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E E 1205 Circuit Analysis

E E 1205 Circuit Analysis. Lecture 03 - Simple Resistive Circuits and Applications. Calculating Resistance. When conductor has uniform cross-section. Temperature Coefficient of Resistance. Metallic conductors have a linear increase of resistance with increased temperature.

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E E 1205 Circuit Analysis

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  1. E E 1205 Circuit Analysis Lecture 03 - Simple Resistive Circuits and Applications

  2. Calculating Resistance When conductor has uniform cross-section

  3. Temperature Coefficient of Resistance Metallic conductors have a linear increase of resistance with increased temperature. To is the reference temperature (usually 20oC) and Ro is the resistance at the reference temperature. a is the temperature coefficient of resistance for the material. At 20oC, some values for a are:

  4. Resistors in Series By KCL: Is = I1= I2 By Ohm’s Law: V1 = R1·I1 and V2 = R2·I2 Combine: Vs = R1I1 + R2I2 = (R1 + R2) Is = ReqIs In General: Req = R1 + R2 +···+ Rn

  5. Resistors in Parallel (1/2) By KVL: Vs = V1 = V2 By KCL: Is = I1 + I2 By Ohm’s Law: and Combine:

  6. Resistors in Parallel (2/2) For two resistors: For many resistors: In terms of conductance:

  7. Voltage Divider Circuit

  8. Loaded Voltage Divider

  9. Voltage Divider Equations Unloaded: Loaded: If RL >> R2:

  10. Current Divider Circuit If there are onlytwo paths: In general:

  11. D’Arsonval Meter Movement • Permanent Magnet Frame • Torque on rotor proportional to coil current • Restraint spring opposes electric torque • Angular deflection of indicator proportional to rotor coil current

  12. D’Arsonval Voltmeter • Small voltage rating on movement (~50 mV) • Small current rating on movement (~1 mA) • Must use voltage dropping resistor, Rv

  13. Example: 1 Volt F.S. Voltmeter Note: d’Arsonval movement has resistance of 50 W Scale chosen for 1.0 volt full deflection.

  14. Example: 10V F.S. Voltmeter Scale chosen for 10 volts full deflection.

  15. D’Arsonval Ammeter • Small voltage rating on movement (~50 mV) • Small current rating on movement (~1 mA) • Must use current bypass conductor, Ga

  16. Example: 1 Amp F.S. Ammeter Note: d’Arsonval movement has conductance of 0.02 S Ga = 19.98 S has ~50.050 mW resistance. Scale chosen for 1.0 amp full deflection.

  17. Example: 10 Amp F.S. Ammeter Ga = 199.98 S has ~5.0005 mW resistance. Scale chosen for 10 amp full deflection.

  18. Measurement Errors • Inherent Instrument Error • Poor Calibration • Improper Use of Instrument • Application of Instrument Changes What was to be Measured • Ideal Voltmeters have Infinite Resistance • Ideal Ammeters have Zero Resistance

  19. Example: Voltage Measurement True Voltage: (If voltmeter removed)

  20. Example: Voltage Measurement Measured Voltage:

  21. Another Voltage Measurement (1/2) True Voltage: (If voltmeter removed)

  22. Another Voltage Measurement (2/2) Measured Voltage:

  23. Example: Current Measurement (1/2) True Current: (If ammeter replaced by short circuit)

  24. Example: Current Measurement (2/2) Measured Current:

  25. Another Current Measurement (1/2) True Current: (If ammeter replaced by short circuit)

  26. Another Current Measurement (2/2) Measured Current:

  27. Measuring Resistance • Indirect • Measure Voltage across Resistor • Measure Current through Resistor • Calculate Resistance (Inaccurate) • d’Arsonval Ohmmeter • Very Simple • Inaccurate • Wheatstone Bridge (Most Accurate)

  28. D’Arsonval Ohmmeter Need to adjust Radj and zero setting each scale change.

  29. Ohmmeter Example 10 mA Full Scale (Outer Numbers) Rb+Radj+Rd’A=150 W Vb=1.5 V Inner (Nonlinear) Scale in Ohms

  30. Wheatstone Bridge Vab= 0 and Iab= 0 Vad = Vbd I1 = I3 I2 = Ix R1I1=R2I2 R3I3=RxIx

  31. Example: Wheatstone Bridge I = 2 A

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