Unit
- Ohm's Law: Defines the relationship between voltage, current, and resistance: V = IR. This linear relationship is foundational for all circuit analysis, but applies only to ohmic materials. In practice, many components like diodes and transistors exhibit non-linear behavior.
- Kirchhoff's Current Law (KCL): States that the algebraic sum of currents entering a node is zero. This law is derived from conservation of charge and is essential for analyzing current distribution in parallel circuits.
- Kirchhoff's Voltage Law (KVL): States that the algebraic sum of voltages around any closed loop is zero. Derived from conservation of energy, KVL helps determine voltage drops across components in series.
- Series Circuits: In a series circuit, current is constant through all components, and total resistance is the sum of individual resistances. Voltage divides proportionally to resistance.
- Parallel Circuits: In a parallel circuit, voltage is constant across all branches, and total conductance is the sum of conductances. Current divides inversely to resistance.
- Power Calculation: Power dissipated by a resistor is P = IV = I^2 R = V^2 / R. Understanding power is critical for component selection and thermal management.
- Practical Limitations: Real components have tolerances, temperature coefficients, and parasitic elements. Ohm's Law gives first-order approximations, but accurate design requires considering these deviations.
- Application Example: Designing a voltage divider: two resistors in series produce an output voltage that is a fraction of the input. This is used in sensor interfaces and biasing circuits.
- Thevenin's Theorem: Any linear two terminal network can be replaced by an equivalent voltage source in series with a resistor. The Thevenin voltage is the open circuit voltage; the Thevenin resistance is the equivalent resistance with sources deactivated. This simplifies complex circuits for load analysis.
- Norton's Theorem: Any linear two terminal network can be replaced by an equivalent current source in parallel with a resistor. The Norton current is the short circuit current; the Norton resistance equals the Thevenin resistance. It is useful for analyzing current driven loads.
- Superposition Theorem: In linear circuits with multiple independent sources, the response (voltage or current) is the sum of responses from each source acting alone. Other sources are deactivated: voltage sources replaced by short circuits, current sources by open circuits. This simplifies analysis of mixed source networks.
- Node Voltage Analysis: A systematic method applying KCL to solve for unknown node voltages. Choose a reference node, then write equations for remaining nodes. This approach reduces the number of equations compared to mesh analysis for circuits with many nodes, and is efficient for simulation.
- Maximum Power Transfer: A load resistor receives maximum power when its resistance equals the source's internal resistance (Thevenin resistance). This principle is critical in impedance matching for communication systems and audio amplifiers to optimize power delivery.
Code Example
SPICE
* Simple Ohm's Law Simulation
V1 1 0 DC 10V
R1 1 0 1k
.DC V1 0 10 1
.PROBE
.ENDThis netlist applies a DC voltage sweep from 0 to 10V across a 1k resistor. The resulting current can be plotted, confirming I = V/R.
Quick Revision
- Ohm's Law (V=IR) is the basis for resistor circuit analysis.
- KCL and KVL are fundamental laws for current and voltage conservation.
- Series and parallel combinations simplify complex resistor networks.
- Power rating must be considered when selecting components.