Correct Answer - Option 2 : 2.5
CONCEPT:
Capacitor:
-
The capacitor is a device in which electrical energy can be stored.
- In a capacitor two conducting plates are connected parallel to each other and carrying charges of equal magnitudes and opposite sign and separated by an insulating medium.
- The space between the two plates can either be a vacuum or an electric insulator such as glass, paper, air, or semi-conductor called a dielectric.
- The capacitance of the parallel place capacitor is given as,
\(⇒ C=k\frac{ϵ_{o}A}{d}\)
Where C = capacitance, k = dielectric constant, ϵo = permittivity of the vacuum, A = area of the plate, and d = distance between the plates
Dielectric constant:
- The ratio of the permittivity of the substance to the permittivity of the vacuum.
\(⇒ k=\frac{\epsilon}{\epsilon_{o}}\)
CALCULATION:
- The capacitance of the parallel plate capacitor is given as,
\(⇒ C=k\frac{ϵ_{o}A}{d}\) -----(1)
- When the capacitance is 40μF,(k = 1 for air)
\(⇒ C=k\frac{ϵ_{o}A}{d}\)
\(⇒ 40\mu=1\times\frac{ϵ_{o}A}{d}\)
\(⇒ 40\mu=\frac{ϵ_{o}A}{d}\) -----(2)
- When the capacitance is 100μF,
\(⇒ C'=k\frac{ϵ_{o}A}{d}\)
\(⇒ 100\mu=k\frac{ϵ_{o}A}{d}\) -----(3)
By equation 2 and equation 3,
⇒ 100 = 40k
⇒ k = 2.5
- Hence, option 2 is correct.
