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Parallel Circuits
Parallel Circuit• A parallel circuit is defined as one having
more than one current path connected to a
common voltage source. Parallel circuits,
therefore, must contain two or more load
resistances which are not connected in
series.
Current in a Parallel Circuit:
• In electrical circuits it is important to
understand how current works. In a parallel
circuit current adds up, unlike a series
circuit where current is constant.
Visual Ex.1- parallel circuit with one
battery and two loads
3amps
1.5amps
1.5amps
3amps
1.5amps
1.5amps
Visual Ex.2- parallel circuit with one
load and two batteries
3amps
1
.
5
a
m
p
s
6v
1.5am
ps
1
.
5
a
m
p
s
1
.
5
a
m
p
s
1
.
5
a
m
p
s
1.5+1.5=3amps
6v
3amps
3amps
Visual Ex. 3-Circuit with multiple
loads
Amps rejoin
at junction
6 amps
3
a
m
p
s
3
a
m
p
s
6v
3
a
m
p
s
Junction: Point at
which 2 wires
meet
3amp 3
a
m
p
s
3 amps
6v
3 amp
3
a
m
p
s
3+3=6 amps
Amps split at
junction
3 amps
Parallel Double Power Source
Resistance in a Parallel Circuit
• Total Resistance: The total resistance of a
circuit can be determined by substituting
total values of voltage and current into
Ohm’s law
• Ohms Law: Rt = Et/It where “t” represents
total
• Total resistance (Rt) is also referred to as
equivalent resistance (Req) .
Resistance
• In parallel circuits the equivalent
resistance will always be smaller than the
resistance of any branch
V=IxR
If voltage is constant then a
smaller R results in a higher I
V=IxR
Resistance: Resistors of Equal Values
Req = R/N where:
Req = Equivalent parallel resistance
R = Ohmic value of one resistor
N = Number of resistors
Resistance: Resistors of unequal
values
• Simplify: Rt = 1 / (1/R1+1/R2+….1/Rn)
Resistance
example 1
•
•
•
•
R1 = 20 ohms
R2 = 30 ohms
R3 = 40 ohms
Use the equation:
20Ω
30Ω
40Ω
Rt =
1/(1R1+1/R2+….1/Rn)
• Substitute:
Rt = 1/(1/20+1/30+1/40)
• Rt= 9.23 ohms
9.23Ω
Resistance
example 2
Original Circuit
R1
20 ohms
R2
30 ohms
Equivalent Circuit
Example: R1 = 20
R2 = 30
Find Req = ?
Equivalent resistance:
Rt = 1/ (1/R1+1/R2)
Req
Rt = 1 / (1/20 + 1/30)
12 ohms
Rt = 12 ohms
Parallel Power Source
Characteristics in a Parallel Circuit
• Parallel Power supplies provide a higher current
capacity. (amps add up) Yet the voltage stays
the same throughout the circuit
• In parallel connection, all positive cell electrodes
are connected to one line, and all negative
electrodes are connected to one line. No more
than one cell is connected between the lines at
any one point.
• The only amps discharged from a battery are the
amps required for a load. This occurs even
though the battery is capable of outputting more.
In Conclusion:
Rules for Solving Parallel D-C Circuits
1. The same voltage exists across each branch
of a parallel circuit and is equal to the source
voltage.
2. The total current of a parallel circuit is equal to
the sum of the currents of the individual
branches of the circuit.
3. The total resistance of a parallel circuit is equal
to the reciprocal of the sum of the reciprocals
of the individual resistances of the circuit.