Question

two wires of same material and length have the radii of their cross-section as r and 2r respectively the ratio of their resistance​

Answer 1

Two wires of same material and length having radii of their cross section r and 2r respectively will have resistance in the ratio 4:1.

• Resistance of wire is given by

                  $R=\frac{pl}{A}$

                  R = resistance

                  p = resistivity

                  l = length of the wire

                  A = area of cross section of the wire

• Here wires are of same material and length, therefore the ratio of their resistances is given by

                   $\frac{R_{1} }{R_{2}}=\frac{A_{2} }{A_{1} }$

                   $\frac{R_{1} }{R_{2}}=\frac{\pi r_{2}^{2} }{\pi r_{1}^{2} }$

• Given, $r_{1}=r,r_{2}=2r$

                    $\frac{R_{1} }{R_{2}}=\frac{({2r})^{2} }{r^{2} }$

                     $\frac{R_{1} }{R_{2}}=\frac{4r^{2} }{r^{2} }$

                   ∴ $R_{1} :R_{2}}=4:1$

Answer 2

Answer:

4:1

Explanation:

R1= l/(22÷7)r^2

R2=l/(22÷7)(2r^^2)

R1/R2=4/1