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

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

• Circuit elements may be connected in series and/or in parallel.
  • i. A series connection is one in which any charge passing through one circuit element must proceed through all elements in that connection and has no other path available. The current in each element in series must be the same.
  • ii. A parallel connection is one in which charges may pass 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 Req .
  • i. The equivalent resistance of a set of resistors in series is the sum of the individual resistances. Relevant equation:
  • ii. The inverse of the equivalent resistance of a set of resistors connected in parallel is equal to the sum of the inverses of the individual resistances. Relevant equation:
  • iii. When resistors are connected in parallel, the number of paths available to charges increases, and the equivalent resistance of the group of resistors decreases.