Question

12. An air capacitor has plates of 6 cm diameter. At
what distance should the plates be placed so as
to have the same capacitance as a sphere of
diameter 90 cm ?
[Ans. 0-5 mm)​

Answer 1

Answer: 0.5mm

Explanation:

Since the capacitance of parallel plate capacitor is €°A/d--------(1)

Where €°= ebsilnot ,A =area of plates

And d = distance B/w plates

Here, circular plates are given so, area is πR^2. (Where R = radius of plates)

So,A=π×(0.03)^2 (As diameter=0.06m)

& Capacitance of a sphere is

4π€°r --------(2)

Where r=radius of sphere.

In this question we have r=0.45 m

Now,since we are given that they are equal.

So, by equating (1)&(2) we get

4π€°r=€°A/d

Now we have

d=A/4πr

Now by putting values we get

d=(0.03)^2/4×0.45

d=0.5mm

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