EGR 101 Introduction to Engineering I 1

Resistors in Parallel

• Resistors connected at a single node pair

• Voltage across each resistor is the same

EGR 101 Introduction to Engineering I 2

Caution on Parallel Connection

• Here, R1 and R3 are not in parallel

• Resistor R1 is in parallel with the series combination of R2 and R3

EGR 101 Introduction to Engineering I 3

Apply KCL and Ohm’s Law

i1 i2 i3 i4

1 2 3 4

1 1 2 2 3 3 4 4

S

S

i i i i i

v i R i R i R i R

EGR 101 Introduction to Engineering I 4

Solving for each current

11

22

33

44

S

S

S

S

vi

R

vi

R

vi

R

vi

R

EGR 101 Introduction to Engineering I 5

Substitute back

1 2 3 4

1 2 3 4 1 2 3 4

1 2 3 4

1 1 1 1

1 1 1 1 1

S

S S S SS S

S

S eq

i i i i i

v v v vi v

R R R R R R R R

i

v R R R R R

EGR 101 Introduction to Engineering I 6

Equivalent Circuit

1 1 2

1 21

1 1 1 1 1.....

.....

k

ieq i k

k

eq i ki

R R R R R

G G G G G

EGR 101 Introduction to Engineering I 7

Special case for only 2 resistors

2 1

1 2 1 2

1 2

1 2

1 1 1

eq

eq

R R

R R R R R

R RR

R R

Product

Sum

EGR 101 Introduction to Engineering I 8

Summary

• Resistors in parallel have the same voltage

• The resistors can be replaced by an “equivalent” resistance whose conductance is the sum of the individual conductances

• The “equivalent” resistor is smaller than the smallest of the individual resistors

Classroom Problem #2

EGR 101 Introduction to Engineering I 9

I3mA

R1

4k

R23k

R310k

R45k

R57k

Determine the equivalent resistance seen by the current source.