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
Current Division
Current division is a technique that can be used to compute the current going through each resistor of a parallel combination of resistors when the current going through all the resistors is known. In general, if we have $n$ resistors connected in parallel and the total current going through them is $I$, the current going through resistor $R_i$ is equal to $$\begin{equation}I_i=I\frac{\frac{1}{R_i}}{\frac{1}{R_1}+\frac{1}{R_2}+...+\frac{1}{R_n}}\end{equation}$$
In the case of only two resistors, the previous equation gives $$\begin{equation}I_1=I\frac{R_2}{R_1+R_2}\end{equation}$$ $$\begin{equation}I_2=I\frac{R_1}{R_1+R_2}\end{equation}$$
For instance, consider the circuit shown in Fig. 1.
Applying current division we obtain $$I_{1}=6\ A \times\frac{\frac{1}{8}}{\frac{1}{4}+\frac{1}{8}}=4\ A$$ $$I_{2}=-6\ A \times\frac{\frac{1}{4}}{\frac{1}{4}+\frac{1}{8}}=-2\ A$$ Notice that, in the last equation, we took $I_2$ with negative sign because the current flows in opposite direction than the current induced by the $6\ A$ current source.