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Understanding Simple Resistive Circuits and Applications

Explore calculating resistance in conductors with varying temperatures, analyzing resistors in series and parallel, and grasping voltage and current divider circuits. Learn about D’Arsonval meter and measurement errors in circuits.

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Understanding Simple Resistive Circuits and Applications

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  1. E E 2315 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 (1/2)

  11. Current Divider Circuit (2/2) If there are onlytwo paths: In general:

  12. 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

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

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

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

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

  17. 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.

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

  19. 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

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

  21. Example: Voltage Measurement Measured Voltage:

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

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

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

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

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

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

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

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

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

  31. Wheatstone Bridge Vab= 0 and Iab= 0 Vad = Vbd R1I1=R2I2 R3I3=RxIx

  32. Example: Wheatstone Bridge

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