2. RESISTIVE CIRCUITS

CIRCUITS by Ulaby & Maharbiz

Piezoresistive sensor

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Ohm’s Law

Voltage across resistor is proportional to current

iR

Resistance: ability to resist flow of electric current

iR

r = resistivity

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ConductivityAll rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

Resistor Codes

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Example 2-1: dc Motor

= 98% of P

What fraction of power supplied by the battery is dissipated in the motor?

Solution:

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Tech Brief 2: Superconductivity

Critical temperature TC is the temperature at which a material becomes superconducting (zero resistance & no power dissipation)

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Kirchhoff’s Current Law

Sum of currents entering a node is zeroAlso holds for closed boundary

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Example

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Kirchhoff’s Voltage Law (KVL)

Sum of voltages around a closed path is zero

Sum of voltage drops = sum of voltage rises

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Example : KCL/KVL

Determine all currents & voltages

Solution:

Three equations w/three unknowns:

Loop 1

Loop 2

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Equivalent Circuits

If the current and voltage characteristics at nodes are identical, the circuits are considered “equivalent”

Identifying equivalent circuits simplifies analysis

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Resistors in Series

Equivalent resistance (series) is sum of resistances

Voltage divided over resistors (voltage divider)

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Adding Sources In Series

Unrealizable Circuit

Combining voltage sources

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Resistors in ParallelAll rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

Source Transformation

Hence,

For the two circuits to be equivalent :

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Example 2-10: Source Transformation

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Circuit with no two resistors sharing the same current or same voltage

R1,R2,R3=Delta

R3,R4,R5=Delta

R2,R3,R5=Y

R1,R3,R4=Y

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Between nodes 1 and 2:

( Assuming no connection at node 3)

Hence,

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Simultaneous solution leads to:

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Example 2-12: Y-Δ CircuitAll rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

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Wheatstone Bridge

Measurement instrument based on differential measurement

Balanced Condition:

Determine unknown resistance based on “balanced” condition

For balanced condition

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Wheatstone Sensor

Determine Vout

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Tech Brief 3: Resistors As Sensors Piezoresistive Sensors

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Tech Brief 3: Resistors As Sensors

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Tech Brief 3: Resistors As Sensors

Thermistor Sensors

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Example 2-16: Piezoresistor Cantilever

(400 times greater than w/o cantilever)

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Linear i-v relationships

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The Diode

Current can flow only from + to – through a diode.

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Multisim

SPICE simulator software Powerful tool for analyzing circuits See tutorial and examples on CD that

accompanies the text

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Multisim: Creating a CircuitAll rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

Multisim: DC Operating Point Solution

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Multisim Solution WindowAll rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

SummaryAll rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press