Question

Find the resistance of a cylindrical wire of length 1.5 m, area of cross section 0.5 cm2 and resistivity 1.6 x 10^8 m. How would the resistivity get affected if the area of cross section is doubled and length is kept same?

Answer 1

We know the formula of resistance is given by :

$\sf{R = \rho \frac{l}{a}}$

Where , R = resistance of the conductor , l= length of conductor , a = area of cross section conductor and $\sf \rho$ = resistivity or specific resistance of conductor

Here , l = 1.5 m

a = 0.5 cm² = 0.00005 m²

$\rho$ = 1.6 × 10⁸ Ωm .

Using these value in the formula

R = 1.6×10⁸ × 1.5 / 0.00005

R = 1.6 × 1.5 × 10⁸ × 10⁵ / 5

R = 2.4 × 10¹³ / 5

R = 0.48 × 10¹³ Ω

When the Area of cross section is doubled keeping the length same , the resistivity will not change as it purely depends upon the nature of the material .

However , resistance will decrease by half in such case .

As , R' = p l / 2a

R' = R/2

New resistance would be

R' = R/2

R' = 0.48 × 10¹³ / 2

R' = 0.24 × 10¹³ Ω

Answer 2

Answer:

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