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
- Superposition
- Source transformation
- The $V_{test}/I_{test}$ method
- Norton equivalent
- Thévenin equivalent
- Max power transfer
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
Voltage Division
Voltage division is a technique that can be used to compute the voltage across each resistor of a series combination of resistors when the voltage across all the resistors is known. For instance, if we have $n$ resistors connected in series and the total voltage across them is $V$, the voltage across resistor $R_i$ is equal to $$\begin{equation}V_i=V\frac{R_i}{R_1+R_2+...+R_n}\end{equation}$$
In the case of only two resistors, the previous equation gives $$\begin{equation}V_1=V\frac{R_1}{R_1+R_2}\end{equation}$$ $$\begin{equation}V_2=V\frac{R_2}{R_1+R_2}\end{equation}$$
For instance, consider the circuit shown in Fig. 1.
Applying voltage division we obtain $$V_{1}=20\ V \times\frac{2}{2+5+3}=4\ V$$ $$V_{2}=20\ V \times\frac{5}{2+5+3}=10\ V$$ $$V_{3}=-20\ V \times\frac{3}{2+5+3}=-6\ V$$ Notice that, in the last equation, we took $V_3$ with negative sign because voltage $V_3$ is defined in opposite direction than the voltage induced by the $20\ V$ voltage source.