Space between two concentric conducting spheres of radii a and b(b a) is filled with a medium of resistivity ρ. The resistance between the two spheres will be :

Question

Space between two concentric conducting spheres of radii a and b(b > a) is filled with a medium of resistivity ρ. The resistance between the two spheres will be : (A) (ρ/4 π)((1/a)-(1/b)) (B) (ρ/2 π)((1/a)-(1/b)) (C) (ρ/2 π)((1/a)+(1/b)) (D) (ρ/4 π)((1/ a )+(1/ b ))

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/a3b3905c29c7b9e04104479e034e0544-.png" /> dR =ρ ⋅ ( dx /4 π x 2) ∫ dR =ρ ⋅ ∫ limits a b ( dx /4 π x 2) R =(ρ/4 π)[-(1/ x )] a b R =(ρ/4 π)[(1/ a )-(1/ b )]

Q. Space between two concentric conducting spheres of radii $a$ and $b (b > a)$ is filled with a medium of resistivity $ρ$ . The resistance between the two spheres will be :

$\frac{ρ}{4 π} (\frac{1}{a} - \frac{1}{b})$

$\frac{ρ}{2 π} (\frac{1}{a} - \frac{1}{b})$

$\frac{ρ}{2 π} (\frac{1}{a} + \frac{1}{b})$

$\frac{ρ}{4 π} (\frac{1}{a} + \frac{1}{b})$

$d R = ρ \cdot \frac{d x}{4 π x ^{2}}$
$\int d R = ρ \cdot a \int b \frac{d x}{4 π x ^{2}}$
$R = \frac{ρ}{4 π} [- \frac{1}{x}]_{a}^{b}$
$R = \frac{ρ}{4 π} [\frac{1}{a} - \frac{1}{b}]$

Q. Space between two concentric conducting spheres of radii a and b(b>a) is filled with a medium of resistivity ρ. The resistance between the two spheres will be :

4πρ​(a1​−b1​)

2πρ​(a1​−b1​)

2πρ​(a1​+b1​)

4πρ​(a1​+b1​)