ECE 2006 Lecture for Chapters 1 & 2 S.Norr

Fundamental Laws of Circuits Ohm’s Law: –The voltage across a resistor is directly proportional to the current through it. –The constant of proportionality is called Resistance

Resistance The electrical resistance, R, of a material is dependent on its Resistivity, Length and Cross-Section. Examples: Copper has a Resistivity of 1.7 x Ohm-meters. Glass has a Resistivity of about Ohm-meters.

Conductance Conductance, G, is the inverse of Resistance It is sometimes easier to consider the Conductance of a material instead of its Resistance. G = 1 / R = I / V

Open/Short Circuits A circuit element having no resistance is considered to be a Short Circuit (infinite conductance) A circuit element having infinite resistance is considered an Open Circuit (zero conductance)

Circuit Topology Branch – Part of a circuit containing only one element, such as a resistor or a source. Node – A point of connection between two or more Branches Loop – Any closed path contained within the circuit of interest

Series and Parallel Two (or more) branches are in Series if they share a single node exclusively. –Branches in Series carry identical current Two (or more) branches are in Parallel if they connect to the same two nodes –Branches in Parallel have identical voltage

Types of Branches Branches that are a Source of Energy: Branches that are a Load (Dissipate Energy): Resistor

Counting Branches and Nodes The number of Branches in a circuit is the same as the number of circuit elements The number of nodes is representative of all places in the circuit where branches connect

Kirchhoff’s Laws Based of the Law of Conservation of Charge (conservation of energy): The algebraic sum of charges within a closed system cannot change. KCL – Kirchhoff’s Current Law: The algebraic sum of currents entering a node (or any closed boundary) is Zero. KVL – Kirchhoff’s Voltage Law: The algebraic sum of voltages around a Loop (or any closed path) is Zero/

KCL Application of KCL is straightforward

KVL Use care in assessing each voltage as a drop or rise:

Series Resistors Elements in series each see the same current Resistors in series add directly: R ac = R ab + R bc Conductances in series add as the inverse of the sum of their inverses

Voltage Division V R = V s *Same/Sum

Resistors in Parallel Elements in parallel are each impressed with the same voltage Resistors in parallel add as the inverse of the sum of their inverses Conductances in parallel add directly

Current Division I R = I S *Opp/Sum

Delta-Wye Transform Resistors in a delta shaped arrangement can be transformed into the corresponding wye shaped circuit: Rx = Adj*Adj/Sum

Wye-Delta Transform Resistors in a wye shaped arrangement can be transformed into the corresponding delta shaped circuit: Rx = Sum of Product Terms/Opposite