Question

1 - The plates of a spherical capacitor have radii of 38.9 mm and 40.2 mm.

(i) Calculate the capacitance. (in F)

(ii) What must be the plate area of a parallel-plate capacitor with the same plate separation and capacitance? (in cm^2)

______________

2 - Now in another experiment, The plates of a spherical capacitor have radii of 37.6 mm and 43.6 mm.

i) Calculate the capacitance. (in F)?

(ii) What must be the plate area of a parallel-plate capacitor with the same plate separation and capacitance?(in cm^2)

Answer 1

Question 1:

r₁ = inner radius = 38.9 mm = 0.0389 m

r₂ = outer radius = 40.2 mm = 0.0402 m

Part i)

capacitance is given as

C = 4_o r₁ r₂ /(r₂ - r₁)

C = 4 (3.14) (8.85 *10^-12) (0.0402) (0.0389)/((0.0402) - (0.0389))

C = 1.34*10^-10 F

Part (ii)

C = _o A / d

d = (r₂ - r₁) = (0.0402) - (0.0389) = 1.3*10^-3 m

C = 1.34*10^-10 F

A = C*d/_o = [1.34*10^-10 F * 1.3*10^-3 m] / 8.85 *10^-12 = 0.0197 m²

A = 1.97 cm²

Question 2:

r₁ = inner radius = 37.6 mm = 0.0376 m

r₂ = outer radius = 43.6 mm = 0.0436 m

Part i)

capacitance is given as

C = 4_o r₁ r₂ /(r₂ - r₁)

C = 4 (3.14) (8.85 *10^-12) (0.0436) (0.0376)/((0.0436) - (0.0376))

C = 3.04*10^-11 F

Part (ii)

C = _o A / d

d = (r₂ - r₁) = (0.0436) - (0.0376) = 6.0*10^-3 m

C = 3.04*10^-11 F

A = C*d/_o = [3.04*10^-11 F * 6.0*10^-3 m] / 8.85 *10^-12 = 0.0206 m²

A = 2.06 cm²