A parallel-plate capacitor has square plates that are 9.00 cmcm on each side and 4.10 apart. The space between the plates is completely filled with two square slabs of dielectric, each 9.00 cmcm on a side and 2.05 thick. One slab is pyrex glass and the other is polystyrene.
If the potential difference between the plates is 86.0 V, how much electrical energy is stored in the capacitor?

2.29 x 10^-7 J.

Explanation:

Hiven:

L = 9 cm

= 0.09 m

d = 2.05 mm

= 2.05 x 10^-3 m

ε° * kpo = 2.56 * 8.854 x 10^-12

= 2.27 x 10-11

ε° * kpo = 5.6 * 8.854 x 10^-12

= 5 x 10-11

V = 86 V

The two plates of polystyrene and pyrex glass as a two separate capacitors connected on series so the total capacitance of series capacitor is given by:

1/CT = 1/Cpy + 1/Cpo        

Capacitance of polystyrene, Cpo = ε° * kpo * A/d

Area = L^2

= 0.09^2

= 0.0081 m^2

d = 0.00205 m

Cpo = 2.27 x 10^-11 * 0.0081/0.00205

= 9 x 10^-11 F

Capacitance of pyrex, Cpy = ε° * kpy * A/d

= 5 x 10^-11 * 0.0081/0.00205

= 2 x 10^-10 F

1/CT = 1/9 x 10^-11 + 1/2 x 10^-10

CT = 6.19 x 10^-11 F

Energy stored in the capacitor

U = 1/2 * C * V^2

= 1/2 * 6.19 x 10^-11 * 86^2

= 2.29 x 10^-7 J.

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