In a manner similar to the way in which we introduced the concept of velocity in order to investigate the rate of change of position with time when we studied mechanics, we define electric current as the rate of flow of electric charge when we study electric circuits. In equation form, the definition is I = q / t where I is the current in Amperes, q is the charge in Coulombs, and t is the time in seconds. The standard convention for identifying the direction in which current flows is to consider as positive the direction in which a positive charge would move under identical circuit conditions.

It is important to remember that a complete loop or closed circuit is necessary for current to flow and that the current is the same in each portion of a single loop circuit. Thus the same current passes through each circuit element; that is to say, the current through the battery, that through the wires, and that through each light bulb in Figure 13.9 on page 260 in the text is the same. It is a common mistake to think that in such a circuit the current starts from the battery and somehow disappears after the last light bulb.

Ohm's Law presents the results of many experimental investigations with many of the common materials used in electrical circuits, such as metals. The goal is to develop an equation relating the potential difference across that circuit element to the current that passes through the element. Ohm's Law states that the electrical current through a given portion of a circuit is equal to the potential difference across that portion of the circuit divided by the resistance. In Chapter 12 we defined potential difference and current. Ohm's Law may be used to define resistance as the proportionality between current and potential difference. In equation form R = D V / I. For DV expressed in Volts and I in Amperes, R will be in Ohms, for which the symbol, W (the Greek letter omega) is used. Thus 1 Ohm is the same as 1 Volt divided by 1 Ampere. Although Ohm's Law applies to a wide variety of materials and those materials are very useful in electrical circuits, the circuit elements that do not obey Ohm's Law such as diodes and transistors are what make twentieth century electronics so interesting.

There are two common ways in which circuit elements may be connected: in series or in parallel. One way to remember the difference between circuit elements connected in series and those connected in parallel is to note that circuit elements connected in series have the same current through each element and those connected in parallel have the same potential difference across each element.

Voltmeters are used to measure potential difference across a circuit element, so a voltmeter must be connected in parallel with the circuit element of interest. Ammeters are used to measure current through a circuit element, so an ammeter must be connected in series with that circuit element.

An electrical current represents the motion of electrical charges. In order to obtain a current flow there must be a closed path for the charge to complete the loop from its source, such as a battery, and back. A potential difference is necessary to produce a current in a circuit element, i.e. if both terminals of a circuit element, such as a resistance, are connected to the same potential, no current will flow in that circuit element. This is true because the potential difference across the circuit element is zero when both ends are connected together.

The equivalent resistance for a number of resistances connected in series can be calculated by merely taking the sum of the individual resistances. This relationship follows directly from the fact that each of the circuit elements connected in series has the same current. For the case of three resistances connected in series the equivalent resistance, R_s, is R_s = R₁ + R₂ + R₃. It may be helpful for you to remember that the equivalent resistance for resistances connected in series is always greater than any of the individual resistors.

The equivalent resistance of resistances connected in parallel is calculated using a reciprocal relationship. This relationship follows directly from the fact that each circuit element connected in parallel has the same potential difference. For three resistances connected in parallel the equivalent resistance, R_p, is 1 / R_p = 1 / R₁ + 1 / R₂ + 1 / R₃ . It may be helpful for you to remember that the equivalent resistance for resistances connected in parallel is always smaller than the smallest of the resistances in the original parallel combination.

The extension of these two equations to circuits involving more than three elements in series or parallel, respectively, consists of merely adding more terms in the same format. The string of electric lights that is used for Christmas tree decorations for which the failure of a single bulb results in the entire string of lights going dark has the bulbs wired in series. The string of lights for which the rest of the bulbs may remain lighted after one fails has the bulbs wired in parallel.

Electrical power represents the rate at which energy is supplied or dissipated by a circuit element. Circuit elements such as batteries convert other forms of energy such as chemical energy to electrical energy, so they supply energy to the circuit while resistances dissipate energy by converting electrical energy to thermal energy. The power delivered by a battery, P, is equal to the product of the electromotive force or potential difference, e, across the terminals of the battery times the current, I, given by the equation P = e I.

In mechanics we measured power in Watts. We use the same units in electrical circuit calculations. This leads to the relationship 1 Watt = (1 Volt) (1 Ampere). For materials that obey Ohm's Law we may make a substitution for the potential difference in terms of the current and resistance to obtain expressions for the power dissipated across a resistor as P = (DV) (I) or P = I² R or P = (Dv)² / R.

For economic reasons electrical power is commonly distributed in the form of an alternating current (a.c.) for which the potential difference and the current supplied by the source, such as a generator, vary with time. Such potential differences and currents often vary in a regular pattern described by the sinusoidal curves shown in Figures 13.17 on page 267 and 13.18 on page 267 in the text. The values of current and voltage, respectively, for such a time varying signal are not constant, so another representation is used for calculating the power supplied by an a.c. source. Effective values are defined to represent the direct current (d.c.) that would produce an amount of power equivalent to that supplied by the time varying current and voltage. Mathematical analysis of this equivalence leads to the simple relationship that describes the a.c. voltage and current in terms of 0.707 times the maximum value of the sinusoidal voltage or current, respectively. This is referred to as the effective value of the current or voltage because a d.c. current and voltage of this magnitude would have the effect of producing the same power in a resistor as the a.c value. The standard a.c. voltage of the United States, as shown in Figure 13.18 on page 267 in the text, has an effective voltage of 115 Volts with a maximum of 162.7 Volts (described as "about 160 volts in Figure 13.18 on page 267 of the text).