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TEC 284

Introduction to Circuit Theory. TEC 284. Structure of Atom. Image Source: Wikipedia. Electric Charge. Charge is measured in Coulombs (C) 1 C = 6.24 x 10 18 electrons Conventional Current flows from positive to negative Electrons actually flow from negative to positive. Current flow.

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TEC 284

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  1. Introduction to Circuit Theory TEC 284

  2. Structure of Atom Image Source: Wikipedia

  3. Electric Charge • Charge is measured in Coulombs (C) • 1 C = 6.24 x 1018 electrons • Conventional Current flows from positive to negative • Electrons actually flow from negative to positive

  4. Current flow

  5. Current • The measure of the rate of electron flow in a circuit • Measured in Amperes (A) • 1 mA (milliamp) = 0.001 A • 1 µA (microamp)= 0.001 mA • Direct Current (DC) • Flow of electricity (current) in an unchanging direction • Alternating Current (AC) • Current flows in different directions

  6. DC vs AC Image Source: Electronics Demystified

  7. Resistance • Opposition that a component of device offers to the flow of an electric current • Unit of resistance is Ohm Ω • 1 kilohm (k Ω) = 1000 Ω • 1 megohm (m Ω) = 1,000 k Ω or 1,000,000 Ω • Good conductors have low resistance • Good insulators have high resistance • Assumption in circuit analysis: Resistance of an ideal resistor is constant and does not vary in time

  8. EMF (Electromotive force) • Standard unit of EMF is the volt (V) • Voltage is the measure of work done to move a charge from one point to another in an electric field • 1 mV (millivolt) = 0.001 V • 1 µV (microvolt)= 0.001 mV • Voltage is referred to as “electric potential” or “electric pressure” • More voltage in a circuit means more potential for current

  9. Ohm’s Law • V = IR • I = V / R • R = V / I • V – Voltage • I – Current • R - Resistance V I R

  10. Resistance

  11. Current, Voltage, Resistance

  12. Exercise: Calculations • DC is 10 V and potentiometer is 10 Ω. What is the current? • Potentiometer is 100 Ω and current is 10 mA. What is voltage across the resistance? • Potentiometer is uncalibrated. Voltmeter reads 24 V and Ammeter 3A. What is the resistance?

  13. Power • Measure in Watts (W) • P = IV • P = I2R • P = V2 / R V I R

  14. Resistive Networks • Resistance in Series • Values are added to get total resistance • Resistance in Parallel • Overall resistance decreases • Conductance (S) siemens • G= 1 / R • Add conductances to get total resistance

  15. Resistors in Parallel • V1 = V2 = V3 • I = I1 + I2 + I3 • 1 / Req = 1 /R1 + 1/R2 + 1/R3

  16. Voltage Divider

  17. Current Divider

  18. Kirchoff’s Laws • Current Law – Kirchoff’s First Rule • The total current entering a junction in a circuit must equal the sum of the currents leaving that junction • Principle of conservation of electric charge I1 = I2 + I3 I2 = I1 – I3 I3 = I1 – I2

  19. Kirchoff’s Laws • Voltage Law – Kirchoff’s Second Rule • The directed sum of the emfs (potential differences) around any closed circuit it zero • Principle of conservation of energy -VB + V1 + V2 = 0 -V2 - V3 + V4 = 0 -VB + V1 - V3 + V4 = 0

  20. Thevenin’s Theorem • It is possible to simplify a linear circuit, no matter how complex to an equivalent circuit with just a single voltage source and series resistance connected to a load • This is true for circuits with passive components (resistors, inductors and capacitors) • Underlying equations are linear (no exponents or roots) • Non-linear (opposition to current changes with voltage/current)

  21. Thevenin’s Theorem • Useful for analyzing circuits where one component is changing • Tedious re-calculation does not need to occur

  22. Thevenin’s Theorem

  23. Thevenin’s Theorem • Advantage of Thevenin Conversion is a simpler circuit which makes load voltage and current easier to solve • Step 1 • The chosen load resistor is removed from the original circuit and replaced with a break (open circuit)

  24. Thevenin’s Theorem • Next, the voltage between the two points where the load resistor used to be attached is determined • Ohm’s and Kirchoff’s voltage law can be used • The voltage between the two load connection points can be figured from one of the battery’s voltage and one of the resistor’s voltage drops

  25. Thevenin’s Theorem Evaluating voltage in the closed loop Kirchoff’s 2nd Law 28 – 4I – I – 7 =0 21 – 5I = 0 21 = 5I I = 21 /5 I = 4.2A Now we have the current, we can find the voltage drop across R1 VTh= 28 – IR1 VTh = 28 – 4 (4.2) = 28 – 16.8 VTh = 11.2 V

  26. Thevenin’s Theorem

  27. Thevenin’s Theorem • Step 2 • Find the Thevenin series resistance for the circuit • Remove all power sources from the circuit and replace them with wires (current sources are replaced with breaks)

  28. Thevenin’s Theorem • Total resistance is R1 and R3 in parallel = 0.8 Ω

  29. Thevenin’s Theorem • With the 2 load resistor attached between the points we can determine the voltage across it • Just a simple series circuit

  30. Thevenin Summary • Find Thevenin Voltage by removing load resistor from original circuit and calculate voltage across open connection points • Find Thev. resistance be removing power sources from original circuit (voltage shorted and current sources open) and calculate total resistance between points • Draw Thev Eq circuit with Thev voltage in series with Thev resistance and load resistor

  31. Norton’s Theorem • Possible to simplify linear circuit to a circuit with just a single current source and parallel resistance connected to a load

  32. Norton’s Theorem • Step 1 • Remove load resistor and place a short connection between load points • Calculate total current between the load points

  33. Norton’s Theorem • Step 2 – Calculate Norton Resistance in the same manner as Thev Resistance

  34. Norton’s Theorem

  35. Norton Summary • Find Norton Current by removing load resistor from original circuit and calculate current across closed connection points • Find Norton resistance be removing power sources from original circuit (voltage shorted and current sources open) and calculate total resistance between points • Draw Norton Eq circuit with Norton Current Source in parallel with Thev resistance and load resistor

  36. Thevenin-Norton Equivalents • RThevenin = RNorton • EThevenin=INortonRNorton

  37. Units

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