Respuesta :
Answer:
The ratio of the new potential energy to the potential energy before the insertion of the dielectric is 0.58
Explanation:
Given that,
Length of plates = 8 cm
Width = 5.52 cm
Distance = 1.99 cm
Dielectric constant = 2.6
Length = 4.4 cm
Potential = 0.8 V
We need to calculate the initial capacitance
Using formula of capacitance
[tex]C=\dfrac{\epsilon_{0}A}{d}[/tex]
Put the value into the formula
[tex]C=\dfrac{8.85\times10^{-12}\times8\times5.52\times10^{-4}}{1.99\times10^{-2}}[/tex]
[tex]C=1.96\times10^{-12}[/tex]
We need to calculate the final capacitance
Using formula of capacitance
[tex]C'=\dfrac{\epsilon_{0}A_{1}}{d}+\dfrac{k\epsilon_{0}A_{2}}{d}[/tex]
Put the value into the formula
[tex]C'=(\dfrac{8.85\times10^{-12}}{1.99\times10^{-2}})((4.4\times5.52)+(3.6\times5.52)2.6)\times10^{-4}[/tex]
[tex]C'=3.37\times10^{-12}[/tex]
We need to calculate the ratio of the new potential energy to the potential energy before the insertion of the dielectric
Using formula of energy
[tex]\dfrac{E}{E'}=\dfrac{\dfrac{1}{2}CV^2}{\dfrac{1}{2}C'V^2}[/tex]
Put the value into the formula
[tex]\dfrac{E}{E'}=\dfrac{1.96\times10^{-12}}{3.37\times10^{-12}}[/tex]
[tex]\dfrac{E}{E'}=0.58[/tex]
Hence, The ratio of the new potential energy to the potential energy before the insertion of the dielectric is 0.58
