wo spherical capacitors has radii of inner and outer spheres as (a, b) and (c, d) respectively. If they have same capacitance then

The capacitance (C) of a spherical capacitor is given by the formula:

C = 4πε₀ (ab/(b-a)) for the first capacitor and C = 4πε₀ (cd/(d-c)) for the second capacitor.

Given that the capacitances are equal, we can set the two equations equal to each other:

4πε₀ (ab/(b-a)) = 4πε₀ (cd/(d-c))

Solving for one of the variables (for example, d) gives:

d = c [1 + (ab/(b-a)) / (cd/(d-c))]

This equation can be used to find the radius of the outer sphere of the second capacitor (d) given the radii of the inner and outer spheres of the first capacitor (a and b), the radius of the inner sphere of the second capacitor (c), and the capacitances of the two capacitors.

The capacitance of a spherical capacitor is given by the formula:

C = 4πε₀ (b-a)/[1/b - 1/a]

where: C is the capacitance, ε₀ is the permittivity of free space, a is the radius of the inner sphere, and b is the radius of the outer sphere.

Given that the two spherical capacitors have the same capacitance, we can set their capacitance equal to each other:

4πε₀ (b-a)/[1/b - 1/a] = 4πε₀ (d-c)/[1/d - 1/c]

Solving this equation will give the relationship between the radii of the inner and outer spheres for the two capacitors.