Question

Find the ratio of resistance of two copper rod X and Y of length 30cm and 10 cm and having radii of 2 cm and 1 cm respectively

Answer 1

Given,

Length of the first rod x = 30cm

Length of the second rod, y = 10cm

Radius of rod, x = 2cm

Radius of rod, y = 1cm

To find,

The ratio of resistance between the two rods.

Solution,

Area of cross-section of rod, x = $\pi (r^{2} )$

                                                   = $\pi (2^{2} ) = 4\pi cm^{2}$

Area of cross-section of rod, y = $\pi (r^{2} )$

                                                   = $\pi (1^{2} )=\pi cm^{2}$

Formula for calculating resistance R = ρ$\frac{Length}{Area}$

Where ρ stands for resistivity which is the same for both rods because both are made of the same copper material.

∴ Resistance of rod, x = r₁ = ρ$(\frac{30}{4\pi } )ohm$

  Resistance of rod, y = r₂ = ρ$(\frac{10}{\pi } ) ohm$

Now the ratio of both resistances,

$\frac{r1}{r2} =\frac{\frac{30}{4\pi } }{\frac{10}{\pi } } =\frac{30}{40}=\frac{3}{4}$

Hence the ratio of resistance between the two rods is 3:4.