Name: Dielectrics in a Capacitor
Uploaded: 2019-07-19
Duration: 6 min 3 s
Description: Let us use our knowledge about dielectrics and capacitors to find out how the use of dielectrics can increase the capacitance of a system. Learn through this...

Question

The plates of a spherical capacitor have radii

37.0 mm

and

40.0 mm .

(a) Calculate the capacitance. (b) What must be the plate area of a parallel-plate capacitor with the same plate separation and capacitance?

Accepted Answer

Given,

The plates of a spherical capacitor have radii $a = 37.0 mm$ and $b = 40.0 mm$ .

Solution for (a):

We know that the capacitance of a spherical capacitor is given by

$C = 4 π ε_{0} (\frac{a b}{b - a})$ .

On substituting the values, we get,

$C = \frac{1}{9 \times 10^{9}} (\frac{(40) (37)}{40 - 37} \times 10^{- 3})$

$∴ C = 54.8 \times 10^{- 12} F or 54.8 pF .$

Solution for (b):

For a parallel plate capacitor, the capacitance is

$C = \frac{ε_{0} A}{d}$

If we construct a parallel plate capacitor with the same capacitance and same separation $(d = b - a)$ , then the area of the plates is

$A = \frac{C d}{ε_{0}} = \frac{C (b - a)}{ε_{0}}$

On substituting the values, we get,

$\Rightarrow A = \frac{(54.8 \times 10^{- 12}) (3 \times 10^{- 3})}{8.85 \times 10^{- 12}}$

$∴ A = 186 {cm}^{2}$ .

The plates of a spherical capacitor have radii $37.0 mm$ and $40.0 mm .$ (a) Calculate the capacitance. (b) What must be the plate area of a parallel-plate capacitor with the same plate separation and capacitance?

Important Questions on Capacitance

Learn and Prepare for any exam you want !

The plates of a spherical capacitor have radii 37.0 mm and 40.0 mm. (a) Calculate the capacitance. (b) What must be the plate area of a parallel-plate capacitor with the same plate separation and capacitance?

Important Questions on Capacitance

Learn and Prepare for any exam you want !

The plates of a spherical capacitor have radii $37.0 mm$ and $40.0 mm .$ (a) Calculate the capacitance. (b) What must be the plate area of a parallel-plate capacitor with the same plate separation and capacitance?