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Non-Simple dc Circuits

Detailed Series/Parallel Circuit Example

Concept Check

Kirchhoff's Rules

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.

Loop rule:
When any closed circuit loop is traversed, the algebraic sum of the changes in potential must equal zero.

Apply the loop theorem by starting at any point in circuit, going around the loop considering all changes in potential, 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 potential is -iR.
  2. For a resistor crossed in the opposite direction of the current, the change in potential is +iR.
  3. If a source of emf is crossed in the same direction as the emf, the change in potential is +.
  4. If a source of emf is crossed in the opposite direction of the emf, the change in potential is -.

Example, going from point A to B

[circuit] [sign convention]

Method of Solving Multiloop Circuits

Adapted from Tipler
  1. Replace any combination of resistors in series or parallel with their equivalent resistance. Label resistors and emfs with symbols.
  2. Choose a direction for the current in each branch of the circuit, and label the currents in a circuit diagram. Add plus and minus signs to indicate the high and low potential sides of each source of emf and resistor (and capacitor).
  3. Apply the junction rule to each junction where the current divides.
  4. In a circuit containing n interior loops, apply the rule to any n loops.
  5. Solve the equations to obtain the values of the unknowns.
  6. Check your results by assigning a potential of zero to one point in the circuit (the ground) and use the values of the currents found to determine the potential at other points in the circuit.

Detailed Multiloop Circuit Example


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Last updated Sept. 15, 1997.
Copyright George Watson, Univ. of Delaware, 1997.