A 5.00- pF, parallel-plate, air-filled capacitor with...

A $5.00-$ pF, parallel-plate, air-filled capacitor with circular plates is to be used in a circuit in which it will be subjected to potentials of up to $1.00 \times 10^{2} \mathrm{V}$ . The electric field between the plates is to be no greater than $1.00 \times 10^{4} \mathrm{N} / \mathrm{C}$ . As a budding electrical engineer for Live-Wire Electronics, your tasks are to (a) design the capacitor by finding what its physical dimensions and separation must be; ( b) find the maximum charge these plates can hold.

A $5.00-$ pF, parallel-plate, air-filled capacitor with circular plates is to be used in a circuit in which it will be subjected to potentials of up to $1.00 \times 10^{2} \mathrm{V}$ . The electric field between the
plates is to be no greater than $1.00 \times 10^{4} \mathrm{N} / \mathrm{C}$ . As a budding electrical engineer for Live-Wire Electronics, your tasks are to (a) design the capacitor by finding what its physical dimensions and separation must be; ( b) find the maximum charge these plates can hold.

Key Concepts

Parallel-Plate Capacitor

A parallel-plate capacitor consists of two conductive plates separated by an insulating medium (dielectric). Its design principles involve controlling the plate area and separation to store electrical energy in the electric field formed between the plates.

Capacitance Formula

The capacitance of a capacitor is defined by how much charge it stores per unit voltage. In the case of a parallel-plate capacitor, the capacitance is given by C = ??A/d, where A is the area of one plate, d is the distance between the plates, and ?? is the permittivity of free space.

Permittivity of Free Space

Permittivity of free space (??) is a physical constant that represents the ability of a vacuum to permit electric field lines. It plays a crucial role in determining the capacitance of devices that use air or vacuum as the dielectric medium.

Electric Field and Plate Separation

The electric field strength between the plates of a capacitor is related to the potential difference and the separation between the plates by the relationship E = V/d. This relation is fundamental when designing capacitors to ensure that the electric field remains below a specified threshold.

Circular Plate Geometry

For capacitors with circular plates, the area of each plate is calculated using the formula A = ?r². Determining the proper radius using this relation is essential in achieving a target capacitance while meeting physical design constraints.

Charge Storage

The maximum charge a capacitor can hold is given by Q = CV, where Q is the charge, C is the capacitance, and V is the voltage applied. This relationship is key to understanding the performance limits and energy storage capacities of capacitors in circuits.

Transcript

00:01 So in this question we have a parallel plate capacitor that is circular shaped.

00:07 And we do not know about the surface area and we do not know about the distance, but we know the capacitance is 5 picou ferret.

00:18 And we know the voltage across it is 100 volts.

00:24 And we want the maximum electric field to be 1 .00 times 10 to the 4.

00:31 New temperature coolant and this is a maximum one we do not want the electric fuel to be any greater than this so in part eight it asks us to find the dimension of it so to find a dimension circular shape parallel plate capacitance we have two things to find one is what is the distance between them and second is what is the radius of the plate so to find the distance between them this is a relatively easy one because the distance turns between two plates times the electric field between the two plates equals a potential difference.

01:09 So if we have the potential difference and the electric field, we can divide them to get the distance.

01:17 So v equals 1 .00 times 10 to the second volts, and electric field is 1 .00 times 10 to the 4th, newton's for colon.

01:29 So this gives us 1 .00 times 10 to the 2nd.

01:35 Negative 2 meter or 1 .00 centimeter.

01:40 So that is a separation between the two plates.

01:43 The second thing we want to find is the radius of the plate.

01:48 And this can be fine using equation 1816.

01:52 So equation 1816 has capacitance equals epsilon a over d...