Concept explainers
Applications.
Electric Circuits. The theory of electric circuits, such as that shown in Figure 3.2.6, consisting of inductors, resistors, and capacitors, is based on Kirchhoff’s laws: (1) At any node (or junction), the sum of currents flowing into that node is equal to the sum of currents flowing into that node is equal to the sum of currents flowing out of that node, and (2) the net voltage drop around each closed loop is zero. In addition to Kirchhoff’s laws, we also have the relation between the current
Kirchhoff’s laws and the current-voltage relation for each circuit element provide a system of algebraic and differential equations from which the voltage and current throughout the circuit can be determined. Problems 27 through 29 illustrate the procedure just described.
Consider the circuit shown in the Figure 3.2.7. Use the method outlined in problem 27 to show that the current
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Differential Equations: An Introduction to Modern Methods and Applications
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