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.

File:Image for KVL.png

V0 = V1 + V2

KCL

Kirchhoff's current law

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

File:Image for KCL.png

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

File:Mesh circuit.png

Example of circuit

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

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

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

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

$\begin{array}{c}{I}_{\text{1}}=\frac{V_{\text{1}}}{R_{\text{1}}+R_{\text{2}}}\end{array}$

$\begin{array}{c}{I}_{\text{2}}=\frac{V_{\text{2}}}{R_{\text{4}}}\end{array}$

$\begin{array}{c}{I}_{\text{3}}=I_{\text{1}}+I_{\text{2}}\\ \end{array}$
$\begin{array}{c}{V}_{\text{R3}}=I_{\text{3}}*R_{\text{3}}\end{array}$

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