E E 1205 Circuit Analysis Lecture 2 Circuit

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E E 1205 Circuit Analysis 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

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

Independent Voltage Source • Voltage may be constant or timedependent • Delivers nominal terminal

Independent Voltage Source • Voltage may be constant or timedependent • Delivers nominal terminal voltage under all conditions

Independent Current Source • Current may be constant or timedependent • Delivers nominal terminal

Independent Current Source • Current may be constant or timedependent • Delivers nominal terminal current under all conditions

Voltage-Controlled Dependent Voltage Source • Terminal voltage is a function of the voltage drop

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

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

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

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

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

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

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

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

Example of a Circuit Model

Kirchhoff’s Voltage Law • The sum of the voltage drops around a closed path

Kirchhoff’s Voltage Law • The sum of the voltage drops around a closed path is zero. • Example: -120 + V 1 + V 2 + V 3 + V 4 = 0

Kirchhoff’s Current Law • A node is a point where two or more circuit

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

Apply KCL to Example

Combine KVL, KCL & Ohm’s Law

Combine KVL, KCL & Ohm’s Law

Lamp Voltage & Battery Voltage

Lamp Voltage & Battery Voltage

Battery Power and Lamp Power Loss: Efficiency:

Battery Power and Lamp Power Loss: Efficiency:

Using Loops to Write Equations KVL @Loop a: KVL @ Loop b: KVL @

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

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.

Combining the Equations • • • There are 5 circuit elements in the problem. va and vb are known. R 1, R 2 and R 3 are known. v 1, v 2 and v 3 are unknowns. ia, ib, i 1, i 2 and i 3 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

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 (1/3) By KCL: By Ohm’s Law:

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

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

Example 1 (3/3)

Example 1 (3/3)

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

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

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

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

Example 2 (4/4) Ohm’s Law: 3 A KCL: 6 A Ohm’s Law: R=3 W

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