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Non-Simple dc Circuits

Real Batteries and Battery Testers [NEW!]

Recitation this week: Battery Testers

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]

Concept Check

Method of Solving Multiloop Circuits

  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 signs to indicate the high potential sides of each emf and resistor.
  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.
Adapted from Tipler

Detailed Multiloop Circuit Example

Another Example -- Quiz 2, Fall'97

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Last updated Feb. 24, 1998.
Copyright George Watson, Univ. of Delaware, 1997.