# 9.1 Electrical current  (Page 5/10)

 Page 5 / 10

It is important to realize that an electrical field is present in conductors and is responsible for producing the current ( [link] ). In previous chapters, we considered the static electrical case, where charges in a conductor quickly redistribute themselves on the surface of the conductor in order to cancel out the external electrical field and restore equilibrium. In the case of an electrical circuit, the charges are prevented from ever reaching equilibrium by an external source of electric potential, such as a battery. The energy needed to move the charge is supplied by the electric potential from the battery.

Although the electrical field is responsible for the motion of the charges in the conductor, the work done on the charges by the electrical field does not increase the kinetic energy of the charges. We will show that the electrical field is responsible for keeping the electric charges moving at a “drift velocity.”

## Summary

• The average electrical current ${I}_{\text{ave}}$ is the rate at which charge flows, given by ${I}_{\text{ave}}=\frac{\text{Δ}Q}{\text{Δ}t}$ , where $\text{Δ}Q$ is the amount of charge passing through an area in time $\text{Δ}t$ .
• The instantaneous electrical current, or simply the current I , is the rate at which charge flows. Taking the limit as the change in time approaches zero, we have $I=\frac{dQ}{dt}$ , where $\frac{dQ}{dt}$ is the time derivative of the charge.
• The direction of conventional current is taken as the direction in which positive charge moves. In a simple direct-current (DC) circuit, this will be from the positive terminal of the battery to the negative terminal.
• The SI unit for current is the ampere, or simply the amp (A), where $1\phantom{\rule{0.2em}{0ex}}\text{A}=1\phantom{\rule{0.2em}{0ex}}\text{C/s}$ .
• Current consists of the flow of free charges, such as electrons, protons, and ions.

## Conceptual questions

Can a wire carry a current and still be neutral—that is, have a total charge of zero? Explain.

If a wire is carrying a current, charges enter the wire from the voltage source’s positive terminal and leave at the negative terminal, so the total charge remains zero while the current flows through it.

Car batteries are rated in ampere-hours $\left(\text{A}·\text{h}\right)$ . To what physical quantity do ampere-hours correspond (voltage, current, charge, energy, power,…)?

When working with high-power electric circuits, it is advised that whenever possible, you work “one-handed” or “keep one hand in your pocket.” Why is this a sensible suggestion?

Using one hand will reduce the possibility of “completing the circuit” and having current run through your body, especially current running through your heart.

## Problems

A Van de Graaff generator is one of the original particle accelerators and can be used to accelerate charged particles like protons or electrons. You may have seen it used to make human hair stand on end or produce large sparks. One application of the Van de Graaff generator is to create X-rays by bombarding a hard metal target with the beam. Consider a beam of protons at 1.00 keV and a current of 5.00 mA produced by the generator. (a) What is the speed of the protons? (b) How many protons are produced each second?

a. $v=4.38\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{5}\frac{\text{m}}{\text{s}}$ ;
b. $\text{Δ}q=5.00\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-3}\text{C},\phantom{\rule{0.8em}{0ex}}\text{no. of protons}=3.13\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{16}$

A cathode ray tube (CRT) is a device that produces a focused beam of electrons in a vacuum. The electrons strike a phosphor-coated glass screen at the end of the tube, which produces a bright spot of light. The position of the bright spot of light on the screen can be adjusted by deflecting the electrons with electrical fields, magnetic fields, or both. Although the CRT tube was once commonly found in televisions, computer displays, and oscilloscopes, newer appliances use a liquid crystal display (LCD) or plasma screen. You still may come across a CRT in your study of science. Consider a CRT with an electron beam average current of $25.00\mu \phantom{\rule{0.2em}{0ex}}\text{A}$ . How many electrons strike the screen every minute?

How many electrons flow through a point in a wire in 3.00 s if there is a constant current of $I=4.00\phantom{\rule{0.2em}{0ex}}\text{A}$ ?

$I=\frac{\text{Δ}Q}{\text{Δ}t},\phantom{\rule{0.8em}{0ex}}\text{Δ}Q=12.00\phantom{\rule{0.2em}{0ex}}\text{C}$
$\text{no. of electrons}=7.46\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{15}$

A conductor carries a current that is decreasing exponentially with time. The current is modeled as $I={I}_{0}{e}^{\text{−}t\text{/}\tau }$ , where ${I}_{0}=3.00\phantom{\rule{0.2em}{0ex}}\text{A}$ is the current at time $t=0.00\phantom{\rule{0.2em}{0ex}}\text{s}$ and $\tau =0.50\phantom{\rule{0.2em}{0ex}}\text{s}$ is the time constant. How much charge flows through the conductor between $t=0.00\phantom{\rule{0.2em}{0ex}}\text{s}$ and $t=3\tau$ ?

The quantity of charge through a conductor is modeled as $Q=4.00\frac{\text{C}}{{\text{s}}^{4}}{t}^{4}-1.00\frac{\text{C}}{\text{s}}t+6.00\phantom{\rule{0.2em}{0ex}}\text{mC}$ .

