Our physical world may be interpreted in terms of matter and energy, both of which exist in a variety of forms.
Matter has been defined as anything that occupies space and possesses mass.
Energy is the ability to do work.
In the 18th Century, Benjamin Franklin introduced the term charge and Charles Coulomb his law and terms: electricity, electric or electrostatic field.
Charge is the fundamental unit of matter responsible for electric phenomena.
There are two kinds of charge, positive and negative, Q denotes a positive and fixed charge, while q or denotes a positive and time-varying charge.
Capital letters are used to denote constant (in time) variables, while small letters are used to denote time-varying variables.
Coulomb [C] is the unit of charge, the accumulated charge on electrons equals 1 [C].
Electricity are physical phenomena arising from the existence of interaction of charges.
Electric field is a region in space wherein a charge, a test charge Q, experiences an electric force F [N]. e
Electric field between two fixed unlike charges is presented in Fig. 1.1.1. Path along which a test charge Q moves when attracted by one charge and repelled by the other is called the electric line of force. Since a basic phenomenon of charge is that like charges repel and unlike charges attract, then, the direction of lines of force is always from the positive charge to the negative charge.
Electric field is uniquely defined in its every point by electric field intensity.
) (t q
1018
24145 .
6
Electric field intensity is defined as the electric force per unit charge at a particular point of space.
e/Q F
K (1.1.1)
Its unit is [N/C]=[V/m].
Fig. 1.1.1 Electric field between two unlike charges with three electric lines of force denoted
Next, work required to move a test charge Q from point A to point B, as shown in Fig. 1.1.2, will be considered.
Fig. 1.1.2 Two paths between points A and B located in an electric field
B
A
B
A
AB F dl Q Kdl
W e (1.1.2)
Joule [J] is the unit of this work. The work performed along a closed path (loop) ACBDA is equal zero.
ACBDA 0
W (1.1.3)
Then, work performed along the path ACB is equal to the work performed along the path ADB. In other words, only location of terminal points designates the work performed, not the path shape.
A work required to move a unit charge Q in an electric field is defined as a voltage.
B
A AB
AB W /Q Kdl
U (1.1.4)
+
C
A B
D
Q F e
In the MKS system of units, a voltage of 1[J/C] is defined to be a volt [V].
If, in an electric field, the reference point P is chosen, then, voltage between this point (node) and the other one A is called a potential or node voltage and will be denoted as
P
A AP
A U Kdl
V (1.1.5)
Consider a work performed along a closed path PABP, as shown in Fig. 1.1.3.
Fig. 1.1.3 Closed path crossing points A, B and P located in an electric field
As then, and finally:
(1.1.6) Thus, a voltage between (across) A and B, or in other words a voltage drop from A to B is also called a potential difference.
To define a flow of electric charge across any area, such as a cross-section of a wire, term of electric current, or simply current is introduced.
A net flow of a charge past a given point, per unit time is defined as electric current. In the MKS system, the unit of current is an ampere [A]=[C/s].
There are two important current types:
direct current (dc),
alternating current (ac).
If a force that moves a charge along a wire is constant, then, the rate of charge transferred is constant and the direct current (dc) can be defined:
(1.1.7a)
AP 0
BP AB
PABP W W W
W
BP AP
AB W W
W
B A
AB V V
U
t Q I /
A B
P
If a rate of flow of charge is varying in time, then, the instantaneous current can be defined:
(1.1.7b) Periodic current is the special case. In this case, the instantaneous value of a waveform changes periodically, through negative and positive values. Sinusoidal current, so called alternating current (ac) is the most important case.
Finally, electric power and electric energy delivered to/supplied by a single element or whole (sub)circuit will be discussed.
Power is the time rate of expending or absorbing energy:
, (1.1.8)
dw is the unit energy in joules and dt is the unit time in seconds. Then, p is the instantaneous power measured in watts [W]=[J/s]. A power associated with a current flow through an element/subcircuit is:
(1.1.9a) As can be seen, the instantaneous power absorbed/supplied by element/subcircuit is simply a product of a voltage across this element/subcircuit and a current flowing through the element/subcircuit.
For the dc case:
(1.1.9b) From (1.1.8), the unit energy:
(1.1.10) Then, the total energy absorbed/supplied within a time interval from to arbitrary time instant t is:
(1.1.11a) For the particular , the total energy absorbed/supplied is:
(1.1.11b) Electric energy absorbed by an element/subcircuit is dissipated as a heat. Such thermal energy , in calories [cal], can be converted from electric energy:
(1.1.12) dt
dq i t
i( ) /
dt dw p /
dt ui dq dq
p dw
I U P
dt p dw
0 0 t
t pdt w
0
T t
T
T pdt
W
0
wth
w wth 0.239
Drill problems 1.1
1. A constant current of 2 A flows through an element. The energy to move the current for 1 second is 10 joules. Find the voltage across the element.
2. Find the energy required to move 2 coulombs of charge through 4 volts.
3. A constant current of I=10 A is delivered to an element for 5 seconds. Find the energy required to maintain a voltage of 10 V.
4. Voltage of energy absorbing element is constant, and its current rises linearly from 0 to 2 mA within period of 2 s, and then, remains constant. Find the absorbed energy during the period of 5 s.
5. When fully charged, a car 12 V battery stored charge is 56 A∙h. How many times car can be started if each attempt lasts 10 s and draws 30 A of current from the battery ?
The power absorbed by a circuit element is shown. At what time is the net energy absorbed a maximum, at what time is the net energy supplied a maximum, at what time the net energy is zero ? Is the total net energy (for the whole period of time) absorbed or supplied?
Fig. P.1.1.6
6. An element absorbs energy as shown. If the current entering its terminal is mA, find the element voltage at ms and ms.
Fig. P.1.1.7
7. A small 1.5-volt alkaline (AA) battery has a nominal life of 150 joules. For how many minutes will it power a calculator that draws a 2 mA current ?
V
10
U u
t i10
1
t t 5
w mJ 15 10
2 6 t ms p W
1 2 3 4 t s 1
−1
8. A CD player uses four AA batteries in series to provide 6 V to the player circuit. Each battery stores 50 watt-seconds of energy. If the player is drawing a constant 10 mA from the battery pack, how long will the player operate at nominal power ?
9. A circuit element with a constant voltage of 4 V across it dissipates 80 J of energy in 2 minutes. What is the current through the element ?