Question

A capacitor,consisting of two metal plates each of area 50cm2 and space 0.2mm apart in air ,is connected across a 120V supply.Calculate (1)the energy stored..(2)the electric flux density and the potential gradient..

Answer 1

To help me to solve

Answer 2

Abdulahi

Answer 3

Rzvggb

Answer 4

question and answer

Answer 5

[AI-generated answer — Explain Bot]

To calculate the energy stored in a capacitor, you can use the formula:

Energy (E) = (1/2) * C * V^2

where C is the capacitance and V is the voltage.

Step 1: Calculate the capacitance (C):
The capacitance of a parallel plate capacitor can be calculated using the formula:

C = (ε * A) / d

where ε is the permittivity of the material between the plates, A is the area of the plates, and d is the distance between the plates.

In this case, the plates are in air, and the permittivity of air is approximately ε = 8.85 x 10^-12 F/m.

Given:
Area (A) = 50 cm^2 = 50 x 10^-4 m^2
Distance (d) = 0.2 mm = 0.2 x 10^-3 m

Using the formula, we can calculate the capacitance (C):

C = (8.85 x 10^-12 F/m) * (50 x 10^-4 m^2) / (0.2 x 10^-3 m)
= 0.110625 F

Step 2: Calculate the energy stored (E):
Given:
Voltage (V) = 120 V

Using the formula for energy stored:

E = (1/2) * C * V^2
= (1/2) * 0.110625 F * (120 V)^2
= 798 J

Therefore, the energy stored in the capacitor is 798 Joules (J).

To calculate the electric flux density and the potential gradient, we need to know the electric field strength (E) between the plates.

The electric field strength can be calculated using the formula:

E = V / d

where E is the electric field strength, V is the voltage, and d is the distance between the plates.

Given:
Voltage (V) = 120 V
Distance (d) = 0.2 mm = 0.2 x 10^-3 m

Using the formula, we can calculate the electric field strength (E):

E = (120 V) / (0.2 x 10^-3 m)
= 6 x 10^5 V/m

Step 3: Calculate the electric flux density (D):

The electric flux density (D) can be calculated using the formula:

D = ε * E

where D is the electric flux density and ε is the permittivity of the material between the plates.

Given:
ε = 8.85 x 10^-12 F/m
E = 6 x 10^5 V/m

Using the formula, we can calculate the electric flux density (D):

D = (8.85 x 10^-12 F/m) * (6 x 10^5 V/m)
= 5.31 x 10^-6 C/m^2

Therefore, the electric flux density is 5.31 x 10^-6 Coulombs per square meter (C/m^2).

Step 4: Calculate the potential gradient (V/m):

The potential gradient can be calculated by dividing the voltage (V) by the distance (d) between the plates.

Given:
Voltage (V) = 120 V
Distance (d) = 0.2 mm = 0.2 x 10^-3 m

Calculating the potential gradient:

Potential Gradient = Voltage / Distance
= 120 V / (0.2 x 10^-3 m)
= 6 x 10^5 V/m

Therefore, the potential gradient is 6 x 10^5 Volts per meter (V/m).

Answer 6

Q = CV

and C = epsilon A/d
You'll have to look up the permittivity of free space number.
Oops. You wanted energy stored. That's 1/2CV^2.
And density is 1/2 epsilon E^2