9.1 Electrical current  (Page 5/10)

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

Car batteries are rated in ampere-hours $(\text{A}·\text{h})$ . 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?

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 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 $25.00\mu \text{A}$ . 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 $I=4.00\text{A}$ ?

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 $I_0=3.00\text{A}$ is the current at time $t=0.00\text{s}$ and $\tau =0.50\text{s}$ is the time constant. How much charge flows through the conductor between $t=0.00\text{s}$ and $t=3\tau$ ?

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

What is the current at time $t=3.00\text{s}$ ?

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

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