EE Electronics fundamentals/Lecture Basic Resistive Circuit Analysis

KVL

kirchhoff's voltage law

Sum of voltages between the start and end of circuits is 0.

V0 = V1 + V2

KCL

kirchhoff's current law

Currents in point are balanced. Sum of currents is 0.

I1+I3=I2

Mesh method

based on KVL

1. Choose the reference point
2. Walk through this loop by labeling voltages(even if undefined)
3. Construct equation
4. Solve equation

*if more loops, then possible to create the system of equation

Example of circuit

Whole resistance: ${\begin{aligned}R=R_{\text{1}}+R_{\text{2}}+R_{\text{3}}\end{aligned}}$
Whole current: ${\begin{aligned}I=V/R=5/600=0.0083\end{aligned}}$

${\begin{aligned}V=I*R_{\text{1}}+I*R_{\text{2}}+I*R_{\text{3}};\end{aligned}}$
${\begin{aligned}5=0.0083*100+0.0083*300+0.0083*200\end{aligned}}$
*if any from this resistors is undefined, we can solve this equation

In general we can use also this equation:
${\begin{aligned}-V+I*R1+I*R2+I*R3=0\end{aligned}}$

Signs for elements mirroring the logic of KVL.

Node method

Example of circuit

1. Choose node
2. Label currents
3. Construct equation
4. Solve equation

${\begin{aligned}I_{\text{1}}={\frac {V_{\text{1}}}{R_{\text{1}}+R_{\text{2}}}}\end{aligned}}$

${\begin{aligned}I_{\text{2}}={\frac {V_{\text{2}}}{R_{\text{4}}}}\end{aligned}}$

${\begin{aligned}I_{\text{3}}=I_{\text{1}}+I_{\text{2}}\\[3pt]\end{aligned}}$
${\begin{aligned}V_{\text{R3}}=I_{\text{3}}*R_{\text{3}}\end{aligned}}$

Also possible to create systems of equations for complex circuits.

Conversions

https://en.wikipedia.org/wiki/Y-%CE%94_transform

References

Book about circuit analyses: https://archive.org/details/engineeringcircu0000hayt_n1c5/

More about KVL on allaboutcircuits.com

More about KCL on allaboutcircuits.com

More about conversions on allaboutcircuits.com