Resistors in Series
• Resistors connected at a single node
• Current through each resistor is the same
ECE 201 Circuit Theory I 1

Identify the current in each Resistor
Apply KCL at each node i
S
         
1 2 3 4 5 6 i
7 a b c d e f g
ECE 201 Circuit Theory I 2

Redraw using a single current
ECE 201 Circuit Theory I 3

To solve for the current, write KVL
 
S i R
S 1
 i R
S 2
 i R
S 3
 i R
S 4
 i R s 5
 i R
S 6
 i R
S 7
 v
S

S
(
1

R
2

R
3

R
4

R
5

R
6

R
7
)
 i R
S eq
0
ECE 201 Circuit Theory I 4

Simplified version of the circuit v
S
 i R
S eq
R eq
 i
7 

1
R i

R
1

R
2

R
3

R
4

R
5

R
6

R
7
ECE 201 Circuit Theory I 5

From a “black box” point of view
• These circuits are “equivalent”
• Same current drawn from the source
ECE 201 Circuit Theory I 6

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
ECE 201 Circuit Theory I 7