Question

A parallel plate capacitor is made up two plates, each having an area of 8.0 x 10 ^-4 m² and separated from each other by 5.0 mm. Half of the space between the plate is filled with glass and other with mica. Find the capacitance of this capacitor.

Given: A = 8.0 x 10^-4m²

d = 5.0 mm = 0.005 m

Answer 1

Given:

$A=\rm 8.0 * 10^{-4}\: m^2$

$d = \rm 5.0\: mm = 0.005\: m$

$\kappa_1=5$

$\kappa_2=6$

The capacitance of two parralel capacitors

$$C=C_1+C_2=\frac{\epsilon_0k_1A/2}{d}+\frac{\epsilon_0k_1A/2}{d}$$

$$C=\frac{\epsilon_0A}{2d}(\kappa_1+\kappa_2)$$

$$C=\frac{8.85*10^{-12}* 8.0 * 10^{-4}}{2*0.005}(5+6)=7.8*10^{-12}\:\rm F$$