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/4π) ((1/a) - (1/b))  (B) (ρ/2π) ((1/a) - (1/b))  (C) (ρ/2π) ((1/a) + (1/b))  (D) (ρ/4π) ((1/a) + (1/b))

Tardigrade Admin · Accepted Answer

dR = ρ. (dx/4π x2) ∫ dR = ρ. ∫ba (dx/4π x2) R = (ρ /4π) [- (1/x)]ba R = (ρ/4π) ((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 :

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

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

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

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

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

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​)