11.5: Compound Direct Current (DC) Circuits

Describe the equivalent resistance of multiple resistors connected in a circuit.

Circuit elements may be connected in series and/or parallel.

• A series connection is one in which circuit elements are connected such that any charge passing through one element must proceed through the other and has no other path available. The current in each element in series must be the same.

• A parallel connection is one in which charges may flow through one of two or more paths. Across each path, the potential difference is the same.

A collection of resistors in a circuit may be analyzed as though it were a single resistor, with an equivalent resistance eq R .

• The equivalent resistance of a set of resistors in series is the sum of the individual resistances.

• The inverse of the equivalent resistance of a set of resistors connected in parallel is equal to the sum of the inverse of their individual resistances.

• When resistors are connected in parallel, the number of paths available to charges increases and the equivalent resistance of the group of resistors decreases.

Describe a circuit with resistive wires and a battery with internal resistance.

Ideal batteries have negligible internal resistance. Ideal wires have negligible resistance.

• 11.5.B.1.i The resistance of wires that are good conductors may normally be neglected because their resistance is much smaller than other elements in a circuit.

• 11.5.B.1.ii The resistance of wires may only be neglected if the circuit contains other elements that have resistance.

• 11.5.B.1.iii The potential difference a battery would supply if it were ideal is the potential difference measured across the terminals when there is no current in the battery and is sometimes referred to as its emf ( ).

11.5.B.2 The internal resistance of a non-ideal battery may be treated as a resistor in series with the battery and the remainder of the circuit.

11.5.B.3 When a battery with internal resistance r is in a circuit with non-zero current, the potential difference between the battery’s terminals is reduced from what it would be if there was no current.