CHAPTER 12 KEY FORMULAS AND EQUATIONS

Chapter Equations for Complex Numbers
Imaginary unit
j =  − 1andj2 =  − 1
(12.1)
 − a = ja(a > 0)
(12.2)
Basic operations
(a + bj) + (c + dj) = (a + c) + (b + d)j
(12.3)
(a + bj) − (c + dj) = (a − c) + (b − d)j
(12.4)
(a + bj)(c + dj) = (ac − bd) + (ad + bc)j
(12.5)
a + bjc + dj = (a + bj)(c − dj)(c + dj)(c − dj) = (ac + bd) + (bc − ad)jc2 + d2
(12.6)
Complex number forms
Rectangular : x + yjPolar : r(cos θ + jsin θ) = r ∠ θ_ Exponential : rejθ
x = rcos θy = rsin θ
(12.7)
r2 = x2 + y2tan θ = yx
(12.8)
x + yj = r(cos θ + jsin θ) = r / θ_  = rejθ
(12.12)
Product in polar form
r1(cos θ1 + jsin θ1)r2(cos θ2 + jsin θ2) = r1r2[ cos(θ1 + θ2) + jsin(θ1 + θ2)] (r1 ∠ θ1_ )(r2 ∠ θ2_ ) = r1r2 ∠ θ1 + θ2_ 
(12.13)
Quotient in polar form
r1(cos θ1 + jsin θ1)r2(cos θ2 + jsin θ2) = r1r2[ cos(θ1 − θ2) + jsin(θ1 − θ2)] r1 ∠ θ1_ r2 ∠ θ2_  = r1r2  ∠ θ1 − θ2_ 
(12.15)
DeMoivre’s theorem
[ r(cos θ + jsin θ)] n = rn(cos n θ + jsin n θ)(r / θ_ )n = rn / nθ_ 
(12.17)
Chapter Equations for Alternating-current Circuits
Voltage, current, reactance
VR = IRVC = IXCVL = IXL
(12.18)
Impedance
VRLC = IZ
(12.19)
Z = R + j(XL − XC)
(12.20)
| Z|  = R2 + (XL − XC)2
(12.21)
Position vectors.
Phase angle
ϕ = tan − 1XL − XCR
(12.22)
Capacitive reactance and inductive reactance
XC = 1ωCandXL = ωL
(12.23)
..................Content has been hidden....................

You can't read the all page of ebook, please click here login for view all page.
Reset
3.129.247.196