PHYS345 PHYS345 Class 3

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Multiloop Circuits, Nodal Analysis

Kirchhoff's Current Law (KCL) - also known as the junction rule:
At any junction point in a circuit where the current can divide, the sum of the currents into the junction must equal the sum of the currents out of the junction.
Kirchhoff's Voltage Law (KVL) - also known as the loop rule:
When any closed circuit loop is traversed, the algebraic sum of the changes in voltage must equal zero.

Apply the loop rule by starting at any point in circuit, going around the loop considering all changes in voltage, until returning to the original point. The following sign conventions must be obeyed:

  1. For a resistor crossed in the same direction as the current, the change in voltage is - iR.
  2. For a resistor crossed in the opposite direction of the current, the change in voltage is + iR.
  3. If a source of emf is crossed in the same direction as the emf, the change in voltage is +.
  4. If a source of emf is crossed in the opposite direction of the emf, the change in voltage is -.

Example, going from point A to B

[circuit] [sign convention]

      Concept Check: Series and Parallel Combinations

      A Digression: Electrical Resistance Heating

Nodal Analysis
Unknowns are nodal voltages, found from application of KCL.

    Detailed Nodal Analysis Example

Relevant Online Resources
Linear Algebra Solver for those pesky simultaneous equations...


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Last updated Sept. 7, 1999.
Copyright George Watson, Univ. of Delaware, 1999.