Lecture 2 - Circuit Elements and Essential Laws E E 1205 Circuit Analysis Lecture 2 - Circuit Elements and Essential Laws

Five Fundamental Elements Ideal Voltage Sources Independent Dependent Ideal Current Sources Resistors Inductors (to be introduced later) Capacitors (to be introduced later)

Independent Voltage Source Voltage may be constant or time-dependent Delivers nominal terminal voltage under all conditions

Independent Current Source Current may be constant or time-dependent Delivers nominal terminal current under all conditions

Voltage-Controlled Dependent Voltage Source Terminal voltage is a function of the voltage drop of a different branch Delivers nominal terminal voltage under all conditions

Current-Controlled Dependent Voltage Source Terminal voltage is a function of the current flow in a different branch Delivers nominal terminal voltage under all conditions

Voltage-Controlled Dependent Current Source Current is a function of the voltage drop of a different branch Delivers nominal terminal current under all conditions

Current-Controlled Dependent Current Source Source current is a function of the current flow in a different branch Delivers nominal terminal current under all conditions

Electrical Resistance (Ohm’s Law) Electrical resistance is the ratio of voltage drop across a resistor to current flow through the resistor. Polarities are governed by the passive sign convention.

Power Consumed by Resistors Resistors consume power. v and i are both positive or both negative.

Conductance Defined Conductance is the reciprocal of resistance. The units of conductance are called siemens (S) The circuit symbol is G

Creating a Circuit Model A circuit model is usually two or more circuit elements that are connected. A circuit model may have active elements (sources) as well as passive elements (such as resistors). By the assumption that electric signal propagation is instantaneous in a circuit, our circuit model has lumped parameters.

Example of a Circuit Model

Kirchhoff’s Voltage Law The sum of the voltage drops around a closed path is zero. Example: -120 + V1 + V2 + V3 + V4 = 0

Kirchhoff’s Current Law A node is a point where two or more circuit elements are connected together. The sum of the currents leaving a node is zero.

Apply KCL to Example

Combine KVL, KCL & Ohm’s Law

Lamp Voltage & Battery Voltage

Battery Power and Lamp Power Loss: Efficiency:

Using Loops to Write Equations KVL @Loop a: KVL @ Loop b: KVL @ Loop c: Loop c equation same as a & b combined.

Using Nodes to Write Equations KCL @ Node x: KCL @ Node y: KCL @ Node z: KCL @ Node w: <== Redundant

Combining the Equations There are 5 circuit elements in the problem. va and vb are known. R1, R2 and R3 are known. v1, v2 and v3 are unknowns. ia, ib, i1, i2 and i3 are unknowns. There are 2 loop (KVL) equations. There are 3 node (KCL) equations. There are 3 Ohm’s Law equations. There are 8 unknowns and 8 equations.

Working with Dependent Sources KVL @ left loop: KCL @ top right node: Substitute and solve:

Example 1 (1/3) By KCL: By Ohm’s Law:

Example 1 (2/3) By KVL: Power:

Example 1 (3/3)

Example 2 (1/4) Find Source Current, I, and Resistance, R.

Example 2 (2/4) Ohm’s Law: 36 V KVL: 48 V Ohm’s Law: 6 A

Example 2 (3/4) KCL: 3 A Ohm’s Law: 12 V KVL: 60 V

Example 2 (4/4) Ohm’s Law: 3 A KCL: 6 A KVL: 24 V Ohm’s Law: R=3 W KCL: I=9 A