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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.”
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 $(\text{A}\xb7\text{h})$ . 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.
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.
$v=4.38\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{5}\frac{\text{m}}{\text{s}}$ ;
b.
$\text{\Delta}q=5.00\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-3}}\text{C},\phantom{\rule{0.8em}{0ex}}\text{no. of protons}=3.13\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{16}$
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 $I=4.00\phantom{\rule{0.2em}{0ex}}\text{A}$ ?
$I=\frac{\text{\Delta}Q}{\text{\Delta}t},\phantom{\rule{0.8em}{0ex}}\text{\Delta}Q=12.00\phantom{\rule{0.2em}{0ex}}\text{C}$
$\text{no. of electrons}=7.46\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{15}$
A conductor carries a current that is decreasing exponentially with time. The current is modeled as $I={I}_{0}{e}^{\text{\u2212}t\text{/}\tau}$ , 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?
$I\left(t\right)=\text{\u2212}{I}_{\text{max}}\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}\left(\omega t+\varphi \right)$
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