ECE 201 Circuit Theory I 1

Resistors in Series

• Resistors connected at a single node

• Current through each resistor is the same

ECE 201 Circuit Theory I 2

Identify the current in each ResistorApply KCL at each node

1 2 3 4 5 6 7Si i i i i i i i

a b c d e f g

ECE 201 Circuit Theory I 3

Redraw using a single current

ECE 201 Circuit Theory I 4

To solve for the current, write KVL

1 2 3 4 5 6 7

1 2 3 4 5 6 7

0

( )S S S S S s S S

S S S eq

v i R i R i R i R i R i R i R

v i R R R R R R R i R

ECE 201 Circuit Theory I 5

Simplified version of the circuit

7

1 2 3 4 5 6 71

S S eq

eq ii

v i R

R R R R R R R R R

ECE 201 Circuit Theory I 6

From a “black box” point of view

• These circuits are “equivalent”

• Same current drawn from the source

ECE 201 Circuit Theory I 7

Summary

• Resistors in series have the same current

• The resistors can be replaced by an “equivalent” resistance equal to the sum of the individual resistors

• The “equivalent” resistance is larger than the largest of the individual resistors