1. 8 Series Circuits UEENEEE104A DC CIRCUITS PURPOSE:
This section introduces the series circuit and the basic laws applicable to series circuits. 8
TO ACHIEVE THE PURPOSE OF THIS SECTION:
At the end of this section the student will be able to:
Define what is meant by the term series circuit and draw circuit diagrams of series connected components.
State the basic laws related to current, voltage, power and equivalent resistance for series connected resistive circuits.
Simplify a series circuit to one containing a single equivalent resistance.

2. Calculate circuit current, applied voltage, equivalent resistance and total power dissipation for a series circuit.
Calculate the voltage drop, current and power dissipation for each resistor in a series circuit.
List the affects of an open circuit and a short circuit on the current flowing in a series circuit. L

3. Electrical Principles BY PETER PHILLIPS
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REFERENCES:
Electrical Principles BY PETER PHILLIPS L

4. 1.WHAT IS A SERIES CIRCUIT?
Series circuit - a circuit in which all components are connected so as to allow only one
path for current to flow.
Switch and Lamp in series
Lamps in series
Figure 1 L

5. + - 2.CURRENT FLOW IN A SERIES CIRCUIT
A series circuit has only one current path, therefore there is only ______________________.
one current R1 + IT I1 R2 I2 R3 - I3
Figure 2
Therefore, the basic rule relating to current in a series circuit states -
same
The current in a series circuit is the _________________ in all parts of the circuit. L

6. Based on the arrangement shown in figure 2, the current in various parts of a series circuit may be expressed mathematically as -
IT = I1 = I2 = I3
where: IT = supply current
I1 = current through resistor R1
I2 = current through resistor R2
I3 = current through resistor R3 L

7. + - 3. RESISTANCE OF A SERIES CIRCUIT
Consider three resistors connected in series. R1 + R2 - R3
Figure 3
As current flows through the circuit it passes through each resistor in turn. That is, the total resistance seen by the power supply will be the combination of all resistances.
Therefore, the basic rule relating to resistance in a series circuit states -
sum
The equivalent or total resistance is equal to the __________ of the individual resistances. L

8. RT = R1 + R2 + R3 RT = R1 + R2 + R3 = 5 + 4 + 11 = 20 Ω
This statement may be expressed mathematically as -
RT = R1 + R2 + R3
where: RT = total circuit resistance
R1 = resistance of resistor R1
R2 = resistance of resistor R2
R3 = resistance of resistor R3
Example: 1
Three resistors having resistances of 5Ω, 4Ω and 11Ω are connected in series. Calculate the total resistance of the circuit.
RT = R1 + R2 + R3 =
= 20 Ω L

9. Example: 2
Determine the resistance of the resistor R2 in the circuit of figure 4. R1 +
35 Ω R2
RT = 75 Ω
22 Ω - R3
RT = R1 + R2 + R3
R2 = RT - R1 – R3
Figure 4
R2 = RT - R1 - R3 =
= 18 Ω L

10. R = V I = V I V = I R R 4. OHM'S LAW AND THE SERIES CIRCUIT
As seen previously, values of voltage, current and resistance may be determined by the application of Ohm's law. The three equations associated with Ohm's law are -
I = V R
R = V I
V = I R
As is the case with the basic electric circuit, Ohm's law may be applied to a series circuit to determine values of voltage, current and resistance.
Ohm's law may be applied to –
an entire series circuit - using total circuit values, for example,
any individual section of a series circuit - using section values, for example, L

11. + RT = R1 + R2 + R3 = 50 + 20 + 30 = 100 Ω - I = V = 200 = 2 A R 100 +
Example: 3
For the circuit of figure 5, determine -
(a) total circuit resistance
(b) circuit current R1 +
50 Ω R2
VT = 200 V
20 Ω
RT = R1 + R2 + R3 =
= 100 Ω
30 Ω - R3
I = V = 200 = 2 A R
Figure 5
Example: 4
Determine the voltage across resistor R2 in the circuit of figure 6. R1 +
IT = 1.5 A
V = I R2
V = I R2
= 1.5 x 40
= 60 V
40 Ω R2 - R3
Figure 6 L

12. + - 5. VOLTAGES IN A SERIES CIRCUIT V1
Consider the circuit shown in figure 7. V1 R1 +
IT = 1 A
10 Ω
6 Ω V2 VT R2
4 Ω - R3 V3
Figure 7
Assuming the current flowing in the circuit and the value of the individual resistances are known,the voltages across each resistor may be determined.
These voltages are known as the circuit ________________________________________.
The circuit voltage drops may be determined by applying Ohm's law to each resistor individually.
voltage drops L

13. The voltage drop across the resistor R1 is determined by applying Ohm's law using only values associated with R1 -
V1 = I R1 = 1 x 10 = 10 V
The voltage drop across the resistor R2 is determined by applying Ohm's law using only values associated with R2 -
V2 = I R2 = 1 x 6 = 6 V
The voltage drop across R3 is determined in the same way, but using only values associated with R3 -
V3 = I R3 = 1 x 4 = 4 V
If each of the individual voltage drops are known, the applied voltage may be determined.
The rule for voltages in a series circuit, known as Kirchhoff's voltage law, is -
The applied voltage is equal to the _________________ of the individual voltage drops..
sum L

