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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

E E 1205 Circuit Analysis

Lecture 03 - Simple Resistive Circuits and Applications

calculating resistance
Calculating Resistance

When conductor has uniform

cross-section

temperature coefficient of resistance
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:

resistors in series
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

resistors in parallel 1 2
Resistors in Parallel (1/2)

By KVL: Vs = V1 = V2

By KCL: Is = I1 + I2

By Ohm’s Law:

and

Combine:

resistors in parallel 2 2
Resistors in Parallel (2/2)

For two resistors:

For many resistors:

In terms of conductance:

voltage divider equations
Voltage Divider Equations

Unloaded:

Loaded:

If RL >> R2:

current divider circuit
Current Divider Circuit

If there are onlytwo paths:

In general:

d arsonval meter movement
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
d arsonval voltmeter
D’Arsonval Voltmeter
  • Small voltage rating on movement (~50 mV)
  • Small current rating on movement (~1 mA)
  • Must use voltage dropping resistor, Rv
example 1 volt f s voltmeter
Example: 1 Volt F.S. Voltmeter

Note: d’Arsonval movement has resistance of 50 W

Scale chosen for 1.0 volt full deflection.

example 10v f s voltmeter
Example: 10V F.S. Voltmeter

Scale chosen for 10 volts full deflection.

d arsonval ammeter
D’Arsonval Ammeter
  • Small voltage rating on movement (~50 mV)
  • Small current rating on movement (~1 mA)
  • Must use current bypass conductor, Ga
example 1 amp f s ammeter
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.

example 10 amp f s ammeter
Example: 10 Amp F.S. Ammeter

Ga = 199.98 S has ~5.0005 mW resistance.

Scale chosen for 10 amp full deflection.

measurement errors
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
example voltage measurement
Example: Voltage Measurement

True Voltage:

(If voltmeter removed)

another voltage measurement 1 2
Another Voltage Measurement (1/2)

True Voltage:

(If voltmeter removed)

example current measurement 1 2
Example: Current Measurement (1/2)

True Current:

(If ammeter replaced by short circuit)

another current measurement 1 2
Another Current Measurement (1/2)

True Current:

(If ammeter replaced by short circuit)

measuring resistance
Measuring Resistance
  • Indirect
    • Measure Voltage across Resistor
    • Measure Current through Resistor
    • Calculate Resistance (Inaccurate)
  • d’Arsonval Ohmmeter
    • Very Simple
    • Inaccurate
  • Wheatstone Bridge (Most Accurate)
d arsonval ohmmeter
D’Arsonval Ohmmeter

Need to adjust Radj and zero setting each scale change.

ohmmeter example
Ohmmeter Example

10 mA Full Scale (Outer Numbers)

Rb+Radj+Rd’A=150 W

Vb=1.5 V

Inner (Nonlinear) Scale in Ohms

wheatstone bridge
Wheatstone Bridge

Vab= 0 and Iab= 0

Vad = Vbd

I1 = I3

I2 = Ix

R1I1=R2I2

R3I3=RxIx