Solved: Electric Circuits. The theory of electric circuits, such as that shown in Figure

Chapter 7, Problem 21

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Electric Circuits. The theory of electric circuits, such as that shown in Figure 7.1.2, consistingof inductors, resistors, and capacitors, is based on Kirchhoffs laws: (1) The net flow of currentinto each node (or junction) is zero, and (2) the net voltage drop around each closed loopis zero. In addition to Kirchhoffs laws, we also have the relation between the current I inamperes through each circuit element and the voltage drop V in volts across the element:V = RI, R = resistance in ohms;C dVdt = I, C = capacitance in farads1;LdIdt = V, L = inductance in henrys.Kirchhoffs laws and the currentvoltage relation for each circuit element provide a system ofalgebraic and differential equations from which the voltage and current throughout the circuitcan be determined. 19 through 21 illustrate the procedure just described.Consider the circuit shown in Figure 7.1.5. Use the method outlined in to showthat the current I through the inductor and the voltage V across the capacitor satisfy thesystem of differential equationsLdIdt = R1I V, C dVdt = I VR2.