Capacitance and charge stored in a parallel-plate capacitor
(a) What is the capacitance of an empty parallel-plate capacitor with metal plates that each have an area of
, separated by 1.00 mm? (b) How much charge is stored in this capacitor if a voltage of
is applied to it?
Strategy
Finding the capacitance
C is a straightforward application of
[link] . Once we find
C , we can find the charge stored by using
[link] .
This small capacitance value indicates how difficult it is to make a device with a large capacitance.
Inverting
[link] and entering the known values into this equation gives
Significance
This charge is only slightly greater than those found in typical static electricity applications. Since air breaks down (becomes conductive) at an electrical field strength of about 3.0 MV/m, no more charge can be stored on this capacitor by increasing the voltage.
Suppose you wish to construct a parallel-plate capacitor with a capacitance of 1.0 F. What area must you use for each plate if the plates are separated by 1.0 mm?
Each square plate would have to be 10 km across. It used to be a common prank to ask a student to go to the laboratory stockroom and request a 1-F parallel-plate capacitor, until stockroom attendants got tired of the joke.
A spherical capacitor is another set of conductors whose capacitance can be easily determined (
[link] ). It consists of two concentric conducting spherical shells of radii
(inner shell) and
(outer shell). The shells are given equal and opposite charges
and
, respectively. From symmetry, the electrical field between the shells is directed radially outward. We can obtain the magnitude of the field by applying Gauss’s law over a spherical Gaussian surface of radius
r concentric with the shells. The enclosed charge is
; therefore we have
Thus, the electrical field between the conductors is
We substitute this
into
[link] and integrate along a radial path between the shells:
In this equation, the potential difference between the plates is
. We substitute this result into
[link] to find the capacitance of a spherical capacitor:
A spherical capacitor consists of two concentric conducting spheres. Note that the charges on a conductor reside on its surface.
Capacitance of an isolated sphere
Calculate the capacitance of a single isolated conducting sphere of radius
and compare it with
[link] in the limit as
.
Strategy
We assume that the charge on the sphere is
Q , and so we follow the four steps outlined earlier. We also assume the other conductor to be a concentric hollow sphere of infinite radius.
Solution
On the outside of an isolated conducting sphere, the electrical field is given by
[link] . The magnitude of the potential difference between the surface of an isolated sphere and infinity is
The capacitance of an isolated sphere is therefore
Significance
The same result can be obtained by taking the limit of
[link] as
. A single isolated sphere is therefore equivalent to a spherical capacitor whose outer shell has an infinitely large radius.
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has
The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50.
A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
C,Calculate quantities of X and Y consumed with a given price.
D,alculate optimum level of output .
