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 Whole resistance: $$\begin{align} R = R_\text{1} + R_\text{2} + R_\text{3} \end{align}$$ Whole current: $$\begin{align} I = V / R = 5 / 600 = 0.0083 \end{align}$$ $$\begin{align} V = I*R_\text{1} + I*R_\text{2} + I*R_\text{3}; \end{align}$$ $$\begin{align} 5 = 0.0083*100 + 0.0083*300 + 0.0083*200 \end{align}$$ * if any from this resistors is undefined, we can solve this equation

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

Signs for elements mirroring the logic of KVL.

Node method



 * 1) Choose node
 * 2) Label currents
 * 3) Construct equation
 * 4) Solve equation

$$\begin{align} I_\text{1} = \frac{V_\text{1}}{R_\text{1}+R_\text{2}} \end{align}$$ $$\begin{align} I_\text{2} = \frac{V_\text{2}}{R_\text{4}} \end{align}$$ $$\begin{align} I_\text{3} = I_\text{1} + I_\text{2} \\[3pt] \end{align}$$ $$\begin{align} V_\text{R3} = I_\text{3}*R_\text{3} \end{align}$$

Also possible to create systems of equations for complex circuits.

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