Electric current
DC Circuits
AC Circuits
Lecture questions
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Electric current
DC Circuits. Ohm's law
Resistance and conductance
Conductivity of electrolytes
Alternating current
Resistor, Capacitor and Inductor AC
Response
Impedance
Electric current
• An electric current is a directed flow of
charged particles.
• It may occur when there is a potential
difference.
• Current, and is the amount of charge
flowing through cross section of a conductor
per second.
q
I
t
dq
I
 qt
dt
I   A
Current density
I
j
S
A
 j  2
m
Direction
• For historical reasons the direction
of the current is taken to be the
direction of the flow of positive
charge.
• The flow of positive charge in one
direction is equivalent to the flow of
negative charge in the opposite
direction.
Electric current
I  q0 nvS
j  q0 nv
• q0 charge of each carrier
• n - concentration (the number of charge
carriers/cubic meter)
• v - average speed of charged particles
• S - cross sectional area of the conductor
Direct current (DC)
• DC is the unidirectional flow of electric charge.
• Galvanic current is a steady direct electric current.
• DC circuit consists of any combination of constant
voltage sources, constant current sources, and
resistors. In this case, the circuit voltages and
currents are constant, independent of time.
• Direct current is produced by sources such as batteries,
thermocouples, solar cells, and others. Direct current
may flow in a conductor such as a wire, but can also
flow through semiconductors, through a vacuum as in
electron or ion beams.
Time dependence of current (or voltage)
Ohm's Law
• deals with the relationship between voltage and
current in an ideal conductor.
• For many conductors, the electric current which
flow through them is directly proportional to the
voltage applied to them.
U
I
R
• where R is called the resistance
• Material that obeys Ohm's Law is called "ohmic"
or "linear" because the potential difference
across it varies linearly with the current
Resistance and conductance
l
R
S
where ρ is the resistivity of the material
1
G
R
G is the conductance of the conductor

1

j  E
is the conductivity of the material
This is also the form of Ohm’s law.
Conductivity of electrolytes
  q0n(b  b )
where q0 is charge of each carrier
n - concentration of electrolyte molecules (the number of
molecules/cubic meter)
α - degree of dissociation
b – is the electrical mobility of the particle is defined as
the ratio of the drift velocity to the magnitude of the
electric field
tissue
cerebrospinal fluid
blood
muscle tissue
brain and nerve
tissue
fat tissue
skin
bone without
periosteum
,   m
0.55
1.66
2
14.3
33.3
10
S
,
m
1.8
0.6
0.5
0.07
0.03
5
10
7
10
7
10
• Galvanization is a method of direct
continuous current medical use: low
voltage current (up to 80V) and small
amperage
(up
to
50mA)(partial
galvanisation: when the current impacts a
small area of the body; whole
galvanisation: when the current impacts
the entire body).
• Medicinal electrophoresis is
a
simultaneous application of direct current
(galvanic current) and small amount of
drug or combination of drugs.
Medicinal electrophoresis
• 1) possibility of effect concentration on a
surface part of body;
2) long duration of procedure action – drug
depot retains for several days;
3) exception of drug effect on alimentary
organs;
4) drug introduction into organism in the
form of ions, i.e. in active form.
Alternating current
Alternating current
• In alternating current (AC, also ac) the movement of
electric charge periodically reverses direction.
• In alternating current (AC) circuits the voltage
oscillates in a sine wave pattern, varying with time as:
U  U m sin t
where ω is the angular frequency related to the
frequency by
  2
Properties of Alternating Current
• Amplitude. Mathematically, the amplitude of a sine wave is
U
the value of that sine
wave at its peak. This is the maximum
value, positive or negative, that it can attain.
• Frequency is the number of complete cycles voltage (or
current) goes through in a unit time. The frequency of the
wave is measured in cycles per second (cycles/sec) and, in
normal usage, is expressed in units of Hertz (Hz). In North
America (primarily the US and Canada), the AC power system
operates at a frequency of 60 Hz. In Europe, including the UK,
Ireland, and Scotland, the power system operates at a
frequency of 50 Hz.
• Period is the time duration of one cycle of the waveform, and
is measured in seconds/cycle. AC power at 50 Hz will have a
period of 1/50 = 0.02 seconds/cycle. A 60 Hz power system
has a period of 1/60 = 0.016667 seconds/cycle. These are often
expressed as 20 ms/cycle or 16.6667 ms/cycle, where 1 ms is
1 millisecond = 0.001 second (1/1000 of a second).
m
Properties of Alternating Current
• Wavelength is the distance which the wave moves in one
cycle. Electrical signals travel through their wires at nearly
the speed of light, which is very nearly 3 × 108 m/s, and is
represented mathematically by the letter ‘c‘.

c

• However, when we speak of an AC power system, it is more
useful to refer to the effective voltage or current. This is the
rating that would cause the same amount of work to be done
(the same effect) as the same value of DC voltage or current
would cause. For a sine wave, the effective voltage of the AC
power system is (or 0.707 times the peak voltage). The
effective voltage is also known as the rms voltage.
U ef 
Um
2
Resistor AC Response
Capacitor AC Response
Inductor AC Response
Series Resonance
• The resonance of a series RLC circuit occurs when the
inductive and capacitive reactances are equal in magnitude
but cancel each other because they are 180 degrees apart in
phase.