Capacitance of a Parallel Plate Capacitor with and Without Dielectric Medium Between the Plates

Define the dielectric constant of a medium. What is its S.I unit?

A parallel plate air capacity 'C' farad, potential 'V' volt and energy 'E' joule. When the gap between the plates is completely filled with dielectric ______.

Two parallel-plate capacitors X and Y have the same area of plates and same separation between them. X has air between the plates, while Y contains a dielectric medium of ε_r = 4.

(i) Calculate capacitance of each capacitor if the equivalent capacitance of the combination is 4 μF.

(ii) Calculate the potential difference between the plates X and Y.

(iii) Estimate the ratio of electrostatic energies stored in X and Y.

Four capacitors, C₁, C₂, C₃ andC₄ are connected as shown in Figure 3 below. Calculate equivalent capacitance of the circuit between points X . and Y.

The dielectric constant decreases if the temperature is increased. Explain this in terms of polarization of the material.

A dielectric slab of dielectric constant K and thickness t is introduced between the two plates of a capacitor of plate-separation d (>t) and common area A. The capacitance of this system is given as:

`C = (∈_o"A")/((d-t)+(t/k))`

How does the capacitance C modify in each of the following cases?

1. The dielectric slab covers half the distance of separation between the two plates.
2. The whole space between the plates is filled with the dielectric.

Two infinitely long parallel conducting plates having surface charge densities +σ cand -σ respectively are separated by a small distance. The medium between the plates is a vacuum. If ε₀ is the dielectric permittivity of the vacuum, then the electric field in the region between the plates is ______.

Net capacitance of three identical capacitors in series is 2 μF. What will be their net capacitance if connected in parallel?