E E 1205 Circuit Analysis

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# E E 1205 Circuit Analysis - PowerPoint PPT Presentation

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

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.

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

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)

By KVL: Vs = V1 = V2

By KCL: Is = I1 + I2

By Ohm’s Law:

and

Combine:

Resistors in Parallel (2/2)

For two resistors:

For many resistors:

In terms of conductance:

Voltage Divider Equations

If RL >> R2:

Current Divider Circuit

If there are onlytwo paths:

In general:

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
• 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

Note: d’Arsonval movement has resistance of 50 W

Scale chosen for 1.0 volt full deflection.

Example: 10V F.S. Voltmeter

Scale chosen for 10 volts full deflection.

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

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

Ga = 199.98 S has ~5.0005 mW resistance.

Scale chosen for 10 amp full deflection.

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

True Voltage:

(If voltmeter removed)

Another Voltage Measurement (1/2)

True Voltage:

(If voltmeter removed)

Example: Current Measurement (1/2)

True Current:

(If ammeter replaced by short circuit)

Another Current Measurement (1/2)

True Current:

(If ammeter replaced by short circuit)

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

Ohmmeter Example

10 mA Full Scale (Outer Numbers)

Vb=1.5 V

Inner (Nonlinear) Scale in Ohms

Wheatstone Bridge

Vab= 0 and Iab= 0