A cylindrical capacitor is constructed using two coaxial cylinders of the same length 10 cm and of radii 2 mm and 4 mm. (a) Calculate the capacitance. (b) Another capacitor of the same length is constructed with cylinders of radii 4 mm and 8 mm. Calculate the capacitance.
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(a) The cylindrical capacitor’s capacitance is 0.8 pF.
(b) When there is a construction of another capacitor with the same length with cylinders of radii 8 mm and 4 mm, then the capacitance is 8 pF.
Explanation:
(a) A cylindrical capacitor’s capacitance is provided by the equation
Therefore, ln .
(b) A capacitor with the same height has the cylinders of radii 8 mm ad 4 mm. when it’s capacitance is calculated, it is found that it is 8 pF. This is same as that of (a). This is because the radii’s ratio is the same.
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