Series Parallel Circuits

1

• Series Parallel Circuits

Benchmark Companies Inc PO Box 473768 Aurora CO
80047
2
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.

3
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.

4
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.

5
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.

6

• 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
7
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.

8
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
9
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
10
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
11
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
12
Find the voltage drop across each resistor.

• V2 I2 x R2
• V2 2 x 50
• V2 100 V

V1 I1 x R1 V1 2 x 10 V1 20 V
V4 I4 x R4 V4 2 x 30 V4 60 V
V3 I3 x R3 V3 2 x 30 V3 60 V
13
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
14
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
15
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 VA 1 x 24 24 V Ans.
V1 I1 x R1 V1 1 x 10 10 V Ans.
Continued
16
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 24 I2 x 40 I2 24/40 0.6 A
V3 I3 x R3 24 I3 x 60 I3 24/60 0.4 A
6. Check IT I2 I3
IT 0.6 0.4
1 1
17

• End of Lesson