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CSE 323a: Measurements &Testing (1)a. 2013-2014. Grading Scheme. Course webpage. http:// www.staff.zu.edu.eg/amabd/page.asp?id=59. References:. William Dunn, Introduction to Instrumentation, Sensors, and Process Control , Artech House , 2006.

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grading scheme
Grading Scheme

Course webpage

http://www.staff.zu.edu.eg/amabd/page.asp?id=59

slide3
References:
  • William Dunn, Introduction to Instrumentation, Sensors, and Process Control, Artech House, 2006.
  • William Bolton, Instrumentation and Control Systems, Elsevier, 2004.
  • Curtis Johnson, Process control instrumentation technology, Prentice-Hall, 6th edition, 2000.
slide6
Resistors, capacitors, and inductors

The three basic passive elements used in electrical circuits.

slide7
Let us have a look at some useful slides from the course 6.091 offered at the Department of Electrical and Computer Science, MIT, available at:

http://ocw.mit.edu/courses/electricalengineering-and-computer-science/

resistors1
Resistors
  • Used as loads in electrical circuits.
  • Resistor parameter: resistance, tolerance, and power rating.
  • Standard values:

10 12 15 18 20 22 27 33 39 47 56 68 82.

  • Common tolerances: ±5%, ±1%.
  • Resistor are color coded.
capacitors1
Capacitors

Used as dc blocking devices, in level shifting, integrating, differentiating, filters, and delay circuits.

capacitors2
Capacitors
  • Capacitors range from 1 pF (10-12) to 100,000 µF (10-1).
  • Typically, capacitors larger than 1 µF are polarized.
  • All capacitors have maximum voltage ratings.
how to read puff capacitor codes
How to read puff capacitor codes
  • Source: http://drakedev.com/pic/capacitors.php
inductors1
Inductors
  • Used as current limiting devices.
  • Found in relays, audio to electrical conversions, electromagnetic devices, light dimmers, and tuned circuits.
  • They are also the basis for transformers and motors.
3 2 circuits with r l and c
3.2 Circuits with R, L, and C

3.2.1 Voltage Step Input

slide21
When the current in the resistor is maximum, the voltage across it is maximum, given by E = IR. i.e. the voltage is said to be in phase with the current.
  • For the capacitor, the voltage is zero when the current is maximum, and the voltage is a maximum when the current is zero. In this case, the voltage lags the current, or there is a phase shift between the voltage and the current of 90°.
  • The voltage across the capacitor builds up exponentially, at a rate determined by the values of R and C.
slide23
Similarly, the voltage and current in the resistor are in phase, but in the inductor are out of phase. The voltage leads the current by of 90°.
  • The voltage across the resistor increases exponentially, at a rate determined by the value of L and R.
time constant
Time constant
  • In RC circuit, the voltage across the capacitor, while charging, is given by:

where E is the source voltage.

  • and while discharging, is given by:
time constant1
Time constant
  • It is the time taken by the response to reach 63.2% of its full change.
  • The time constant of RC circuit is given by RC, while for RL circuit, it is L/R.
  • Practically, the response will complete its full change in 4 to 5 time constants.
time constant2
Time constant
  • Applies not only to electrical circuits, but also to sensor outputs when there is a change in the measured variable.
  • The output signal from the sensor changes exponentially, so that there is a delay before the sensor output reaches its final value.
3 2 3 sine wave inputs
3.2.3 Sine-wave inputs
  • Assuming that the circuit is capacitive.
slide28
In series RLC circuit, the same current will flow through all three devices.
  • When an ac sine wave is applied to RLC circuits, the same phase shift between voltage and current occurs as when a step voltage is applied:
      • IR and VRare in phase;
      • ICleads VCby 90°;
      • ILlags VLby 90°;
  • That is,
      • VCand VLare 180° out of phase; and
      • VCand VLare 90° out of phase with VR
vector addition
Vector addition
  • Since the voltages and currents in capacitors and inductors are not in phase, they have impedance and not resistance.
  • Impedance and resistance cannot be directly added.
  • However, they can be combined using vectors.
slide30
E: supply voltage
  • VR, VL , VC are voltage across resistor, inductor, capacitor
example
Example
  • What is the current flowing in the series RLC if R = 27 kΩ, C = 2.2 nF, L = 33 mH, E = 20V and the input frequency = 35 kHz?
resonance
Resonance
  • XLand XCare frequency dependent.
  • As the frequency increases, XL and XC.
  • A frequency can be reached where XL= XC, and the voltage across these components are equal, opposite, and cancel.
  • At this frequency, Z=R, E=IR, and the current is maximum.
  • This frequency is called the resonant frequency of the circuit.
  • At resonance:
slide33
When the input frequency is below the resonant frequency XC> XL, the circuit is capacitive.
  • Above the resonant frequency XC< XL, the circuit is inductive.
  • Plotting the input current against the input frequency shows a peak at the resonant frequency as shown:
slide34
Example

What is the resonant frequency of the series RLC if R = 27 kΩ, C = 2.2 nF, and L = 33 mH? What is the current at this frequency?

The current can be obtained as (at resonance Z = R)

I = E/R = 20/(27 x 103) = 0.740 mA

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