Question

A 12.0 V (potential source) is connected across a 6.00mf air filled capacitor. how much energy can be stored this way? what is the energy density when the plates of the capacitor are circular of radius 0.1m and separated by a distance of 10mm?

Answer 1

Answer:

(I). The store energy is 0.432 J.

(II). The energy density is 687.54 J/m³.

Explanation:

Given that,

Voltage = 12.0 V

Capacitor = 6.00 mf

Radius = 0.1 m

Distance = 10 mm

(I). We need to calculate the energy store

Using formula of store energy

$U=\dfrac{1}{2}CV^2$

Where, C = capacitor

V = voltage

Put the value into the formula

$U=\dfrac{1}{2}\times6.00\times10^{-3}\times(12.0)^2$

$U=0.432\ J$

(II). We need to calculate the energy density

Using formula of energy density

$\rho=\dfrac{E}{V}$

$\rho=\dfrac{E}{\pi r^2 d}$

Where, r = radius

d = distance

Put the value into the formula

$\rho=\dfrac{0.432}{2\times\pi\times(0.1)^2\times10\times10^{-3}}$

$\rho=687.54\ J/m^3$

Hence, (I). The store energy is 0.432 J.

(II). The energy density is 687.54 J/m³.