Objective of Lecture Explain mathematically how resistors in series are combined and their equivalent resistance. Chapter 2.5 Explain mathematically how resistors in parallel are combined and their equivalent resistance. Chapter 2.6 Rewrite the equations for conductances.

Series Resistors

Series Resistors (con’t) Use KVL

Series Resistors (con’t) Use KVL Use Ohm’s Law

Series Resistors (con’t) Use KVL Use Ohm’s Law Substitute into KVL equation

Equivalent Resistance: Series Connections R eq is equal to the sum of the resistors in series. In this case: R eq = R 1 + R 2

General Equations: Series Resistors If S resistors are in series, then where V in may be the applied voltage or the total voltage dropped across all of the resistors in series.

Parallel Resistors

Parallel Resistor (con’t) Use KCL

Parallel Resistor (con’t) Use KCL Use Ohm’s Law

Parallel Resistor (con’t) Use KCL Use Ohm’s Law Substitute into KCL equation

Equivalent Resistance: Parallel Connections 1/R eq is equal to the sum of the inverse of each of the resistors in parallel. In this case: 1/R eq = 1/R 1 + 1/R 2 Simplifying (only for 2 resistors in parallel) R eq = R 1 R 2 /(R 1 + R 2 )

General Equations: Parallel Resistors If P resistors are in parallel, then where I in may be the total current flowing into and out of the nodes shared by the parallel resistors.

If you used G instead of R In series: The reciprocal of the equivalent conductance is equal to the sum of the reciprocal of each of the conductors in series In this example 1/G eq = 1/G 1 + 1/G 2 Simplifying (only for 2 conductors in series) G eq = G 1 G 2 /(G 1 + G 2 )

If you used G instead of R In parallel: The equivalent conductance is equal to the sum of all of the conductors in parallel In this example: G eq = G 1 + G 2

Electronic Response: For the same value resistors As you increase the number of resistors in series Does R eq increases or decreases? As you increase the number of resistors in parallel Does R eq increases or decreases?

Summary The equivalent resistance and conductance of resistors in series are: where S is the total number of resistors in series. The equivalent resistance and conductance of resistors in parallel are: where P is the total number of resistors in parallel.