Respuesta :
Answer:
0.25
Explanation:
A = area of each plate = 30 cm² = 30 x 10⁻⁴ m²
d = separation between the plates = 5 mm = 5 x 10⁻³ m
[tex]C_{air}[/tex] = Capacitance of capacitor when there is air between the plates
k = dielectric constant = 4
[tex]C_{dielectric}[/tex] = Capacitance of capacitor when there is dielectric between the plates
Capacitance of capacitor when there is air between the plates is given as
[tex]C_{air} = \frac{\epsilon _{o}A}{d}[/tex] eq-1
Capacitance of capacitor when there is dielectric between the plates is given as
[tex]C_{dielectric} = \frac{k \epsilon _{o}A}{d}[/tex] eq-2
Dividing eq-1 by eq-2
[tex]\frac{C_{air}}{C_{dielectric}}=\frac{\frac{\epsilon _{o}A}{d}}{\frac{k \epsilon _{o}A}{d}}[/tex]
[tex]\frac{C_{air}}{C_{dielectric}}=\frac{1}{k}[/tex]
[tex]\frac{C_{air}}{C_{dielectric}}=\frac{1}{4}[/tex]
[tex]\frac{C_{air}}{C_{dielectric}}=0.25[/tex]
Charge stored in the capacitor when there is air is given as
[tex]Q_{air}=C_{air}V[/tex] eq-3
Charge stored in the capacitor when there is dielectric is given as
[tex]Q_{dielectric}=C_{dielectric}V[/tex] eq-4
Dividing eq-3 by eq-4
[tex]\frac{Q_{air}}{Q_{dielectric}}=\frac{C_{air}V}{C_{dielectric} V}[/tex]
[tex]\frac{Q_{air}}{Q_{dielectric}}=\frac{C_{air}}{C_{dielectric}}[/tex]
[tex]\frac{Q_{air}}{Q_{dielectric}}=0.25[/tex]
