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

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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?  
 
{{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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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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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>.
  
 
[[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>.]]

Revision as of 19:07, 11 October 2017

20.309: Biological Instrumentation and Measurement

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This is Part 1 of Assignment 6.

Question 1

Consider the following circuit composed of a network of resistors:

Circuit1.png


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  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


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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


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  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.

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