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Series Parallel Circuits
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Introduction to Combination Circuits
Advantages of Series Circuits
 A series circuit may be used to connect small voltages
to obtain high voltages.
 High voltages may be reduced by connecting
resistances in series.
 Series circuits provide a means for reducing and
controlling the current by connecting resistances in
series.
 Series circuits are used where different voltage drops
and a constant current are needed.
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Disadvantage of Series Circuits
 Since the current is constant in a series circuit we
are forced to use only those devices which
require the same current.
 If any part of a series circuit should burn out it
would cause an open circuit and put the entire
circuit out of operation.
 Series circuits are used where different voltage
drops and a constant current are needed.
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Advantages of Parallel Circuits
 If a break should occur in any branch of a parallel
circuit, it would not affect the other branch circuits.
 Any device may be operated independently of any
other device.
 In a parallel circuit, more branches (devices) may
be added at any time.
Disadvantages of Parallel Circuits
 As more devices are added more current is drawn till
eventually the fuse blows.
 Parallel circuits are used where a constant voltage
and a large current are required.
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Combination Circuits
 If we combine series circuits with parallel circuits, we
produce a combination circuit.
 A combination circuit makes it possible to obtain the
different voltages of a series circuit and the different
currents of a parallel circuit.
 Simple combination circuits are of two types.
1. A parallel-series circuit in which one or more groups of
resistances in series are connected in parallel.
2. A series-parallel circuit in which one or more groups of
resistances in parallel are connected in series.
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General Method for Solving Combination
Circuits
1. A group of resistances is a simple combination of two or
more resistances which are arranged in either simple
series or simple parallel circuits. Identify these groups.
2. Every group must be removed from the circuit as a unit
and replaced by a single resistor which offers the
identical resistance. This equivalent resistance is the
total resistance of the group.
Continued
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General Method for Solving Combination
Circuits
3. Redraw the circuit, using the equivalent resistance
in place of each group.
4. Solve the resulting simple circuit for all missing
values.
5. Go back to the original circuit to find the voltage,
current, and resistance for each resistance in the
circuit.
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Solving Parallel-Series Circuits
Example
Two groups of resistors are Group A (that has 10-,
and 50  resistors connected in series) and Group
B (that has two 30  resistors connected in
series). Find all the missing values connected in
parallel across a 120 V source of voltage, current,
and resistance.
Continued
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Solution
1. Identify groups A and B as series circuits.
2. Find the equivalent resistance of each group.
3. Since the resistors of groups A and B are in series.
RA = R1 + R2
RA = 10 + 50 = 60 
Ans.
RB = R3 + R4
RB = 30 + 30 = 60 
Ans.
Continued
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Solution
4. Redraw the circuit, using these 60  resistors in
place of the series groups.
5. Solve the new parallel circuit.
Find the voltage for each group.
VT = VA = VB = 120 V
Ans.
Find the current in each group:
VA = IA x RA
120 = IA x 60
IA = 120/60 = 2 A Ans.
VB = IB x RB
120 = IB x 60
IB = 120/60 = 2 A Ans.
Continued
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Find the total current IT.
IT = IA + IB
IT = 2 + 2 = 4 A
Ans.
Find the total resistance RT.
VT = IT x RT
120 = 4 x RT
RT = 120/4 = 30 
Ans.
6. Go back to the original circuit to find the voltage
and current for each resistor. Find the current in
each resistor.
IA = I1 = I2 = 2 A
Ans.
IB = I3 = I4 = 2 A
Ans.
Continued
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Find the voltage drop across each resistor.
V1 = I1 x R1
V1 = 2 x 10
V2 = I2 x R2
V1 = 20 V
V2 = 100 V
V3 = I3 x R3
V3 = 2 x 30
V4 = I4 x R4
V3 = 60 V
V4 = 60 V
V2 = 2 x 50
V4 = 2 x 30
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Solving Series-Parallel Circuits
Example
A resistor R1 = 10  is in series with two parallel
resistors R2 = 40  and R3 = 60 . The three
resistors are connected across a voltage source
of 34 V. Find all the values of voltage, current,
and resistance.
Continued
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Solution
1. Find the resistance of the parallel group A (R2 and R3).
2. Since R2 and R3 are in parallel,
RA = (R2 x R3)  (R2 + R3)
RA = (40 x 60)  (40 + 60) = 24  Ans.
3. Redraw the circuit using this 24  resistor RA in
place of the parallel combination.
4. Solve the new series circuit. Find the total resistance
RT.
RT = R1 + R4
RT = 10 + 24 = 34  Ans.
Continued
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Find the total current IT.
VT = IT x RT
34 = IT x 34
IT = 34/34 = 1 A
Ans.
Find the current in each part of the series circuit.
IT = I1 = IA = 1 A
Ans.
Find the voltage in each part of the series circuit.
VA = IA x RA
V1 = I1 x R1
VA = 1 x 24 = 24 V Ans.
V1 = 1 x 10 = 10 V Ans.
Continued
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5. Go back to the parallel group A to find V, I, and R
for each resistance in the group. Since VA
represents the total voltage of the parallel group A.
VA = V2 = V3 = 24 V
Find the current in each resistor of group A.
V2 = I2 x R2
V3 = I3 x R3
24 = I2 x 40
24 = I3 x 60
I2 = 24/40 = 0.6 A
I3 = 24/60 = 0.4 A
6. Check:
IT = I 2 + I3
IT = 0.6 + 0.4
1=1
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End of Lesson
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