Correct Answer - Option 1 : Decrease by 80 volts
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.
Parallel plate capacitor:
- A parallel plate capacitor consists of two large plane parallel conducting plates separated by a small distance.
- 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 electric field intensity at the outer region of the parallel plate capacitor is always zero whatever be the charge on the plate.
- The electric field intensity in the inner region between the plates of a parallel plate capacitor remains the same at every point.
- When the dielectric medium is filled in the space between the plates of the parallel plate capacitor, its capacitance increases.
- The electric field intensity in the inner region between the plates of a parallel plate capacitor is given as,
| For Vacuum |
For Dielectric Medium |
| \(E=\frac{σ}{\epsilon_o}=\frac{Q}{A\epsilon_o}\) |
\(E'=\frac{σ}{\epsilon_oK}=\frac{Q}{A\epsilon_oK}\) |
- The potential difference between the plates is given as,
| For Vacuum |
For Dielectric Medium |
| \(V=\frac{Qd}{A\epsilon_o}\) |
\(V'=\frac{Qd}{A\epsilon_oK}\) |
- The capacitance C of the parallel plate capacitor is given as,
| For Vacuum |
For Dielectric Medium |
| \(C=\frac{Q}{V}=\frac{A\epsilon_o}{d}\) |
\(C'=\frac{Q'}{V'}=\frac{A\epsilon_oK}{d}\) |
Where A = area of the plates, d = distance between the plates, Q = charge on the plates, σ = surface charge density, and K = dielectric constant
CALCULATION:
Given Vo = 120 volts, and K = 3
Where Vo = potential difference between the plates of a parallel plate capacitor when there is a vacuum between the plates
- When there is a vacuum between the plates of a parallel plate capacitor, the potential difference between the plates of the capacitor is given as,
\(⇒ V_o=\frac{Qd}{A\epsilon_o}\) -----(1)
- When the gap between the plates is filled with the medium of dielectric constant K, the potential difference between the plates of the capacitor is given as,
\(⇒ V=\frac{Qd}{A\epsilon_oK}\) -----(2)
By equation 1 and equation 2,
\(⇒ V=\frac{V_o}{K}\)
\(⇒ V=\frac{120}{3}\)
⇒ V = 40 volts
- So the potential difference between the plates will decrease by,
⇒ ΔV = Vo - V
⇒ ΔV = 120 - 40
⇒ ΔV = 80 volts
- Hence, option 1 is correct.
