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- 1. Electric Circuit Analysis Circuit elements Ahsan Khawaja Ahsan_khawaja@comsats.edu.pk Lecturer Room 102 Department of Electrical Engineering
- 2. Base Quantity SI base units Name Symbol length meter m mass kilogram kg time second s electric current ampere A temperature kelvin K amount of substance mole mol luminous intensity candela cd
- 3. Prefixes •Used to emphasize the significantly large or small numerical figures. •Some common prefixes….. - yocto y - zepto z - atto a - femto f - pico p - nano n - micro - milli m - centi c - deci d Deka da hecto h kilo k mega M giga G tera T peta P exa E zetta Z yotta Y
- 4. Charge • In SI system, charge is measured in coulombs (C). • The charge on an electron is -1.602 x 10-19 C. • Hence 1 C of charge, there are 1/(1.602 x 10-19) = 6.24 x 1018 electrons. • Denoted by ‘ q ’.
- 5. Current • ‘I’, is the rate at which charge is transferred or "flows" through a device. • Mathematically, dq(t) dt i(t) = where i = the current in amperes (A) q = the charge in coulombs (C) the amount of charge passing through a device per unit of time. ampere is coulomb per second.
- 6. i t 0 5 10 15 20 -1 -0.5 0 0.5 1 0 5 10 15 20 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0 5 10 15 20 -3 -2 -1 0 1 2 3 4 5 0 5 10 15 20 0 0.2 0.4 0.6 0.8 1 Direct Current (dc) Alternating/Sinusoidal Current (ac) Exponential Current Damped Sinusoidal Current Transient Current Types of current
- 7. Current sign convention Proper definition of current vector requires: •direction of the arrow(polarity). •value (magnitude) A negative current of - A flowing in one direction is the same as a current of + A flowing in the opposite direction.
- 8. Electronic VS conventional current Electrons flow from negative terminal to positive terminal but conventional current flows in the opposite direction.
- 9. Example DC current. Find the charge passing through a point in a conductor if the current passing through the conductor has the waveform indicated. i t 2 A Solution: The current does not change with time. Hence, a charge of 2 C is passing through the point each second.
- 10. Example For the given current, which is given in graphical form, find the charge passing through a given point in the time interval 0-4 s. t (sec) 10 A 10 2 43 i(t)
- 11. t (sec) 10 A 10 2 43 i(t) Solution: 4 0 q(t) i(t)dt 1 2 0 1 10tdt 10dt 3 4 2 3 ( 10t 30)dt (10t 30)dt Ans = + - + C = C
- 12. Voltage • Recognized by the 18th century Italian physicist Allessandro Antonio Volta. • Voltage" or "potential difference” is defined as the energy required to move a unit charge through an element. • Measured in volts (V). • Mathematically, dw dq V w = the energy in joules (J volt is joule per coulomb.
- 13. Voltage sign convention
- 14. DC and AC voltage • Like electric current, a constant voltage is called a “dc voltage” and is represented by V”, whereas a sinusoidally time-varying voltage is called an “ac voltage” and is represented by “v • A dc voltage is usually produced by a battery and an ac voltage is produced by an electric generator.
- 15. Passive Sign Convention • The passive sign convention is satisfied when the current enters through the positive(plus- marked) terminal of an element as shown. circuit elementv – + i i . . . The passive sign convention.
- 16. Example Solution: p = W p = W p = W Total power W W + W 600 W + 300 V – + 60 V – + 60 V – + 240 V – 2 A 2 A 1.5 A 0.5 A 3 4 2 Find the power dissipated for the following circuit. Hint: P = V x I What is the power generated by the source?
- 17. Voltage VS Current The voltage across an element can be • linearly proportional to the current through it (a resistor) • proportional to derivative (an inductor) of the current with respect to time. • proportional to integral (a capacitor) of the current with respect to time.
- 18. Voltage and Current Sources Two types of basic electrical elements: • passive elements.(dissipate power) • active elements. (generate power) Active elements such as voltage and current sources can be classified as either independent or dependent sources.
- 19. Independent Voltage Sources An ideal independent source is an active element that can supply a specified voltage or current that is completely independent of a current or voltage elsewhere in the circuit. vsVs (a) and (b) DC independent voltage source symbols. (c) AC independent voltage source symbol. (a) (b) (c) V
- 20. Independent Current Sources (a) (b) (a) A time-varying independent current source. (b) A constant (DC) independent current source. i I
- 21. Dependent Sources • Dependent, or controlled, source is a source in which the source voltage or current is determined by another voltage or current elsewhere in the circuit being analyzed. • It is usually represented by diamond-shaped symbol. (a) (b) (a) A dependent voltage source. (b) A dependent current source. v i
- 22. Dependent sources of four types 1. A voltage-controlled voltage source (VCVS) 2. A current-controlled voltage source (CCVS). 3. A voltage-controlled current source (VCCS). 4. A current-controlled current source (CCCS).
- 23. VCVS i v = vx v = vx vx is somewhere (not shown) and is a constant. i = whatever
- 24. CCVS i v = ix v = ix i = whatever ix is somewhere (not shown) and is a constant.
- 25. VCCS i = vx i = vx vx is somewhere (not shown) and is a constant. v = whateverv
- 26. CCCS i = ix i = ix v = whatever ix is somewhere (not shown) and is a constant. v
- 27. Resistance ‘R’ • Unit of resistance is ohms (Ω) 1 Ω = 1 V / A • Resistance in a circuit arises due to collisions between the electrons carrying the current with the fixed atoms inside the conductor. • Experiments show that for many materials, including most metals, the resistance remains constant over a wide range of applied voltages or currents.
- 28. Ohm’s Law • Ohm’s Law is an empirical relationship that is valid only for certain materials – Materials that obey Ohm’s Law are said to be ohmic V V = R I Ohm’s law
- 29. Parallel connection Series connection R1 R2 R3 R1 R2 R3 Req = R1 + R2 + R3 1/Req = 1/R1+1/R2+1/R3
- 30. Q2. What is the ratio of the current flowing through each resistor (I1:I2) in the circuit? 1. 1:1 2. 3:1 3. 1:4 4. Need more info. 6 V R1 = 10 R2 = 30
- 31. Ra Rb 1/Req = 1/Ra + 1/Rb Req is smaller than Ra and Rb 20 25 Req ≈ 10 1000 = 1k 2 Req < 2 Practically all the current flows Though the bottom one!! Practical considerations for ‘R’