Question

If the radius of each of the plates is increased by a factor of
root2 and their distance of separation decreased
to half of its initial value, calculate the ratio of the capacitance in the two cases.

Answer 1

Answer:

4:1

Explanation:

Initially,Let the radius be r and distance between the circular plates be d.

Capacitance(C) = $\frac{ \epsilon \: A}{d}$

When radius is increased by factor √2 and distancs is decreased to 1/2.

$New\:Area=\small{\pi R^2=\pi(\sqrt2r)^2=2\pi r^2=2A}$

$Distance=\frac{d}{2}$

Hence,

$Capacitance(C') = \frac{\epsilon (2A)}{\frac{d}{2}}$

$Capacitance(C') = 4\frac{\epsilon A}{d}$

$Capacitance(C') = 4C$

Hence, C'/C = 4C/C = 4:1

Required ratio of the capacitane in the two cases is 4 : 1.

Answer 2

Question :

If the radius of each of the plates is increased by a factor of

√2 and their distance of separation decreased

to half of its initial value, calculate the ratio of the capacitance in the two cases.

To find :

The ratio of the capacitance in the two cases.

Let us assume :

• radius = x

• distance = y

Solution :

Capacitance(C) = ϵ A/y

According to the question,

distance decreased by 1/2

radius increases by √2

We know that,

Area = πr²

So, here

New area = πX²

= π (√2x)²

= 2πx² → 2A

Distance = y/2

Now,

Capacitance(C") = ϵ(2A)/y/2

Capacitance (C") = 4C

Now to get the ratio :

C"/C

4C/C

4

So the ratio is 4 : 1