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ECE 2006

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.

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ECE 2006

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  1. ECE 2006 Lecture for Chapters 1 & 2 S.Norr

  2. 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

  3. 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 10-8 Ohm-meters. Glass has a Resistivity of about 1012 Ohm-meters.

  4. 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

  5. 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)

  6. 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

  7. 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

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

  9. 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

  10. 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/

  11. KCL • Application of KCL is straightforward

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

  13. Series Resistors • Elements in series each see the same current • Resistors in series add directly: • Rac = Rab + Rbc • Conductances in series add as the inverse of the sum of their inverses

  14. Voltage Division VR = Vs*Same/Sum

  15. 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

  16. Current Division • IR = IS*Opp/Sum

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

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

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