Circuit Theory
Learning Objectives
- Explain the relationship between voltage, current, and resistance using Ohm's Law
- Apply Kirchhoff's Current and Voltage Laws to analyze circuit nodes and loops
- Simplify complex linear networks using Thevenin's and Norton's equivalent circuits
- Distinguish between series and parallel circuit configurations and calculate their properties
- Analyze AC circuits using impedance, phasors, and frequency response concepts
- Apply network theorems including Superposition, Maximum Power Transfer, and Millman's Theorem
- Design and evaluate passive and active filter circuits for signal conditioning
Quick Answer
Circuit theory is the mathematical and conceptual framework for analyzing how voltage, current, and power behave in electrical networks. It begins with Ohm's Law (V = IR), which links the three fundamental quantities, and builds up through Kirchhoff's Laws — which enforce conservation of charge and energy — to powerful simplification tools like Thevenin's and Norton's theorems. AC analysis extends these ideas into the frequency domain using impedance and phasors, while topics like filters, signal-to-noise ratio, and power calculations connect theory directly to practical design decisions.
Topics at a Glance
| Topic | Core Idea | Key Formulas |
|---|---|---|
| Ohm's Law | Voltage, current, and resistance are proportionally linked | V = IR, P = IV |
| Kirchhoff's Laws | Conservation of charge (KCL) and energy (KVL) at nodes and loops | ΣI = 0, ΣV = 0 |
| Series and Parallel Circuits | Two fundamental ways to connect components | R_s = R1+R2; 1/R_p = 1/R1+1/R2 |
| Thevenin's and Norton's Theorems | Any linear network simplifies to a single source + resistance | V_th = V_oc; I_N = I_sc |
| AC and DC Circuits | DC: steady current; AC: sinusoidal, uses impedance | Z = R + jX; P = VIcos(θ) |
| Frequency Response | How gain and phase vary with frequency | f_c = 1/(2πRC) |
| Network Theorems | Toolkit of circuit simplification methods | Superposition, Millman's, Max Power |
| Filters | Frequency-selective circuits (LPF, HPF, BPF, BSF) | H(s) = 1/(1+sRC) |
| Signal and Noise Analysis | Characterising signal quality and noise sources | SNR(dB) = 10·log(P_s/P_n) |
| Power Calculations | Active, reactive, and apparent power in circuits | P = IV, Q = IVsin(θ), S = IV |
Key Terms
| Term | Definition | Related Concept |
|---|---|---|
| Node | A junction point where two or more circuit branches meet | KCL |
| Loop / Mesh | A closed path in a circuit | KVL |
| Impedance (Z) | AC equivalent of resistance, combining R with reactance (X); measured in ohms | AC circuits |
| Thevenin equivalent | Simplification of any linear two-terminal network to V_th in series with R_th | Norton's theorem |
| Cutoff frequency | Frequency at which output power falls to half its passband value (-3 dB point) | Filters, frequency response |
| Power factor | cos(θ), ratio of active to apparent power; equals 1 for purely resistive loads | AC power |
| Signal-to-noise ratio | Ratio of signal power to noise power, usually expressed in decibels | Signal and noise analysis |
| Superposition | Principle that responses from multiple independent sources can be summed separately | Network theorems |
Related Topics
Prerequisites: Basic electricity concepts (charge, voltage, current), SI units, algebra and trigonometry
Related Topics: Semiconductor devices, Operational amplifiers, Digital electronics, Electromagnetic theory
Next Topics: Analog circuit design, Power electronics, Control systems, Communication systems