Parallel Circuits – Chapter 5
• A parallel circuit provides more than one current
path between any two points.
• Each current path in a parallel circuit is referred
to as a branch.
Two Branches
Three Branches
How many branches?
Parallel Circuit Characteristics

Voltage and Current Values

Voltage is the same across all components
(a) No parallel branches
(b) V1 = V2 = VS
Parallel Circuit Characteristics

Current Characteristics

Source current is the sum of all branch currents
I T  I1  I 2 ...  I n
where
In = the current through the nth branch in
the
circuit
The total current in the circuit is IT = I1 + I2 + I3
IT = 5mA + 10mA + 20mA = 35mA
Parallel Circuit Characteristics

Voltage and Current Values

Current through each branch is determined by the source voltage and
the resistance of the branch.
I branch
VS

Rbranch
TEAM ACTIVITY
Use Ohm’s law to calculate the resistance in each
branch.
TEAM ACTIVITY
10
R1 
 2000
0.005
10
R2 
 1000
0.010
10
R3 
 500
0.020
TEAM ACTIVITY
Use Ohm’s law to calculate the total resistance.
TEAM ACTIVITY
10
RT 
 285.71
0.035
TEAM ACTIVITY
10
R1 
 2000
0.005
10
R2 
 1000
0.010
10
R3 
 500
0.020
10
RT 
 285.71
0.035
1
1
1
Calculate


R1 R2 R3
1
RT
Summary
1
1
1
1



R1 R2 R3 RT
I1  I 2  I 3  IT
V1  V2  V3  VS
1
 RT
1
1
1


R1 R2 R3
Common Mistake
1
1
1
1



 R1  R2  R3  RT
R1 R2 R3 RT
Series Circuit
TEAM ACTIVITY
P1 
P2 
P3 
PT 
TEAM ACTIVITY
P1  0.05W
P2  0.1W
PT  0.35W
P3  0.2W
PT  P1  P2  P3
Special Case – Equal Resistances
• When any number of equal resistances are
connected in parallel, the total resistance is
equal to the value of one resistor divided by the
number of branches
Shorthand notation
for parallel
Special Case – Equal Resistances
Shorthand notation
for parallel
1
1 1 1 3
   
RT R R R R
R 5.1k 
RT  
 1.7 k 
3
3
Adding Additional Branches
• The addition of a parallel branch decreases the
resistance of the circuit
• single branch in (a) draws 5mA from the source
• additional branch in (b) increases the current
drawn from the source to 10mA
TEAM ACTIVITY
Determine the branch currents and the total
current for each circuit. Check with MultiSim.
Vs
8V
R1
1kOhm
R2
200 Ohm
Vs
12 V
R1
1.5kOhm
R2
3kOhm