Difference between revisions of "Assignment 6, Part 1: Pre-lab questions"

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[[Category:Optical Microscopy Lab]]
 
[[Category:Optical Microscopy Lab]]
 
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__NOTOC__
  
 
This is Part 1 of [[Assignment 6 Overview| Assignment 6]].
 
This is Part 1 of [[Assignment 6 Overview| Assignment 6]].
 
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==Problems==
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==Question 1==
  
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{{Template:Assignment Turn In|message=your answers to the following questions}}
 
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====Question 1====
 
 
Consider the following circuit composed of a network of resistors:
 
Consider the following circuit composed of a network of resistors:
 
[[Image: Circuit1.png|center|250px|thumb]]
 
[[Image: Circuit1.png|center|250px|thumb]]
  
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'''a)''' Combining resistance values in parallel and in series, draw a simplified version of the circuit containing the given voltage source (10V) and one equivalent resistor. Label the equivalent resistance value.  
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{{Template:Assignment Turn In|message=
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<ol type="a">
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<li>Combining resistance values in parallel and in series, draw a simplified version of the circuit containing the given voltage source (10V) and one equivalent resistor. Label the equivalent resistance value.  
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</li>
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<li>
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Find the voltage values for the nodes <math>V_A</math> and <math>V_B</math> in the above diagram.
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</li>
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</ol>
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'''b)''' Find the voltage values for the nodes <math>V_A</math> and <math>V_B</math> in the above diagram.
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==Question 2==
  
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====Question 2====
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{{Template:Assignment Turn In|message = Referring to the circuit shown below, what value of <math>R_L</math> (in terms of <math>R_1</math> and <math>R_2</math>) will result in the maximum power being dissipated in the load?  
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Referring to the circuit shown below, what value of <math>R_L</math> (in terms of <math>R_1</math> and <math>R_2</math>) will result in the maximum power being dissipated in the load?  
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}}
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Hint: this is much easier to do if you first remove the load, and calculate the equivalent Thevenin output resistance <math>R_T</math> of the divider looking into the node labeled <math>V_{out}</math> (the [[Electronics primer]] has a section on Thevenin Equivalent circuits). Then express <math>R_L</math> for maximal power transfer in terms of <math>R_T</math>.
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Hint: this is much easier to do if you first remove the load, and calculate the equivalent Thevenin output resistance <math>R_T</math> of the divider looking into the node labeled <math>V_{out}</math>. Then express <math>R_L</math> for maximal power transfer in terms of <math>R_T</math>.
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[[Image: VoltageDivider.jpg|center|200px|thumb|A voltage divider formed by <math>R_1</math> and <math>R_2</math> driving a resistive load <math>R_L</math>.]]
 
[[Image: VoltageDivider.jpg|center|200px|thumb|A voltage divider formed by <math>R_1</math> and <math>R_2</math> driving a resistive load <math>R_L</math>.]]
  
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==Question 3==
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====Question 3====
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In the following circuit, R = 10 k&Omega; and C = 10 nF.
 
In the following circuit, R = 10 k&Omega; and C = 10 nF.
 
[[Image: Filter1.jpg|center|220px|thumb]]
 
[[Image: Filter1.jpg|center|220px|thumb]]
  
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'''a)''' Find the transfer function <math>{V_{out} \over V_{in}}</math>.
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{{Template:Assignment Turn In|message =  
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'''b)''' What type of filter is this? Justify your answer.
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'''c)''' What is the cutoff frequency of this filter? Write your answer in units of Hz. Remember that <math>\omega = 2 \pi f </math>.
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<ol type="a">
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<li>Find the transfer function <math>{V_{out} \over V_{in}}</math>.</li>
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<li>What type of filter is this? Justify your answer.</li>
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<li>What is the cutoff frequency of this filter? Write your answer in units of Hz. Remember that <math>\omega = 2 \pi f </math>.</li>
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</ol>
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}}
 
Note: You may find the pages on [[Impedance Analysis]] and [[Bode plots| Transfer Functions and Bode Plots]] helpful for this problem.
 
Note: You may find the pages on [[Impedance Analysis]] and [[Bode plots| Transfer Functions and Bode Plots]] helpful for this problem.
  
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{{Template: Assignment 6 navigation}}
 
{{Template:20.309 bottom}}
 
{{Template:20.309 bottom}}

Latest revision as of 20:28, 3 April 2018

20.309: Biological Instrumentation and Measurement

ImageBar 774.jpg


This is Part 1 of Assignment 6.

Question 1

Consider the following circuit composed of a network of resistors:

Circuit1.png


Pencil.png
  1. Combining resistance values in parallel and in series, draw a simplified version of the circuit containing the given voltage source (10V) and one equivalent resistor. Label the equivalent resistance value.
  2. Find the voltage values for the nodes $ V_A $ and $ V_B $ in the above diagram.


Question 2


Pencil.png

Referring to the circuit shown below, what value of $ R_L $ (in terms of $ R_1 $ and $ R_2 $) will result in the maximum power being dissipated in the load?


Hint: this is much easier to do if you first remove the load, and calculate the equivalent Thevenin output resistance $ R_T $ of the divider looking into the node labeled $ V_{out} $ (the Electronics primer has a section on Thevenin Equivalent circuits). Then express $ R_L $ for maximal power transfer in terms of $ R_T $.

A voltage divider formed by $ R_1 $ and $ R_2 $ driving a resistive load $ R_L $.

Question 3

In the following circuit, R = 10 kΩ and C = 10 nF.

Filter1.jpg


Pencil.png
  1. Find the transfer function $ {V_{out} \over V_{in}} $.
  2. What type of filter is this? Justify your answer.
  3. What is the cutoff frequency of this filter? Write your answer in units of Hz. Remember that $ \omega = 2 \pi f $.


Note: You may find the pages on Impedance Analysis and Transfer Functions and Bode Plots helpful for this problem.

Navigation

Back to 20.309 Main Page.

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