Assignment 6, Part 1: Pre-lab questions

This is Part 1 of Assignment 6.

Question 1

Consider the following circuit composed of a network of resistors:

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. Find the voltage values for the nodes $ V_A $ and $ V_B $ in the above diagram.

Question 2

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.

Find the transfer function $ {V_{out} \over V_{in}} $. What type of filter is this? Justify your answer. 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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