Q. 304.1( 7 Votes )

# A spherical capac

Answer :

Radius of the outer shell (r_{1}) = 13cm = 0.13m

Radius of the inner shell (r_{2}) = 12cm = 0.12m

Charge on the outer surface of the inner shell = 2.5 μC = 2.510^{-6}C

Dielectric constant of liquid () = 32

Since, Potential difference between the two shells,

∴ Δ

Where, = Absolute Permittivity of free space = 8.8510^{-12}C^{2}N^{-1}m^{-2}

Therefore

(a) Capacitance,

⇒ C = 5.5510^{-9}F

Hence, the capacitance of the capacitor = 5.5510^{-9}F

(b) The potential of a capacitor (V), is given as:

⇒

⇒ V = 450 V

Hence, the potential of the inner sphere = 450V

(c) Radius of the isolated sphere(R) = 12 cm = 0.12m

Capacitance of an isolated sphere = 4πε_{0}R

∴ C = 4 × 3.14 × 8.85 × 10^{-12} × 0.12

C = 1.3310^{-11}F

Where, ϵ_{0} is the Absolute Permittivity of free space = 8.8510^{-12}C^{2}N^{-1}m^{-2}__The capacitance of the isolated sphere is less than that of the concentric spheres because the outer sphere of the concentric spheres is earthed. Hence, the potential difference is less and the capacitance is more than the isolated sphere.__

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