Abstract
In this chapter, we define current and voltage, which are among the principal quantities of interest in circuit analysis. We present Ohm’s law, which is one of the fundamental laws of electrical engineering, and which is the defining relation for resistance and conductance.
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- 1.
After the French physicist Charles Augustin de Coulomb (1736–1806).
- 2.
In practical applications, two charges can be considered point charges if their radii are much smaller than their separation.
- 3.
Total charge is the algebraic sum of charge. Thus, the net charge of a hydrogen atom, which consists of one electron and one proton, is zero.
- 4.
We have Ben Franklin to thank for this unfortunate accident of history. He decided to call the static charge induced on glass by rubbing the glass with silk positive and stated that the direction of current is from positive to negative (from glass to silk). Had he made either of these choices the other way, the positive direction of current would be in the direction of electron flow.
- 5.
Explicit time-dependence often is omitted for the sake of brevity. Thus, in (2.2) q stands for q(t) and i for i(t). Also, current defined by (2.2) is called conduction current. When you study electromagnetism, you will learn about another kind of current called displacement current, that does not involve flow of charge. Conduction current is the current of interest in ordinary circuit analysis, where we are relatively unconcerned with the inner workings of circuit elements.
- 6.
After the French Mathematician and Physicist André Marie Ampére (1775–1836), who discovered basic laws of electromagnetism.
- 7.
To avoid using vector notation, we assume the force f(x) is directed along the x-axis, in either the same direction as the motion or opposite to the direction of motion.
- 8.
After the English physicist James Prescott Joule (1818–1889).
- 9.
In this discussion, we are concerned only with energy exchanged between the gravitational field and a single mass. There may be other forces acting on the mass in addition to that due to gravity, but they do not affect the energy exchange between the mass and the field; for example, we can throw a mass toward the ground, in which case additional energy is transferred to the mass, but the energy transferred to the mass from the field is unaffected by the throwing.
- 10.
Note that electric potential is not the same as potential energy. The unit of electric potential is that of energy divided by charge.
- 11.
After Count Alessandro Volta (1745–1827), an Italian inventor who discovered hydrolysis and invented the battery and the electric condenser (now called a capacitor).
- 12.
The terms rise and drop arise from analogy with gravity, where a mass gains potential energy if we raise it and loses potential energy if we lower (or drop) it.
- 13.
In general (and usually), both voltage and current vary with time.
- 14.
After the German physicist Georg Simon Ohm (1787–1854).
- 15.
In reference works, resistivity often is specified in μΩ cm (10–8 Ω m).
- 16.
Metals are good conductors because the outer electrons of metal atoms are only loosely held and are relatively free to “drift” through the solid under the influence of an applied voltage.
- 17.
Resistivity can also vary with pressure, strain, strength and direction of an applied magnetic field, and other things. The operation of various transducers (e.g., strain gauges) is based upon such effects.
- 18.
Handbook of Chemistry and Physics (76th Ed.), edited by David R. Lide, CRC Press, 1995.
- 19.
Ibid. The temperature coefficients were obtained from the slopes of linear-least-squares fits to the resistivity data given there.
- 20.
We treat transformers and inductors in Chapter 9.
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Glisson, T.H. (2011). Current, Voltage, and Resistance. In: Introduction to Circuit Analysis and Design. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9443-8_2
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DOI: https://doi.org/10.1007/978-90-481-9443-8_2
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