Linear Circuit Analysis
1. Introduction
2. Basic Concepts
- Charge, current, and voltage
- Power and energy
- Linear circuits
- Linear components
- Nodes and loops
- Series and parallel
- R, L & C combinations
- V & I combinations
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 (DC)
5. Additional Analysis Techniques (DC)
- Superposition
- Source transformation
- The $V_{test}/I_{test}$ method
- Norton equivalent
- Thévenin equivalent
- Max power transfer
- DC analysis of L & C
6. AC Analysis
7. Magnetically Coupled Circuits
8. Polyphase Systems
9. Operational Amplifiers
10. Laplace Transforms
11. Time-Dependent Circuits
- Introduction
- Inductors and capacitors
- First-order transients
- Second-order transients
-
Parallel RLC circuits
Series RLC circuits - Nodal analysis
- Mesh analysis
- Laplace transforms
- Additional techniques
12. Two-Port Networks
Appendix
Capacitor Combinations
Series
If two or more capacitors — $C_1$, $C_2$, ..., $C_n$ — are connected in series, they are equivalent to a single capacitor with $$\begin{equation}C_{eff}=\frac{1}{\frac{1}{C_1}+\frac{1}{C_2}+...+\frac{1}{C_n}}\end{equation}$$ That means we can replace one of the $n$ capacitors with an equivalent capacitor of capacitance $C_{eff}$ and short-circuit (wire) the remaining capacitors.
For instance, consider the circuit in Fig. 1, in which capacitors $C_1$ and $C_2$ are connected in series. In this circuit, we can keep one capacitor, say $C_1$, set its value to $C_{eff}=\frac{1}{\frac{1}{C_1}+\frac{1}{C_2}}$, and replace capacitor $C_2$ with a wire.
Parallel
If two or more capacitors — $C_1$, $C_2$, ..., $C_n$ — are connected in parallel, they are equivalent to a single capacitor with $$\begin{equation}C_{eff}=C_1+C_2+...+C_n\end{equation}$$ That means we can replace one of the $n$ capacitors with an equivalent capacitor of capacitance $C_{eff}$ and remove the other capacitors.
For instance, consider the circuit in Fig. 2, in which capacitors $C_3$, $C_4$, and $C_5$ are connected in parallel. In this circuit, we can keep one of the capacitors, say $C_3$, set its value to $C_{eff}=C_3+C_4+C_5$, and remove capacitors $C_4$ and $C_5$ from the circuit. Similarly, we could keep $C_4$ and remove $C_3$ and $C_5$, or keep $C_5$ and remove $C_3$ and $C_4$.