Basic elements of electric circuits PhDr. Michal Trnka, PhD. ÚLFBFIaTM LF UK v Bratislave michal.trnka@fmed.uniba.sk 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.
Content Electric quantities basic terms and laws Measurement of electric quantities Elements of electric circuit 2
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) Q I = t Q C = = t s André-Marie Ampère 1775-1836 3 I [I ]= A (ampere)
Kirchhoff s laws I 1 st Kirchhoff s law Algebric sum of currents in a nodal point of net is zero: n k = 1 I k = 0 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 I 1 I 2 = 0 For the chosen node B: +I 1 + I 2 I = 0 Gustav Robert Kirchhoff 1824-1887 4
Kirchhoff s laws II 2 nd Kirchhoff s law Potential drop on resistors in any loop of the net equals the sum of electromotoric potentials of sources: n m R I = U k k ej k = 1 j = 1 For chosen circuit branches: R 1 I 1 = U e R 2 I 2 = U e 5
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 R 1 G I = G U = G = S ( siemens ) Werner von Siemens 1816-1892 6
Electric resistance Electric resistance Physical quantity expressing ability of materials to obstruct passing of electrically charged particles R = U I 1 G = R = = Ω ( ) 1 R V A ohm Georg Simon Ohm 1789-1854 7
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 I = U R Fig. 2: Electric scheme of a circuit expressing the Ohm s law. Relation among voltage (U), resistance (R) and current (I). Georg Simon Ohm 1789-1854 8
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] 9
Electric impedance II Impedance (Z) has two compounds: Resistance (R): real compound Capacitance (X c ): imaginary compound Z = R 2 + X 2 C 10
Electric capacity Electric capacity (C) Passive electric quantity Expresses ratio of electric charge and electric voltage on a capacitor C Q = C = F ( farad ) U Michael Faraday 1791-1867 11
Inductance Inductance (L) Passive electric quantity Expresses dependence of magnetic flow oo electric current L Φ = L = H ( henry ) I L = inductance (H) Φ = magnetic flow (Wb) I = intensity of current (A) Joseph Henry 1797-1878 12
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: 2 2 U W = U I t W = R I t W = t R 13
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 14
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] 15
Measurement of electric current III Shunt Fig. 5: Shunt [www.elektrika.cz] Fig. 6: Analogue ammeter Fig. 7: Measurement of electric current by digital ammeter [www.allaboutcircuits.com] 16
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 17
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 18
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 Fig. 11: Measurement of electric voltage using a digital voltmeter [www.allaboutcircuits.com] 19
Elements of an electric circuit and their signs 20
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: 21
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 = U 1 + U 2 + U 3 R = R 1 + R 2 + R 3 22
Connection of resistors II 2. Parallel connection of resistors 0 = I - I 1 - I 2 - I 3 I = I 1 + I 2 + I 3 1 1 1 1 = + + R R R R 1 2 3 G = G 1 + G 2 + G 3 23
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: 24
Connection of capacitors I Connection of capacitors serial All capacitors have equal charge Q Total voltage of capacitors is: o U = U 1 + U 2 + U 3 + + U n Voltage on individual capacitors: o Q Q Q Q U 1 =, U 2 =, U 3 =,..., U n = C C C C 1 2 3 25 n
Connection of capacitors II Connection of capacitors parallel There is equal voltage U on all capacitors Capacitors have different charges for different capacities: o Q 1 = C 1 U, Q 2 = C 2 U, Q 3 = C 3 U,, Q n = C n U Total charge Q: o Q = Q 1 + Q 2 + Q 3 + + Q n 26
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 W = E = 2 We can obtain following variations of relation for work: 1 1 2 W = Q U = C U 2 2 27 Q C 2
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 Sign: 28
Diode Diode Semi-conductor electronic component It conducts electric current only in one direction rectifies the current Composition: cathode anode Sign: 29
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: 30
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 31