ELEC 101, Spring 1998
Prof. Rich Kozick

## Homework 5

Date Assigned: Monday, February 9, 1998
Date Due: Monday, February 16, 1998

1. Reading: The following sections in the Bobrow text will be relevant to class and lab during the next week: 2.1 on nodal analysis, 2.2 which reviews solving simultaneous linear equations, 2.4 on op amps, 2.6 for the concept of superposition, and pages 891-893 on digital-to-analog (D/A) conversion.

2. Bridge circuit: Recall the bridge circuit that we used in Lab 3 to detect a difference in temperature. Let us consider how we can calibrate the bridge to account for non-identical thermistors.

[CIRCUIT DIAGRAM IS NOT AVAILABLE IN HTML DOCUMENT.]

Suppose the thermistors RT1 and RT2 are not identical. At room temperature, RT1 = 5000 ohms and RT2 = 6000 ohms. At a higher temperature, RT1 = 3000 ohms and RT2 = 4000 ohms. Suppose that RA = sqrt(5000*3000) = 3870 ohms, but that RB is a potentiometer whose resistance can be varied from 100 ohms to 10,000 ohms.

(a) What value should RB have in order to "balance the bridge", i.e., set vout = 0 V, at room temperature? Please explain.

(b) If vout is a positive voltage, which thermistor is warmer? Please explain.

3. Nodal analysis: Please do problems 2.6, 2.8, and 2.10.

4. Operational amplifiers: Please do problem 2.35. Explain your reasoning.

5. Design an op amp circuit such that the output voltage is one-fourth the input voltage, i.e.,
vo = 0.25 vi. (Hint: You may need more than one op amp.)

6. Specify an op amp circuit whose output voltage is the average of three input voltage sources:
vout = (va + vb + vc)/3. Specify values for all resistors in your circuit diagram.

7. Consider the electronic ohmmeter shown below. To use the ohmmeter, an unknown resistance R is connected as shown, and then the value of R is obtained by measuring the voltage vo and then computing R = -1000 vo.

[CIRCUIT DIAGRAM IS NOT AVAILABLE IN HTML DOCUMENT.]

1. Since vo is always within the range -10 volts to +10 volts, what is the maximum value of R that can be measured with this circuit?
2. How can the circuit be modified in order to measure resistance values up to 100 k ohms? Explain the reasoning behind your modification, and explain how the value of R is computed from vo in your circuit.
Thank you.