What is the current at time $t=3.00\phantom{\rule{0.2em}{0ex}}\text{s}$ ?

$\begin{array}{}\\ \\ I\left(t\right)=0.016\frac{\text{C}}{{\text{s}}^{4}}{t}^{3}-0.001\frac{\text{C}}{\text{s}}\hfill \\ I\left(3.00\phantom{\rule{0.2em}{0ex}}\text{s}\right)=0.431\phantom{\rule{0.2em}{0ex}}\text{A}\hfill \end{array}$

The current through a conductor is modeled as $I\left(t\right)={I}_{m}\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}\left(2\pi \left[60\phantom{\rule{0.2em}{0ex}}\text{Hz}\right]t\right)$ . Write an equation for the charge as a function of time.

The charge on a capacitor in a circuit is modeled as $Q\left(t\right)={Q}_{\text{max}}\phantom{\rule{0.2em}{0ex}}\text{cos}\phantom{\rule{0.2em}{0ex}}\left(\omega t+\varphi \right)$ . What is the current through the circuit as a function of time?

$I\left(t\right)=\text{−}{I}_{\text{max}}\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}\left(\omega t+\varphi \right)$

what is flux
Total number of field lines crossing the surface area
Kamru
Basically flux in general is amount of anything...In Electricity and Magnetism it is the total no..of electric field lines or Magnetic field lines passing normally through the suface
prince
what is temperature change
Celine
a bottle of soft drink was removed from refrigerator and after some time, it was observed that its temperature has increased by 15 degree Celsius, what is the temperature change in degree Fahrenheit and degree Celsius
Celine
process whereby the degree of hotness of a body (or medium) changes
Salim
Q=mcΔT
Salim
where The letter "Q" is the heat transferred in an exchange in calories, "m" is the mass of the substance being heated in grams, "c" is its specific heat capacity and the static value, and "ΔT" is its change in temperature in degrees Celsius to reflect the change in temperature.
Salim
what was the temperature of the soft drink when it was removed ?
Salim
15 degree Celsius
Celine
15 degree
Celine
ok I think is just conversion
Salim
15 degree Celsius to Fahrenheit
Salim
0 degree Celsius = 32 Fahrenheit
Salim
15 degree Celsius = (15×1.8)+32 =59 Fahrenheit
Salim
I dont understand
Celine
the question said you should convert 15 degree Celsius to Fahrenheit
Salim
To convert temperatures in degrees Celsius to Fahrenheit, multiply by 1.8 (or 9/5) and add 32.
Salim
what is d final ans for Fahrenheit and Celsius
Celine
it said what is temperature change in Fahrenheit and Celsius
Celine
the 15 is already in Celsius
Salim
So the final answer for Fahrenheit is 59
Salim
what is d final ans for Fahrenheit and Celsius
Celine
what are the effects of placing a dielectric between the plates of a capacitor
increase the capacitance.
Jorge
besides increasing the capacitance, is there any?
Bundi
mechanical stiffness and small size
Jorge
why for an ideal gas internal energy is directly proportional to thermodynamics temperature?
two charged particles are 8.45cm apart. They are moved and the force on each of them is found to have tripled. How far are they now?
what is flux
Bundi
determining dimensional correctness
determine dimensional correctness of,T=2π√L/g
PATRICK
somebody help me answer the question above
PATRICK
calculate the heat flow per square meter through a mineral roll insulation 5cm thick if the temperature on the two surfaces are 30degree Celsius and 20 degree Celsius respectively. thermal conduction of mineral roll is 0.04
what are the elementary compositions of a cell?
poles, chemical
prabir
when a current pass through a material does the velocity varies
no.
prabir
what is spin entropy ?and disorder in ferromagnetic material
diagram of an hall effect sensor
if a magnetised wire having dipole moment M is bent in the form of arc subtending angle of 45°at centre,new magnetic moment is
prabir
is this book for preparing IIT or neet?
is it possible to increase the temperature of a gas without adding heat to it?
I'm not sure about it, but I think it's possible. If you add some form of energy to the system, it's a possibility. Also, if you change the pression or the volume of the system, you'll increase the kinetic energy of the system, increasing the gas temperature. I don't know if I'm correct.
playdoh
For example, if you get a syringe and close the tip(sealing the air inside), and start pumping the plunger, you'll notice that it starts getting hot. Again, I'm not sure if I am correct.
playdoh
you are right for example an adiabatic process changes all variables without external energy to yield a temperature change. (Search Otto cycle)
when a current pass through a material does the velocity varies
lovet
yes at adiabatic compression temperature increase
Nepal
how to draw a diagram of a triode
whate is fckg diagrame?
Arzoodan
why do we use integration?
To know surfaces below graphs.
Jan
To find a Primitive function. Primitive function: a function that is the origin of another
playdoh
yes
Dharmdev
what is laps rate
Dharmdev
Г=-dT/dZ that is simply defination
Arzoodan
what is z
Dharmdev
to find the area under a graph or to accumulate .e.g. sum of momentum over time is no etic energy.
Naod
Z is alt.,dZ altv difference
Arzoodan