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% Document Info
\author{Kevin694}
\pdfinfo{
  /Title (basic-circuit-analysis-2.pdf)
  /Creator (Cheatography)
  /Author (Kevin694)
  /Subject (Basic Circuit Analysis 2 Cheat Sheet)
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\noindent
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    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Basic Circuit Analysis 2 Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Kevin694} via \textcolor{DarkBackground}{\uline{cheatography.com/18728/cs/1904/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}Kevin694 \\
  \uline{cheatography.com/kevin694} \\
  \end{tabulary}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 13th May, 2016.\\
   Page {\thepage} of \pageref{LastPage}.
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  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
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\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{1.14471 cm} x{3.83229 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Basic Concepts (H1)}}  \tn
% Row 0
\SetRowColor{LightBackground}
Current & I{[}A{]}=Q{[}C{]}/t{[}s{]} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Voltage & U{[}V{]}=W{[}J{]}/Q{[}C{]} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Power & P{[}W{]}= W / t = U * I \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
Energy & W = P * t \tn 
% Row Count 4 (+ 1)
% Row 4
\SetRowColor{LightBackground}
Coulomb & 1C = 6,241*10\textasciicircum{}18\textasciicircum{} elek. \tn 
% Row Count 5 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.9908 cm} x{2.9862 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Resistance (H2)}}  \tn
% Row 0
\SetRowColor{LightBackground}
Ohm's Law & I{[}A{]} = U{[}V{]} / R{[}Ohm{]} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Resistivity & R = rho * (l{[}m{]}/A{[}m\textasciicircum{}2\textasciicircum{}{]}) \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Power Absorbtion & P = V\textasciicircum{}2\textasciicircum{}/R = I\textasciicircum{}2\textasciicircum{}R \tn 
% Row Count 3 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{DC Circuits (H3)}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Voltage Law (KVL):}} \newline % Row Count 1 (+ 1)
The sum of all voltage drops equals the sum of al voltage rises in a mesh. \newline % Row Count 3 (+ 2)
{\bf{Current Law (KCL):}} \newline % Row Count 4 (+ 1)
The sum of all currents entering a closed surface equals the sum of all leaving one. \newline % Row Count 6 (+ 2)
{\bf{Equivalent Resistor:}} \newline % Row Count 7 (+ 1)
Rt = (R1 * R2) / (R1+R2) \newline % Row Count 8 (+ 1)
(in case of 2 resistors paralllel)% Row Count 9 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{DC Circuits Analysis (H4)}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Source Transformation:}} \newline % Row Count 1 (+ 1)
Current and Voltage source with 1 resistor are interchangable. \newline % Row Count 3 (+ 2)
I = V / R and U = I * R \newline % Row Count 4 (+ 1)
{\bf{Mesh Analysis:}} \newline % Row Count 5 (+ 1)
Applying KVL to a mesh. \newline % Row Count 6 (+ 1)
{\bf{Nodal Analysis:}} \newline % Row Count 7 (+ 1)
Applying KCL to a node.% Row Count 8 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Equivalent Circuits (H5)}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Thevenin Circuit:}} \newline % Row Count 1 (+ 1)
Circuits can be reduced to voltage source with resistor in serie.  \newline % Row Count 3 (+ 2)
Rt = Rth {\emph{(open circuit and independent sources deactivated)}} \newline % Row Count 5 (+ 2)
Vth = {\emph{open}} circuit voltage \newline % Row Count 6 (+ 1)
Isc = current in {\emph{short-circuit}} between a and b \newline % Row Count 7 (+ 1)
{\bf{Norton Circuit:}} \newline % Row Count 8 (+ 1)
Found by source transformation of Thevenin \newline % Row Count 9 (+ 1)
Isc equals In \newline % Row Count 10 (+ 1)
{\bf{Maximum Power Transfer:}} \newline % Row Count 11 (+ 1)
Vth\textasciicircum{}2\textasciicircum{} / 4Rth \newline % Row Count 12 (+ 1)
{\bf{Milliman's Theorem:}} \newline % Row Count 13 (+ 1)
Multiple voltage sources with resistors can be combined into one by transformations giving one voltage source. \newline % Row Count 16 (+ 3)
Vm = (G1V1 + .. + GnVn) / (G1 + .. + Gn) \newline % Row Count 17 (+ 1)
Rm = 1 / (G1 + .. + Gn) \newline % Row Count 18 (+ 1)
{\bf{Delta-Y Transformation:}} \newline % Row Count 19 (+ 1)
Ra = (R1 * R2) / (R1 +R2 + R3) \newline % Row Count 20 (+ 1)
Rb = (R2 * R3) / (R1+ R2 + R3) \newline % Row Count 21 (+ 1)
