Direct Current Circuits
1. Basic Concepts
Direct current (DC) circuit analysis deals with constant currents and voltages, while alternating current (AC) circuit analysis deals with time-varying voltage and current signalswhose time average values are zero. The DC circuit components are the constant voltage source, constant current source, and resistor. Electronics also deals with charge Q, electric E and magnetic B fields, as well as,
potential V.
2. The Schematic Diagram
The schematic diagram consists of idealized circuit elements each of which represents some property of the actual circuit. Figure shows some common circuit elements encountered in DC circuits. A two-terminal network is a circuit that has only two points of interest, say A and B.
a) ideal voltage source, b) ideal current source and c) resistor.
3. Kirchoff’s Laws
The conservation of energy and conservation of charge when applied to electrical circuits are known as Kirchoff’s laws.
Conservation of energy – zero algebraic sum of the voltage drops vi around a closed circuit loop (imaginary loop)
Kirchhoff's Voltage Law
Conservation of charge – zero algebraic sum of the currents Ik flowing into a point (total charge in, equals total charge out)
Kirchhoff's Current Law
When applying these laws to solve for circuit unknowns we will find the following defini-
tions useful:
- an element is an impedance (resistance) or EMF (ideal voltage source or ideal current source),
- a node is a point where three or more current-carrying elements are connected,
- a branch is one element or several in series connecting two adjacent nodes, and
- an interior loop is a circuit loop not subdivided by a branch.
Using these definitions we can apply Kirchoff’s laws to a circuit to solve for the unknown
quantities. The general procedure is:
- define the currents and voltages on a diagram,
- apply Kirchoff’s laws to loops and nodes,
- write down a set of linear algebraic equations, and
- solve for the unknowns.
3.1. Series and Parallel Combinations of Resistors
3.2. Voltage Divider
3.3. Current Divider
3.4. Branch Current Method
3.5. Loop Current Method
4. Equivalent Circuits
Equivalent circuits is often the hardest concept and most numerically intensive in the course. Since Ohm’s law and Kirchoff’s equations are linear, we can replace any DC circuit by a simplified circuit. Just like a combination of resistors and Ohm’s law could give an equivalent resistor, a combination of circuit elements and Kirchoff’s laws can give an equivalent circuit.
4.1. Thevenin’s and Norton’s Theorems
4.2. Determination of Thevenin and Norton Circuit Elements
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