14. VT = V1 + V2 + V3 This statement may be expressed mathematically as -
where: VT = the applied voltage
V1 = the voltage drop across resistor R1
V2 = the voltage drop across resistor R2
V3 = the voltage drop across resistor R3 L

15. For the series circuit shown in figure 8, determine -
Example: 5
For the series circuit shown in figure 8, determine -
(a) total circuit resistance
(b) the voltage drop across each resistor
(c) the supply voltage. R1
(a)
RT = R1 + R2 + R3 =
= 33.6 Ω
IT = 0.6 A
5.6Ω VT
10Ω R2
18 Ω
(b)
V1 = I R1 = 0.6 x 5.6 = 3.36V R3
V2 = I R2 = 0.6 x 10= 6 V
V3 = I R3 = 0.6 x 18 = 10.8V
Figure 8
VT = V1 + V2 + V3 =
= V
(c) L

16. Example: 6
Determine the voltage drop across the resistor R3 in the circuit of figure 9. R1
16 V
VT = V1 + V2 + V3
V3 = VT - V1 – V2
VT = 32 V
7 V R2 R3
V3 = VT - V1 – V2
= 32 –
= 9 V
Figure 9 L

17. + - 6. VOLTAGE DIVIDER CIRCUIT
The voltage drop across a particular resistor in a series circuit may be determined using the voltage divider. The advantage of the voltage divider is that voltage drops may be determined without knowing the circuit current. The basic arrangement for the voltage divider is shown in figure 10. + R1 VT R2 V2 -
Figure 10
Example: 7
For the circuit of figure 10, assume the supply voltage is 10V, R1 has a value of 1kΩ and R2 a value of 3kΩ. Determine the voltage drop across the resistor R2. L

18. PT = P1 + P2 + P3 7. POWER IN A SERIES CIRCUIT
Each component in a series circuit dissipates power and the total power delivered to a circuit is supplied by the circuit power supply. Therefore, it can be stated -
sum
The total power supplied to a series circuit is equal to the ____________ of the
powers dissipated by each component.
Writing this statement in the form of an equation gives -
PT = P1 + P2 + P3
where: PT = total power dissipated
P1 = power dissipated by component 1
P2 = power dissipated by component 2
P3 = power dissipated by component 3 L

19. + - Example: 8 For the circuit shown in figure 11, calculate the -
(a) circuit current
(b) total circuit resistance
(c) voltage drop across R1
(d) applied voltage
(e) power dissipated by each resistor
(f) total power dissipated + R1
150Ω VT R2
50 V
100 Ω -
Figure 11
I = V2 R2
= 50
100
= 0.5A
(a)
(d)
VT = V1 + V2 =
= 125 V
(e)
(f)
PT = P1 + P2 =
= 62.5 W
P1 = V1 x I
=75 x 0.5
= 37.5W
(b)
RT = R1 + R2 =
= 250 Ω
P2 = V2 x I
=50 x 0.5
= 25W
(c)
V1 = I x R1
=0.5 x 150
= 75 V L

20. + + - - 8. EFFECT OF AN OPEN CIRCUIT IN A SERIES CIRCUIT
Consider three lamps connected in series, as shown in figure 12. What would be the effect on the circuit of say lamp 2 going open circuit?
Lamp 1
Lamp 1 + - + -
Open circuit
Lamp 2
Lamp 3
Lamp 3
Figure 13
Figure 14
The open circuit would cause the circuit current to _____________________________.
Drop to zero L

21. The effects of an open circuit in any part of a series circuit are –
circuit current is ________________
the resistance of the circuit is ________________
the voltage across the open circuit equals the _____________________
the voltage across all other components equals _________________
all components in the circuit _______________ working.
zero
infinite
supply volts
zero
stop
9. EFFECT OF A SHORT CIRCUIT IN A SERIES CIRCUIT
Consider three lamps connected in series, as shown in figure 14. What would be the effect on the circuit of say lamp 3 going short circuit? L

22. + + - - Lamp 1 Lamp 1 Short circuit Lamp 2 Lamp 2 Lamp 3 Lamp 3
Figure 14
Figure 15
The short circuit would cause the circuit current to _____________________________.
increase
The effects of a short circuit in any part of a series circuit are –
circuit current is ________________
the resistance of the circuit is ________________
the voltage across the short circuit equals _____________________
the voltage across all other components _________________
all components in the rest of the circuit work _______________ because of the
increased voltage drop across them.
increased
decreased
Zero volts
increases
harder L

23. Equations lesson 7 Series Circuit IT = I1 = I2 = I3 RT = R1 + R2 + R3
VT = V1 + V2 + V3 L

24. The End