Rc = (R1 * R3) / (R1+ R2 + R3) \newline % Row Count 22 (+ 1)
R1 = (RaRb + RaRc + RbRc) / Rb \newline % Row Count 23 (+ 1)
R2 = (RaRb + RaRc + RbRc) / Rc \newline % Row Count 24 (+ 1)
R3 = (RaRb + RaRc + RbRc) / Ra% Row Count 25 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Operational Amplifier (H6)}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{U+ = U- and I+ = I- = 0 \newline % Row Count 1 (+ 1)
{\bf{inverter:}} \newline % Row Count 2 (+ 1)
Vo=-(Rf/Ri)*Vi \newline % Row Count 3 (+ 1)
{\bf{summer:}} \newline % Row Count 4 (+ 1)
\seqsplit{Vo=-((Rf/Ra)Va+(Rf/Rb)Vb+(Rf/Rc)Vc)}% Row Count 5 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.69218 cm} x{3.28482 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Capacitors (H8)}}  \tn
% Row 0
\SetRowColor{LightBackground}
Capacitance & C = Q / U \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Capacitance & C = e * (A/d) \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Capacitance parallel & Ct = C1 + C2 + .. \tn 
% Row Count 4 (+ 2)
% Row 3
\SetRowColor{white}
Capacitance series & 1 / Ct = (1/C1) + (1/C2) etc. \tn 
% Row Count 6 (+ 2)
% Row 4
\SetRowColor{LightBackground}
Energy Storage & Wc = 0.5CV\textasciicircum{}2\textasciicircum{}2 \tn 
% Row Count 8 (+ 2)
% Row 5
\SetRowColor{white}
Time-varying Current & i = dq/dt = C * dv/dt \tn 
% Row Count 10 (+ 2)
% Row 6
\SetRowColor{LightBackground}
RC time constant & tau = Rth * C \tn 
% Row Count 12 (+ 2)
% Row 7
\SetRowColor{white}
RC expression voltage & v(t) = v(oo) + {[}v(0+) - v(00){]}e\textasciicircum{}-t/tau\textasciicircum{} V \tn 
% Row Count 14 (+ 2)
% Row 8
\SetRowColor{LightBackground}
RC expression current & i(t) = i(oo) + {[}i(0+) - i(00){]}e\textasciicircum{}-t/tau\textasciicircum{} A \tn 
% Row Count 16 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.84149 cm} x{3.13551 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Inductors (H9)}}  \tn
% Row 0
\SetRowColor{LightBackground}
Flux & v = N * dphi/dt \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Inductance & L {\emph{ i = N }} phi \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Coil inductance & L = (N\textasciicircum{}2\textasciicircum{}*mu*A)/l \tn 
% Row Count 4 (+ 2)
% Row 3
\SetRowColor{white}
Inductor series & Lt = L1+ L2 + Ln \tn 
% Row Count 6 (+ 2)
% Row 4
\SetRowColor{LightBackground}
Inductor parallel & 1 / Lt = (1/L1) + (1/L2) etc. \tn 
% Row Count 8 (+ 2)
% Row 5
\SetRowColor{white}
Energy Storage & Wl=0.5Li\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 9 (+ 1)
% Row 6
\SetRowColor{LightBackground}
RC time constant & tau = L / Rth \tn 
% Row Count 11 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.04057 cm} x{2.93643 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Alternating Current (H10)}}  \tn
% Row 0
\SetRowColor{LightBackground}
Frequency & f {[}Hz{]} = 1 / T {[}s{]} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Angular Velocity & omega {[}rad/s{]} = 2*pi*f \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Average Value factor & 2 / pi = 0.637 \tn 
% Row Count 5 (+ 2)
% Row 3
\SetRowColor{white}
Resistor Power & Pav = Vm\textasciicircum{}2\textasciicircum{} / 2R = Im\textasciicircum{}2\textasciicircum{}R / 2 \tn 
% Row Count 7 (+ 2)
% Row 4
\SetRowColor{LightBackground}
Effective Value (RMS) & Veff = Vm / 2\textasciicircum{}0.5\textasciicircum{} \tn 
% Row Count 9 (+ 2)
% Row 5
\SetRowColor{white}
Inductor Law & Xl = omega*L and Im = Vm / Xl \tn 
% Row Count 11 (+ 2)
% Row 6
\SetRowColor{LightBackground}
Capacitor Law & Xc = -1/(omega*C) \tn 
% Row Count 12 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Component Behavior (H10)}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Resistor:}} \newline % Row Count 1 (+ 1)
Current and Voltage in phase. \newline % Row Count 2 (+ 1)
v=Vm * sin(omega*t+phi) \newline % Row Count 3 (+ 1)
i=Im * sin(omga * t+phi) \newline % Row Count 4 (+ 1)
{\bf{Inductor:}} \newline % Row Count 5 (+ 1)
Voltage leads Current by 90 deg. \newline % Row Count 6 (+ 1)
v=Xl * Im*cos(omega*t + phi) \newline % Row Count 7 (+ 1)
i=Im*sin(omega*t + phi) \newline % Row Count 8 (+ 1)
{\bf{Capacitor:}} \newline % Row Count 9 (+ 1)
Current leadsVoltage by 90 deg. \newline % Row Count 10 (+ 1)
v=Vm*sin(omega*t+phi) \newline % Row Count 11 (+ 1)
i=omega * C * Vm * cos(omega*t + phi)% Row Count 12 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.74195 cm} x{3.23505 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{AC Circuit Analysis (H12)}}  \tn
% Row 0
\SetRowColor{LightBackground}
