By Martin Vömel, Dieter Zastrow
Read Online or Download Aufgabensammlung Elektrotechnik, Bd.2, Magnetisches Feld und Wechselstrom PDF
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Extra resources for Aufgabensammlung Elektrotechnik, Bd.2, Magnetisches Feld und Wechselstrom
Are the components of A in the direction of the x, y, z axes, so they are the projection of A onto these axes with the angles a, β, γ. Thus, Л, = Л cos a, Л, = Acosß, A = A cosy, and we can write A = Acosaâ, + A cos/3«, + A cos yd-. We can use this equation to evaluate Л=Щ = (л, Àf = (Л? + А] + Л,2 )'/2 = (Л2 cos2 а + Л2 cos2 ß + A2 cos2 yf or A = A (cos2 a + cos2 ß+cos2 7) ' from which we can conclude that 1 = cos2 a + cos2 ß+cos2 γ (law of cosines in 3-D). 8. In cylindrical coordinates, we can now define a set of three mutually perpendicular unit vectors âp, άψ, and â..
7 Find the phasors for the following field quantities: a. Ex(z, f) = £ocos(ux - ßz + &)(Vlm) b. E,(z, t) = 100e-3:cos(ö» - 5z + /r/4)(V/m) с IIXz, t) = //„««(ft* + ßz)(Alm) d. 8 19 Find the instantaneous time domain sinusoidal functions corresponding to the following phasors: a. EXz) = £„e*(V/m) b. Ey(z)= lOOe-'V^V/m) с IXz) = 5 +j4(A) d. 9 Write the phasor expression / for the following current using a cosine reference. a. i(t) = /,,cos(û» - л/6) b. 10 Find the instantaneous V(t) for the following phasors using a cosine reference.
Appendix A contains a review of statistical definitions, examples, and interpretations. html for additional information. 6 INTRODUCTION TO COMPLEX VARIABLES Complex numbers are frequently used in the applications of electromagnetic applications. In this section, the definition and fundamental operations of complex numbers and complex variables will be reviewed. , and j = V^T. 6 Introduction to Complex Variables 13 where \:\ and Θ are both real and are called the amplitude and phase of г. -|sinö.
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