1. Lecture 03 - Simple Resistive Circuits and Applications
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:
Material
20oC
Aluminum
Copper

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 only two 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 = S has ~ mW resistance.
Scale chosen for 1.0 amp full deflection.

17. Example: 10 Amp F.S. Ammeter
Ga = S has ~ 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 d’Arsonval Ohmmeter
Measure Voltage across Resistor
Measure Current through Resistor
Calculate Resistance (Inaccurate)
d’Arsonval Ohmmeter
Very Simple
Inaccurate
Wheatstone Bridge (Most Accurate)

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

29. 10 mA Full Scale (Outer Numbers) Inner (Nonlinear) Scale in Ohms
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