Download Parallel Circuits

Parallel Circuits
Definition: Parallel Circuit
A circuit that provides more than one current path
between any two points is said to be a parallel circuit.
EGR 101
1
Example
Circuit (a) provides two current paths between points
(nodes) A and B.
Circuit (b) provides three current paths between Ground
and the + terminal of the battery.
The PC Board circuit provides four current paths
between the input terminals.
EGR 101
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Currents in the Parallel Branches
Kirchhoff’s Current Law
IT
IT  I1  I 2
IT  I1  I 2  I 3
EGR 101
IT  I1  I 2  I 3  I 4
3
KCL
The voltages across the parallel components are equal!
I1 R1  I 2 R2  VS
I1 R1  I 2 R2  I 3 R3  VS
VS
I1 
R1
I1 
VS
V
, I2  S
R1
R2
VS
I2 
R2
I3 
VS
R3
EGR 101
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Equivalent Resistance
I T  I1  I 2  I 3
VS
I1 
R1
I2 
VS
R2
I T  I1  I 2  I 3
VS
I3 
R3
VS VS VS VS



Req R1 R2 R3
VS
IT 
Req
1
1
1
1
 

Req R1 R2 R3
EGR 101
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Special Case for 2 Resistors
1
1
1
 
Req R1 R2
1
R2  R1

Req
R1 R2
R1 R2
Req 
R1  R2
EGR 101
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Common Mistake
R1 R2 R3
Req 
R1  R2  R3
EGR 101
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Equal Resistors in Parallel
R1  R2  R3  R
R1  R2  R
2
R1 R2
R
Req 

R1  R2 2 R
Req 
R
2
1
1
1
1
 

Req R1 R2 R3
1
1 1 1 3
   
Req R R R R
R
Req 
3
EGR 101
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Total (Equivalent) Resistance Is Always
Lower Than Any Individual Resistor
Consider the following circuit.
By the numbers, the total (Equivalent) Resistance is
equal to 10V/10mA, or 1 kΩ.
EGR 101
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What About the Power?
VS2
P1 
R1
V S2
P2 
R2
VS2
1 
2 1
PS 
 VS   
Req
 R1 R2 
PS  P1  P2
The power delivered by the source is equal to the
sum of the individual powers dissipated in the
resistors.
EGR 101
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Summary
EGR 101
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