Question

A parallel-plate capacitor has square plates that are 8.00 cm on each side and 3.80 mm apart. The space between the plates is completely filled with two square slabs of dielectric, each 8.00 cm on a side and 1.90 mm 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?

Answer 1

Answer:

The electrical energy is stored in the capacitor is $1.95\times10^{-7}\ J$.

Explanation:

Given that,

Side = 8.00 cm

Distance = 3.80 mm

Potential difference = 86.0 V

We need to calculate the capacitance of polystyrene

Using formula of capacitance

$C_{po}=\dfrac{k\epsilon_{0}A}{d}$

Put the value into the formula

$C_{po}=\dfrac{2.6\times8.85\times10^{-12}\times(8.00\times10^{-2})^2}{1.9\times10^{-3}}$

$C_{po}=7.75\times10^{-11}\ F$

$C_{po}=77.5\ pF$

We need to calculate the capacitance of Pyrex glass

Using formula of capacitance

$C_{py}=\dfrac{k\epsilon_{0}A}{d}$

Put the value into the formula

$C_{py}=\dfrac{5.6\times8.85\times10^{-12}\times(8.00\times10^{-2})^2}{1.9\times10^{-3}}$

$C_{py}=1.66\times10^{-10}\ F$

$C_{py}=166\ pF$

We need to calculate the capacitor

Using formula of capacitor

$\dfrac{1}{C}=\dfrac{1}{C_{po}}+\dfrac{1}{C_{py}}$

$\dfrac{1}{C}=\dfrac{1}{77.5\times10^{-12}}+\dfrac{1}{166\times10^{-12}}$

$C=52.8\times10^{-12}\ F$

We need to calculate the electrical energy is stored in the capacitor

Using formula of stored energy

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

Put the value into the formula

$U=\dfrac{1}{2}\times52.8\times10^{-12}\times(86)^2$

$U=1.95\times10^{-7}\ J$

Hence, The electrical energy is stored in the capacitor is $1.95\times10^{-7}\ J$.