm is drawn, the resistance of the wire.

Step-by-step solution

length of metal wire, l₁=1 ~cm =10⁻² ~m aligned & r₁=1 ~mm =10⁻³ ~m & R₁=3 10⁻³ aligned Resistivity of wire is given as aligned & =R A l . & =3 10⁻³ r₁^2 l₁ =3 10⁻³ 3.14 (10⁻³ )^2 10⁻² & =9.42 10⁻⁷ - m aligned Again for second case, aligned l₂= & 3 ~cm =3 10⁻² ~m , r₂=0.5 ~mm =5 10⁻⁴ ~m R₂ & = l₂ A₂ = l₂ r₂^2 & =9.42 10⁻⁷ 3 10⁻² 3.14 (5 10⁻⁴ )^2 & =0.36 10⁻¹ & =0.036 aligned