Kirchhoff’s Rules Quiz

PDF page 1007: Kirchhoff’s rules for circuit analysis are applications of conservation laws to circuits. The first rule is the application of conservation of charge, while the second rule is the application of conservation of energy. Conservation laws, even used in a specific application, such as circuit analysis, are so basic as to form the foundation of that application.

PDF page 1007: developed in Resistors in Series and Parallel and Electromotive Force: Terminal Voltage. There are, however, two circuit analysis rules that can be used to analyze any circuit, simple or complex. These rules are special cases of the laws of conservation of charge and conservation of energy. The rules are known as Kirchhoff’s rules, after their inventor Gustav Kirchhoff (1824–1887).

PDF page 1007: developed in Resistors in Series and Parallel and Electromotive Force: Terminal Voltage. There are, however, two circuit analysis rules that can be used to analyze any circuit, simple or complex. These rules are special cases of the laws of conservation of charge and conservation of energy. The rules are known as Kirchhoff’s rules, after their inventor Gustav Kirchhoff (1824–1887).

PDF page 1007: • Kirchhoff’s first rule—the junction rule. The sum of all currents entering a junction must equal the sum of all

PDF page 1007: currents leaving the junction.

PDF page 1007: Kirchhoff’s first rule (the junction rule) is an application of the conservation of charge to a junction; it is illustrated in

PDF page 1007: Kirchhoff’s rules for circuit analysis are applications of conservation laws to circuits. The first rule is the application of conservation of charge, while the second rule is the application of conservation of energy. Conservation laws, even used in a specific application, such as circuit analysis, are so basic as to form the foundation of that application.

PDF page 1008: Kirchhoff’s second rule (the loop rule) is an application of conservation of energy. The loop rule is stated in terms of potential, , rather than potential energy, but the two are related since . Recall that emf is the potential difference of a source when no current is flowing. In a closed loop, whatever energy is supplied by emf must be transferred into other forms by devices in the loop, since there are no other ways in which energy can be transferred into or out of the circuit. Figure 21.23 illustrates the changes in potential in a simple series circuit loop. Kirchhoff’s second rule requires . Rearranged, this is , which means the emf equals the sum of the (voltage) drops in the loop.

PDF page 1008: FIGURE 21.22 The junction rule. The diagram shows an example of Kirchhoff’s first rule where the sum of the currents into a junction

PDF page 1008: . Here must be 11 A, since is 7 A and is 4 A.

PDF page 1009: what direction it is going. For example, in Figure 21.21, Figure 21.22, and Figure 21.23, currents are labeled , , , and , and arrows indicate their directions. There is no risk here, for if you choose the wrong direction, the current will be of the correct magnitude but negative.

PDF page 1011: emfs, and currents. If a current is unknown, you must assign it a direction. This is necessary for determining the signs of potential changes. If you assign the direction incorrectly, the current will be found to have a negative value—no harm done.

PDF page 1009: • When a resistor is traversed in the same direction as the current, the change in potential is

PDF page 1009: . (See Figure 21.24.)

PDF page 1009: • When an emf is traversed from to + (the same direction it moves positive charge), the change in potential is

PDF page 1009: +emf. (See Figure 21.24.)

PDF page 1009: direction to go around it, clockwise or counterclockwise. For example, in Figure 21.23 the loop was traversed in the same direction as the current (clockwise). Again, there is no risk; going around the circuit in the opposite direction reverses the sign of every term in the equation, which is like multiplying both sides of the equation by

PDF page 1010: assumptions have been made about their directions. Locations on the diagram have been labeled with letters a through h. In the solution we will apply the junction and loop rules, seeking three independent equations to allow us to solve for the three unknown currents. Solution We begin by applying Kirchhoff’s first or junction rule at point a. This gives 21.54

PDF page 1010: since flows into the junction, while and flow out. Applying the junction rule at e produces exactly the same

PDF page 1009: direction to go around it, clockwise or counterclockwise. For example, in Figure 21.23 the loop was traversed in the same direction as the current (clockwise). Again, there is no risk; going around the circuit in the opposite direction reverses the sign of every term in the equation, which is like multiplying both sides of the equation by

PDF page 1011: many independent equations as unknowns.) To apply the loop rule, you must choose a direction to go around the loop. Then carefully and consistently determine the signs of the potential changes for each element using the four bulleted points discussed above in conjunction with Figure 21.24.