Resistors in Parallel
Download
Report
Transcript Resistors in Parallel
Resistors in Parallel
• Resistors connected at a single node pair
• Voltage across each resistor is the same
EGR 101 Introduction to Engineering I
1
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
2
Apply KCL and Ohm’s Law
i1
i2
i3
i4
iS i1 i2 i3 i4
vS i1R1 i2 R2 i3 R3 i4 R4
EGR 101 Introduction to Engineering I
3
Solving for each current
vS
i1
R1
vS
i2
R2
vS
i3
R3
vS
i4
R4
EGR 101 Introduction to Engineering I
4
Substitute back
iS i1 i2 i3 i4
1
vS vS vS vS
1
1
1
iS
vS
R1 R2 R3 R4
R1 R2 R3 R4
iS
1
1
1
1
1
vS Req R1 R2 R3 R4
EGR 101 Introduction to Engineering I
5
Equivalent Circuit
k
1
1
1
1
1
.....
Req i 1 Ri R1 R2
Rk
k
Geq Gi G1 G2 ..... Gk
i 1
EGR 101 Introduction to Engineering I
6
Special case for only 2 resistors
1
1
1 R2 R1
Req R1 R2
R1 R2
R1 R2
Req
R1 R2
Product
Sum
EGR 101 Introduction to Engineering I
7
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
EGR 101 Introduction to Engineering I
8
Classroom Problem #2
Determine the equivalent resistance seen by the current
source.
R2
3k
R4
5k
R3
10k
R5
7k
R1
4k
I
3mA
EGR 101 Introduction to Engineering I
9