Download Basic elements of electric circuits

KEGA 004UK-4/2011
Basic elements of
electric circuits
PhDr. Michal Trnka, PhD.
ÚLFBFIaTM LF UK v Bratislave
[email protected]
The presentation is a part of the project KEGA 004UK-4/2011 (MESR&S SR):
„Electromagnetic biosignals and electromagnetic radiation – electronic education of
Medical Biophysics (creation of e-learning courses)“
Principal investigator: Assoc. Prof. Katarína Kozlíková, RN., PhD.
KEGA 004UK-4/2011
Content
Electric quantities ─ basic terms and laws
Measurement of electric quantities
Elements of electric circuit
© Michal Trnka, 2011
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Electric current in an electric circuit
Electric current
–
Directed flow of electrically charged particles in a conductor
–
It is expressed by amount of electric charge dQ passing
through cross-section of the conductor during elementary
time interval dt.
Fig. 1: Scheme of expression of an
amount of electric charge passing through
conductor (S – area of conductor)
© Michal Trnka, 2011
∆Q
I =
∆t
Q  C
=
I  =
s
t 
[I ]= A (ampere)
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André-Marie Ampère
1775 - 1836
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Kirchhoff’s laws I
1st Kirchhoff’s law
n
–
Algebric sum of currents in a nodal point of net is zero:
Ik
∑
k
=0
=1
where n number of currents in the node
(currents entering the node are considered positive, currents leaving the node negative)
For the chosen node A:
+I – I1 – I2 = 0
For the chosen node B:
+I1 + I2 – I = 0
© Michal Trnka, 2011
2011/12 Basic elements of electric circuits
Gustav Robert Kirchhoff
1824 - 1887
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Kirchhoff’s laws II
2nd Kirchhoff’s law
–
Potential drop on resistors in any loop of the net
equals the sum of electromotoric potentials of sources:
n
m
Rk ⋅ I k = ∑U ej
∑
k
j
=1
=1
For chosen circuit branches:
R1 · I1 = Ue
R2 · I2 = Ue
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Electric conductivity
Electric conductivity (G)
– Expresses ability of a conductor to conduct electric
current
– Expresses
amount
of
current
passing
through
a conductor at unit voltage on its ends
I = G ⋅U
R =
© Michal Trnka, 2011
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G
G  = S ( siemens )
Werner von Siemens
1816 - 1892
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Electric resistance
Electric resistance
– Physical quantity expressing ability of materials to
obstruct passing of electrically charged particles
U
R =
I
1
G
=R
R  = V ⋅ A −1 = Ω (ohm )
Georg Simon Ohm
1789 - 1854
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Ohm’s law
Ohm’s law:
– Electric current passing through closed electric circuit is
directly proportional to voltage of the source and
inversely proportional to electric resistance of the circuit
U
I =
R
Fig. 2: Electric scheme of a circuit expressing the Ohm’s law.
Relation among voltage (U), resistance (R) and current (I).
© Michal Trnka, 2011
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Georg Simon Ohm
1789 - 1854
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Electric impedance I
Impedance (Z)
– Apparent resistance of electrotechnical element
– Characterizes properties of the element for
alternating current
– Basic property we need to know to analyze
alternating electric circuits
– Unit: Ohm [Ω]
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Electric impedance II
Impedance (Z) has two compounds:
– Resistance (R): real compound
– Capacitance (Xc): imaginary compound
Z = R + XC
2
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Electric capacity
Electric capacity (C)
– Passive electric quantity
– Expresses ratio of electric charge
and electric voltage on a capacitor
Q
C =
U
C  = F (farad )
Michael Faraday
1791 - 1867
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Inductance
Inductance (L)
– Passive electric quantity
– Expresses dependence of magnetic flow
oo electric current
L=
Φ
I
L  = H ( henry )
L = inductance (H)
Φ = magnetic flow (Wb)
I = intensity of current (A)
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Joseph Henry
1797 - 1878
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Work of constant
electric current
In an external part of electric circuit, electric
forces perform work (W) to transfer charge (Q)
W = Q ⋅U
–
Using different expression of individual quantities we can
obtain following relations for work of electric current:
W = U ⋅ I ⋅t
© Michal Trnka, 2011
W = R ⋅ I 2 ⋅t
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U2
W =
⋅t
R
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Measurement of electric current I
Electric current is measured by a device called –
ammeter
– Ammeter is connected serially, so that all measured
current flow through it
Fig. 3: Scheme of ammeter connection in an electric circuit
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Measurement of electric current II
Measurement
range
of an ammeter can be
increased by set of parallely connected shunts
(resistors) directly in the device
Fig. 4: Measurement of electric current – left is a sign for an
ammeter, right scheme of a shunt [Kukurová, 2007]
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Measurement of electric current III
Shunt
Fig. 5: Shunt [www.elektrika.cz]
Fig. 6: Analogue ammeter
Fig. 7: Measurement of electric current
ammeter [www.allaboutcircuits.com]
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by
digital
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Measurement of electric voltage I
Electric voltage is measured by – voltmeter.
