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Conductor capacitance

1.

Explain the concept of "conductor capacitance"!

Solution:

fyzika-kapacita-vodica-1.gif


2.

Derive the dimension of the physical unit farad = F. Show that it holds: C2.N-1.m-2 = F.m-1

Solution:

 fyzika-kapacita-vodica-2.gif

Thus we have shown that 1 F = A2.kg-1.m-2.s4 and that C2.N-1.m-2 = F.m-1


3.

Calculate the capacitance of a plate capacitor composed of 11 plates with dimensions 3 cm and 2 cm, if the distance between the plates is 0.2 mm. The dielectric between the plates is mica with εr = 6. There are 10 gaps between the 11 plates.

Solution:

Analysis:

S = a.b = 3cm·2cm = 6 cm2 = 6·10-4 m2,  l = 2·10-4 m,  εr = 6, ε0 = 8,854·10-12 C2.N-1.m2

fyzika-kapacita-vodica-3.gif 

The capacitance of the capacitor is C' = 1594 pF.


4.

What is the voltage between the plates of an air capacitor with two square plates of side 10 cm, separated by 2 cm, if its charge is 8,854·10–3 μC?

Solution:

Analysis:

S = a2 = (10 cm)2 = 100 cm2 = 10-2 m2,  l = 2·10–2 m,  Q = 8,854·10–9 C, ε0 = 8,854·10–12 F·m-1

fyzika-kapacita-vodica-4.gif


5.

What is the capacitance of our Earth?

Solution:

Analysis:

R = 6378 km = 6.378·106 m, ε0 = 8,854·10-12 F·m-1, εr = 1

fyzika-kapacita-vodica-5.gif 

The Earth's capacitance is C = 709.27 μF