ELEC 101, Spring 2005
Prof. Rich Kozick

## Homework 7

Date Assigned: Monday, February 28, 2005
Date Due: Monday, March 7, 2005 ** CHANGED TO Wednesday, March 9 **

Please hand in your lab notebooks on Thursday, March 3 so that I can grade Labs 1-5.

1. Reading: The relevant reading is in Sections 3.1, 3.2, and 3.3. We will not cover every topic in the text, and we will emphasize capacitors more than inductors. The concept of a time constant is very important.

2. Please solve the following problems in Chapter 3 of the Bobrow text.
• Problem 3.7.
• Problem 3.28. What is the time constant for this circuit?
• Repeat problem 3.28 for the case that the switch is opened for t < 0, and the switch is closed for t >= 0. What is the time constant for the circuit in this case?

3. Please solve problem 3.48 in the text. Note that the voltage source has value 0 volts for t < 0, and V volts for t >= 0. Thus it is equivalent to "closing a switch" at time t = 0 to connect an ideal source with value V volts.

Hint: Write KCL at the "-" input of the op amp. Use the ideal op amp assumptions.

Also answer the following questions for this circuit.

• What is the time constant?
• Sketch vo(t).
• After a long time, i.e., t >> 0, does this look like an inverting amplifier? Please explain.

4. Please analyze the RC circuit that we used in Lab 6 for the following cases. Assume that Vs = 12 V, C = 1 microfarad, R = 1,000 ohms, and Rs = 100 ohms.
• Assume that the switch was closed for a long time, and that it is opened at time t=0. Find the expression for v(t) and make a sketch of the voltage versus time. Label the voltage and time axes on your plot, and indicate the value and location of the time constant on your plot.
• Now assume that the switch is initially opened, and that the capacitor is initially uncharged (i.e., v(0) = 0 V). Suppose that the switch is closed at time t=0.
Find the expression for v(t) and make a sketch of the voltage versus time. Label the voltage and time axes on your plot, and indicate the value and location of the time constant on your plot.
• Why is the time constant different for the two cases?
Thank you.