Voltmeter is connected to the source of measured
voltage parallely.
Fig. 8: Scheme of connection of a voltmeter in an electric circuit
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Measurement of electric voltage II
Measurement of electric voltage
– Current passing through the device is proportional to
measurement voltage
– For higher voltage corresponding with current than value
of basic range, we input so called current limiting resistor
serially with the voltmeter
– We can change the measurement range by a system of
switchable current limiting resistors
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Measurement of electric voltage III
Fig. 9: Measurement of electric voltage – left is a sign for voltmeter,
right scheme of current limiting resistor [Kukurová, 2007]
Fig. 10: Analogue voltmeter
© Michal Trnka, 2011
Fig. 11: Measurement of electric voltage
using a digital voltmeter
[www.allaboutcircuits.com]
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Elements of an electric circuit and
their signs
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Resistor
Resistor
–
Passive, linear electronic element, in which electric
energy changes to heat and which has the only,
constant parameter - electric resistance
Function:
–
Limits current flowing through the circuit and
decreases voltage in the circuit when loaded
Sign:
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Connection of resistors I
We can regulate current flowing through
individual parts of a circuit by resistors
– (higher resistance – smaller current and opposite)
Different values of resistance can be achieved by connection of resistors
1. Serial connection of resistors
U = U1 + U2 + U3
R = R1 + R2 + R3
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Connection of resistors II
2. Parallel connection of resistors
0 = I - I1 - I 2 - I 3
I = I1 + I 2 + I 3
1
R
=
1
R1
+
1
R2
+
1
R3
G = G1 + G2 + G3
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Capacitor
Capacitor
– Passive element of a circuit, in which energy of
electric field is accumulated without heat losses
– It has one, constant parameter - electric
capacity
Sign:
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Connection of capacitors I
Connection of capacitors – serial
– All capacitors have equal charge Q
– Total voltage of capacitors is:
o U = U1 + U2 + U3 + … + Un
– Voltage on individual capacitors:
o U = Q , U = Q , U = Q , ..., U = Q
1
2
3
n
C1
C2
C3
Cn
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Connection of capacitors II
Connection of capacitors – parallel
– There is equal voltage U on all capacitors
– Capacitors have different charges for different
capacities:
o Q1 = C1·U, Q2 = C2·U, Q3 = C3·U, …, Qn = Cn·U
– Total charge Q:
o Q = Q 1 + Q 2 + Q3 + … + Q n
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Energy of a charged capacitor
When a capacitor is being charged or discharged,
electric charge moves in electric field, thus electrostatic
forces perform work
During charging, the capacitor obtains energy, during
discharging it losses energy
Total electric work during discharge of a capacitor is:
1 Q 2
W = E =
2 C
We can obtain following variations of relation for work:
W
© Michal Trnka, 2011
1
1
=
Q ⋅U = C ⋅U
2
2
2
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Coil
Coil
–
Passive electric element, in which energy of magnetic
field is accumulated without heat losses
–
It has one, constant parameter - inductance
Usage:
–
Electromagnet
–
Inductor
–
In transformers
© Michal Trnka, 2011
Sign:
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Diode
Diode
–
Semi-conductor electronic component
–
It conducts electric current only in one direction –
rectifies the current
Composition:
–
cathode
–
anode
Sign:
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Transistor
Transistor
–
Semi-conductor component
–
Basic property – amplification ability
–
Basic part of integrated circuits
–
Based on three areas of semi-conductor crystal:
• Emitter
• Base
• Collector
–
According to type of conductivity we differ PNP and NPN
Sign:
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Literature
ČIČMANEC, P. Všeobecná fyzika 2: Elektrina a magnetizmus.
Bratislava : UK, 2001. 617 s., ISBN 80-223-1687-3
KÚDELČÍK, J., HOCKICKO, P. Základy fyziky. Žilina : EDIS, 2011.
272 s., ISBN 978-80-554-0341-0
HERMAN, S., L. Delmar ´s Standard Textbook of Electricity. Clifton
Park, NY : Delmar, 2009. 1115 s., ISBN 978-1-111-3915-3
KUKUROVÁ, E., WEIS, M. Slovensko–anglický súbor pamäťových
máp základov fyziky & informatiky. Bratislava : Asklepios, 2007. 250 s.,
ISBN 978-80-7167-099-5
Note:
If not stated else, the author of figures is the author of the text
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