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Table 42 Analogy between electrical and uid circuits Electrical element or equation Voltage or potential difference, v1 v2 Current ow, i Resistor, R Capacitor, C Inductor, L P = i2R Wp = 1 Cv 2 2 Wk =

Note Typing the code in the Source view adds the buttons in the Design view, but the opposite is true as

Property Potential variable Flow variable Resistance Capacitance Inductance Power dissipation Potential energy storage Kinetic energy storage

Hydraulic or uid analogy Pressure difference, P 1 P2 Fluid volume ow rate, qf Fluid resistor, Rf Fluid capacitor, Cf Fluid inertor, If 2 P f = q f Rf Wp = 1 Cf p 2 2

41 The current waveform shown in Figure 416 ows through a 50-mH inductor Plot the inductor voltage, vL (t)

i (t) (mA) 15 10 5 0 1 2 3 4 5 6 7 8 t (ms) v(t) (V) 15 10 5 0 1 2 3 4 5 6 7 8 t (ms)

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42 The voltage waveform of Figure 417 appears across a 1,000- F capacitor Plot the capacitor current, iC (t) 43 Calculate the energy stored in the inductor (in joules) at t = 3 ms by the waveform of Exercise 41 Assume i( ) = 0 44 Perform the calculation of Exercise 43 for the capacitor if vC ( ) = 0 V

well. While in Design view, you can add buttons, textboxes, and other controls from the toolbox just as you do with Windows applications.

1147 512 22

45 Compute and plot the inductor energy (in joules) and power (in watts) for the case of Exercise 41

In 2, the general concept of an ideal energy source was introduced In the present chapter, it will be useful to speci cally consider sources that generate time-varying voltages and currents and, in particular, sinusoidal sources Figure 418 illustrates the convention that will be employed to denote time-dependent signal sources

Square wave x (t)

+ v (t) _

i (t)

myCmd.CommandText = strSQLCommand; myCmd.ExecuteNonQuery(); myConn.Close(); myConn = null; myCmd = null; } } This code accesses Microsoft SQL Server but after we had tested that the testware was working, we could go back and overload the Save() method (yet again) to include a version for Access or Oracle.

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+ v (t), i(t) _

Sinusoidal source A x (t)

x (t)

One of the most important classes of time-dependent signals is that of periodic signals These signals appear frequently in practical applications and are a useful approximation of many physical phenomena A periodic signal x(t) is a signal that satis es the following equation: x(t) = x(t + nT ) n = 1, 2, 3, (417)

Summary

where T is the period of x(t) Figure 419 illustrates a number of the periodic waveforms that are typically encountered in the study of electrical circuits Waveforms such as the sine, triangle, square, pulse, and sawtooth waves are provided in the form of voltages (or, less frequently, currents) by commercially available signal (or waveform) generators Such instruments allow for selection of the waveform peak amplitude, and of its period As stated in the introduction, sinusoidal waveforms constitute by far the most important class of time-dependent signals Figure 420 depicts the relevant parameters of a sinusoidal waveform A generalized sinusoid is de ned as follows: x(t) = A cos( t + ) (418)

where A is the amplitude, the radian frequency, and the phase Figure 420 summarizes the de nitions of A, , and for the waveforms x1 (t) = A cos( t) where f = natural frequency = 1 (cycles/s, or Hz) T (419) and x2 (t) = A cos( t + )

39 24 46

x1 (t)

x2 (t)

= radian frequency = 2 f (radians/s) = 2 t T (radians) = 360 t T (degrees)

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