This document discusses series circuits and Kirchhoff's voltage law. It begins by introducing direct current and resistance in series circuits. It then explains that the total resistance of components in series is the sum of the individual resistances. Kirchhoff's voltage law states that the algebraic sum of the potential rises and drops around any closed loop is equal to zero. This means that the applied voltage in a series circuit equals the sum of the voltage drops across the individual elements. The document provides examples of applying Kirchhoff's voltage law to solve for voltages in series circuits.

1. Electrical circuits
ELE 111
Lecture-3
Series Circuits-Kirchhoff’s Voltage Law
Prof. Dr. Tarek Haweel

2. Introduction
Two types of current are readily available, direct current
(dc) and sinusoidal alternating current (ac)
We will first consider direct current (dc)
Insert Fig 5.1

3. Introduction
If a wire is an ideal conductor, the potential difference
(V) across the resistor will equal the applied voltage of
the battery.
V (volts) = E (volts)
Current is limited only by the resistor (R). The higher the
resistance, the less the current.

4. Series Resistors

5. Series Resistors
The total resistance of a series
configuration is the sum of the resistance
levels.
The more resistors we add in series, the
greater the resistance (no matter what
their value).
N
T R
R
R
R
R
R 




 ...
4
3
2
1

6. Series Resistors

7. Series Resistors
When series resistors have the same value,
Where N equals the number of resistors in the
string.
The total series resistance is not affected by the
order in which the components are connected.
NR
RT 

8. Series Resistors

9. Series Resistors

10. Series Circuits

11. Series Circuits

12. Series Circuits

13. Series Circuits
Total resistance (RT) is all the source
“sees.”
Once RT is known, the current drawn
from the source can be determined
using Ohm’s law:
Since E is fixed, the magnitude of the
source current will be totally
dependent on the magnitude of RT .
T
s
R
E
I 

14. Series Circuits

15. Series Circuits

16. Series Circuits

17. Series Circuits
The polarity of the voltage across a resistor is
determined by the direction of the current.
When measuring voltage, start with a scale that will
ensure that the reading is lower than the maximum
value of the scale. Then work your way down until a
reading with the highest level of precision is made.
3
3
2
2
1
1 IR
V
IR
V
IR
V 



18. Power Distribution in a Series Circuit

19. Power Distribution in a Series Circuit

20. Power Distribution in a Series Circuit

21. Power Distribution in a Series Circuit

22. Voltage Sources in Series
Voltage sources can be connected in series to
increase or decrease the total voltage applied to
the system.
Net voltage is determined by summing the
sources having the same polarity and subtracting
the total of the sources having the opposite
polarity.

23. Voltage Sources in Series

24. Voltage Sources in Series

25. Kirchhoff’s Voltage Law
Kirchhoff’s voltage law (KVL) states that the
algebraic sum of the potential rises and drops
around a closed loop (or path) is zero.

26. Kirchhoff’s Voltage Law
The applied voltage of a series circuit equals the sum of
the voltage drops across the series elements:
 The sum of the rises around a closed loop must equal the sum of
the drops.
 The application of Kirchhoff’s voltage law need not follow a path
that includes current-carrying elements.
 When applying Kirchhoff’s voltage law, be sure to concentrate on
the polarities of the voltage rise or drop rather than on the type of
element.
 Do not treat a voltage drop across a resistive element differently
from a voltage drop across a source.

  drops
rises V
V

27. Kirchhoff’s Voltage Law

28. Kirchhoff’s Voltage Law

29. Kirchhoff’s Voltage Law

30. Kirchhoff’s Voltage Law

31. Kirchhoff’s Voltage Law

32. Kirchhoff’s Voltage Law

33. Kirchhoff’s Voltage Law