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 (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: (11.3) 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: (11.4) 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 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. q p +1.602 10 19– coulomb×= i d q dt C/sec()= i n n=1 N ∑ 0 Kirchhoff’s current law= i i 1 i 2 i 3 +++ 0= ©2002 CRC Press LLC 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 (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: (11.3) 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: (11.4) 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 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. q p +1.602 10 19– coulomb×= i d q dt C/sec()= i n n=1 N ∑ 0 Kirchhoff’s current law= i i 1 i 2 i 3 +++ 0= ©2002 CRC Press LLC . between two FIGURE 11 .1 A simple electrical circuit. q p +1. 602 10 19 – coulomb×= i d q dt C/sec()= i n n =1 N ∑ 0 Kirchhoff’s current law= i i 1 i 2 i 3 +++ 0= 2002 CRC Press LLC since. between two FIGURE 11 .1 A simple electrical circuit. q p +1. 602 10 19 – coulomb×= i d q dt C/sec()= i n n =1 N ∑ 0 Kirchhoff’s current law= i i 1 i 2 i 3 +++ 0= 2002 CRC Press LLC . 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