FUNDAMENTALS OF ELECTRIC CIRCUITS 5TH EDITION SOLUTIONS

-— iN Zc Figure 11.8 A Line-to-line and line-to-neutral voltages. Thus the circuit shown in Fig. 11.7 gives the correct value of the line cur-rent but only the a-phase component of the neutral current. Whenever this single-phase equivalent circuit is applicable, the line currents form[r]

response of a series RLC circuit. 8,1 Introduction to the Natural Response of a Parallel RLC Circuit The first step in finding the natural response of the circuit shown in Fig. 8.1 is to derive the differential equation that the voltage v must satisfy. We choose to find the volt[r]

of finding the current generated in the seriesconnected elements by the release of initially stored energy in the inductor, capacitor, or both. The task is defined by the circuit shown in Fig. 8.3 on page 266. As before, the initial inductor current, I{h and the initial capacitor volta[r]

to infinity, the solution for v(t) would become v(t) = 98sinl000rV, t > 0. Thus, in this case the oscillation is sustained, the maximum amplitude of the voltage is 98 V, and the frequency of oscillation is 1000 rad/s. We may now describe qualitatively the difference between an u[r]

Vmin - Vi Th NOTE: Assess your understanding of this Practical Perspective by trying Chapter Problems 7.103-7.105. Summary A first-order circuit may be reduced to a Thevenin (or Norton) equivalent connected to either a single equiva-lent inductor or capacitor. (See page 214.) The natural resp[r]

±5 V, the circuit reaches saturation when the second amplifier saturates. When one of the op amps satu-rates, we no longer can use the linear model to predict the behavior of the circuit. NOTE: Assess your understanding of this material by trying Chapter Problem 8.63. Two Integr[r]

sucrl responses can be overdamped, underdamped, or critically damped. These terms describe the impact of the dissipative element (R) on the response. The neper frequency, a, reflects the effect of R. (See pages 268 and 269.) • The response of a second-order circuit is overdamped[r]

reduces to solving the circuit shown in Fig. 7.11. 7.2 The Natural Response of an RC Circuit 221 Deriving the Expression for the Voltage We can easily find the voltage v(t) by thinking in terms of node voltages. Using the lower junction between R and C as the reference node and sum-min[r]

After introducing the techniques for analyzing the natural and step responses of first-order circuits, we discuss some special cases of interest. The first is that of sequential switching, involving circuits in which switching can take place at two or more instants[r]

You should verify (in Problem 7.38) that the solution to Eq. 7.47 is identi-cal to that given in Eq. 7.42. At this point, a general observation about the step response of an RL circuit is pertinent. (This observation will prove helpful later.) When we derived the differential equation for the[r]

because at t — 00 the two coils are ideal short circuits. The division of current between ideal short circuits cannot be found from Ohm's law. NOTE: Assess your understanding of this material by using the general solution method to solve Chapter Problems 7.68 and 7.69. 7.[r]

ground, has been added. The result is a three-terminal circuit containing three capacitors, as shown in Fig. 6.33. The actual values of the capacitors in Figs. 6.32 and 6.33 are in the range of 10 to 50 pF, depending on the exact geometry of the switch, how Practical Perspective[r]

and, by similar manipulation, Q = VcffIcffsm($v-ed. (10.22) The effective value of the sinusoidal signal in power calculations is so widely used that voltage and current ratings of circuits and equipment involved in power utilization are given in terms of rms values. For[r]

346 Sinusoidal Steady-State Analysis in Fig. 9.57 depicts these observations. The dotted phasors represent the pertinent currents and volt-ages before the addition of the capacitor. Thus, comparing the dotted phasors of I, RJL, ja>L-[l, and Vv with their solid counterparts clear[r]

analyzing power, which will be familiar from your studies in Chapters 1 and 4, although some additional mathematical tech-niques are required here to deal with sinusoidal, rather than dc, signals. w -_.:. Practical Perspective Heating Appliances In Chapter 9 we calculated the steady-state voltages a[r]

(b)58.4W. Practical Perspective Heating Appliances A handheld hair dryer contains a heating element, which is just a resistor heated by the sinusoidal current passing through it, and a fan that blows the warm air surrounding the resistor out the front of the unit. This is shown schematically[r]

37/2/ V I '\ IT Figure 9.9 A A plot showing that the voltage and cur-rent at the terminals of a resistor are in phase. which states that the phasor voltage at the terminals of a resistor is simply the resistance times the phasor current. Figure 9.8 shows the circuit dia-gram for a resi[r]

terms of a desired steady-state sinusoidal response and design the circuit or system to meet those characteristics. If the device satis-fies the specifications, the designer knows that the circuit will respond satisfactorily to nonsinusoidal inputs. The subsequent chapters of this book[r]

Transformer 335 behavior of the transformer is required in the analysis of both communication and power systems. In this section, we will discuss the sinusoidal steady-state behavior of the linear transformer, which is found primarily in communica-tion circuits. In Sectio[r]

Fig. 9.48 shows the phasor quantities 10/30°, 12 /150% 5/-45°, and 8/-170°. Constructing phasor diagrams of circuit quantities generally involves both currents and voltages. As a result, two different magnitude scales are necessary, one for currents and one for voltages. The ability to visual[r]