Question

A parallel-plate capacitor has square plates that are 8.00cm on each side and 4.20mm apart. The space between the plates is completely filled with two square slabs of dielectric, each 8.00cm on a side and 2.10mm thick. One slab is pyrex glass and the other is polystyrene1) If the potential difference between the plates is 76.0V , how much electrical energy is stored in the capacitor?U =_____

Answer 1

`U=1.29* 10^(-7)\ J`

Step-by-step explanation:

Given that

a= 8 cm (square)

A= a ² = 64 cm²

d= 4.2 mm

d₁= 2.1 mm ,K₁= 4.7

d₂=2.1 mm , K₂=2.6

We know that capacitance given as

`C_1=(K_1\varepsilon _oA)/(d_1)`

`C_1=(4.7* 8.85* 10^(-12)* 64* 10^(-4))/(2.1* 10^(-3))`

`C_1=1.26* 10^(-10)\ F`

`C_2=(K_2\varepsilon _oA)/(d_2)`

`C_2=(2.6* 8.85* 10^(-12)* 64* 10^(-4))/(2.1* 10^(-3))`

`C_2=0.701* 10^(-10)\ F`

Net capacitance

`C=(C_1C_2)/(C_1+C_2)`

`C=(1.26* 10^(-10)* 0.701* 10^(-10))/(1.26* 10^(-10)+0.701* 10^(-10))\ F`

`C=4.5* 10^(-11)\ F`

We know that stored energy given as

`U=(CV^2)/(2)`

V= 76 V

`U=(4.5* 10^(-11)* 76^2)/(2)\ J`

`U=1.29* 10^(-7)\ J`