Page 196 - The Mechatronics Handbook

since current consists of the flow of very large numbers of charge particles. The other charge-carrying
particle in an atom, the proton, is assigned a positive sign and the same magnitude. The charge of a
proton is
q p = +1.602 × 10 – 19 coulomb (11.2)

Electrons and protons are often referred to as elementary charges.
Electric current is defined as the time rate of change of charge passing through a predetermined area.
If we consider the effect of the enormous number of elementary charges actually flowing, we can write
this relationship in differential form:
dq
i = ------ C/sec) (11.3)
(
dt
The units of current are called amperes (A), where 1 A = 1 C/sec. The electrical engineering convention
states that the positive direction of current flow is that of positive charges. In metallic conductors, however,
current is carried by negative charges; these charges are the free electrons in the conduction band, which
are only weakly attracted to the atomic structure in metallic elements and are therefore easily displaced
in the presence of electric fields.
In order for current to flow there must exist a closed circuit. Figure 11.1 depicts a simple circuit,
composed of a battery (e.g., a dry-cell or alkaline 1.5-V battery) and a light bulb.
Note that in the circuit of Fig. 11.1, the current, i, flowing from the battery to the resistor is equal to
the current flowing from the light bulb to the battery. In other words, no current (and therefore no
charge) is “lost” around the closed circuit. This principle was observed by the German scientist G.R.
Kirchhoff and is now known as Kirchhoff’s current law (KCL). KCL states that because charge cannot
be created but must be conserved, the sum of the currents at a node must equal zero (in an electrical circuit,
a node is the junction of two or more conductors). Formally:
N
∑ i n = 0 Kirchhoff’s current law (11.4)
n=1
The significance of KCL is illustrated in Fig. 11.2, where the simple circuit of Fig. 11.2 has been augmented
by the addition of two light bulbs (note how the two nodes that exist in this circuit have been emphasized
by the shaded areas). In applying KCL, one usually defines currents entering a node as being negative
and currents exiting the node as being positive. Thus, the resulting expression for the circuit of Fig. 11.2 is

i + i 1 + i 2 + i 3 = 0

Charge moving in an electric circuit gives rise to a current, as stated in the preceding section. Naturally,
it must take some work, or energy, for the charge to move between two points in a circuit, say, from
point a to point b. The total work per unit charge associated with the motion of charge between two

FIGURE 11.1 A simple electrical circuit.

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