Linear Circuit Analysis
1. Introduction
2. Basic Concepts
- Currents and voltages
- Linear circuits
- Linear components
- Loops and nodes
- Series and parallel
- R, L & C combinations
- V & I combinations
- Power and energy
3. Simple Circuits
- Ohm's law
- Kirchhoff's current law
- Kirchhoff's voltage law
- Single loop circuits
- Single node-pair circuits
- Voltage division
- Current division
4. Nodal and Mesh Analysis
5. Additional Analysis Techniques
6. AC Analysis
7. Operational Amplifiers
8. Laplace Transforms
9. Time-Dependent Circuits
- Introduction
- First-order transients
- Nodal analysis
- Mesh analysis
- Laplace transforms
- Additional techniques
10. Two-port networks
Ohm's Law
Ohm’s law states that the current through a resistor is directly proportional to the voltage across the resistor. Denoting the constant of proportionality with $R$ (the resistance), one can express Ohm's law mathematically as $$\begin{equation}V=RI\end{equation}$$ or $$\begin{equation}I=\frac{V}{R}\end{equation}$$ where voltage $V$ and current $I$ are shown in Fig. 1. It is important to note that the value of the current that we obtain using Ohm's law depends on how we define voltage $V$. As shown in the figure, the current obtained using Ohm's law is assumed to flow from the $+$ to the $-$ nodes (however, depending on the value of $V$ this current can be either positive or negative).
If we introduce the conductance as the inverse of the resistance $C=1/R$, Ohm's law becomes $V=I/C$ or $I=CV$. The unit for resistance is ohm ($Ω$); the unit for conductance is siemens ($S$), also known as mho.
Sample Solved Problems
See also
Kirchhoff's current law (KCL)
Kirchhoff's voltage law (KVL)