Impedantie & Z=V/I \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Impedantie (2) & Z=R+jX \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Admitantie & Y=1/Z \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
AC Current & I=(Im/2\textasciicircum{}0.5\textasciicircum{})*hoek \tn 
% Row Count 4 (+ 1)
% Row 4
\SetRowColor{LightBackground}
AC Voltage & V=((R * Im)/2\textasciicircum{}0.5\textasciicircum{})*hoek \tn 
% Row Count 5 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{AC Circuit Analysis (H13)}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Mesh Analysis:}} \newline % Row Count 1 (+ 1)
Transform current to voltage source \newline % Row Count 2 (+ 1)
Use of KVL \newline % Row Count 3 (+ 1)
{\bf{Nodal Analysis:}} \newline % Row Count 4 (+ 1)
Transform voltage to current source \newline % Row Count 5 (+ 1)
Use of KCL% Row Count 6 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{AC Y-Delta transformation (H14)}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Delta-Y Transformation:}} \newline % Row Count 1 (+ 1)
Za = (Z1 * Z2) / (Z1 +Z2 + Z3) \newline % Row Count 2 (+ 1)
Zb = (Z2 * Z3) / (Z1 +Z2 + Z3) \newline % Row Count 3 (+ 1)
Zc = (Z1 * Z3) /(Z1 +Z2 + Z3) \newline % Row Count 4 (+ 1)
Z1 = (ZaZb + ZaZc + ZbZc) / Zb \newline % Row Count 5 (+ 1)
Z2 = (ZaZb + ZaZc + ZbZc) / Zc \newline % Row Count 6 (+ 1)
Z3 = (ZaZb + ZaZc + ZbZc) / Za% Row Count 7 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.23965 cm} x{2.73735 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Maximum Power Absorbed (H14)}}  \tn
% Row 0
\SetRowColor{LightBackground}
The load is the Zth conjungate & Zl = Zth\textasciicircum{}*\textasciicircum{} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Max. Power Absorbed & Vth\textasciicircum{}2\textasciicircum{}/(4Rth) (Vth is RMS of {\bf{Vth}}) \tn 
% Row Count 4 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Power in AC circuits (H15)}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Instantaneous Power:}} \newline % Row Count 1 (+ 1)
p = V * I cos(theta) \newline % Row Count 2 (+ 1)
cos(theta) = Power Factor (PF) \newline % Row Count 3 (+ 1)
theta = fase spanning - fase stroom \newline % Row Count 4 (+ 1)
{\bf{Reactive Power:}} \newline % Row Count 5 (+ 1)
Q = V * I * sin(theta) \newline % Row Count 6 (+ 1)
{\bf{Complex Power:}} \newline % Row Count 7 (+ 1)
{\bf{S}}=P+jQ \newline % Row Count 8 (+ 1)
{\bf{Apparent Power:}} \newline % Row Count 9 (+ 1)
S=VI \newline % Row Count 10 (+ 1)
1hp = 745,7 W% Row Count 11 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.79172 cm} x{3.18528 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Transformers (H16)}}  \tn
% Row 0
\SetRowColor{LightBackground}
Ratio & v1/v2 = N1/N2 = i2/i1 \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Reflected Impedance & {\bf{Zr}} = {\bf{V1}}/{\bf{I1}} = a\textasciicircum{}2\textasciicircum{}{\bf{Z2}} \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Current rating & kVA transformer / voltage rating \tn 
% Row Count 5 (+ 2)
% Row 3
\SetRowColor{white}
PhiMax & PhiM = (sqrt(2)*Vrms)/(wN) \tn 
% Row Count 7 (+ 2)
% Row 4
\SetRowColor{LightBackground}
coupling coefficient & k = M / sqrt(L1*L2) \tn 
% Row Count 9 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{p{0.4177 cm} x{1.33664 cm} x{1.04425 cm} x{1.37841 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{4}{x{5.377cm}}{\bf\textcolor{white}{tijd-fase formules}}  \tn
% Row 0
\SetRowColor{LightBackground}
 & weerstand & spoel & condensator \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Z & R & jwL & 1/(jwC) \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
R & R & 0 & 0 \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
X & 0 & wL & -1/(wC) \tn 
% Row Count 4 (+ 1)
% Row 4
\SetRowColor{LightBackground}
Y & 1/R & 1/(jwL) & jwC \tn 
% Row Count 5 (+ 1)
% Row 5
\SetRowColor{white}
G & 1/R & 0 & 0 \tn 
% Row Count 6 (+ 1)
% Row 6
\SetRowColor{LightBackground}
B & 0 & -1/(wL) & wC \tn 
% Row Count 7 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}----}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{3-Phase (H17)}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Vline = sqrt(3)*Vphase \newline % Row Count 1 (+ 1)
I line = sqrt(3)*Iphase% Row Count 2 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Dot rule transformer}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Primary I into dot and secondary I out of dot: \newline % Row Count 1 (+ 1)
I1 and I2 both positive or negative.% Row Count 2 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}