Exercise 13
Review of Circuits and Error Analysis
I. Purpose
The purpose of this exercise is to let you review electrical measurements, circuits and
error analysis before the test next week. Make sure that your instructor checks each part and be
especially certain to ask questions about anything you feel you still don’t understand.
II. Equipment
function generator
BNC and banana cables
resistor board
digital oscilloscope
6 V battery
multimeter
knife switch
PART A: Resistors
(1) Identify the 300  and 1000  resistors on the resistor board and fill in the following table.
UNIT
Measured value
uncertainty
Resistance of 300 resistor
Resistance of 1 kresistor
(2) Using the resistor board, connect the 1 k and the 300  resistors in parallel as shown below
and measure the combined resistance and its uncertainty. Show your instructor.
R parallel =
(3) Based on your measurements of the 1 k and the 300  resistors, what do you expect the
parallel resistance to be (give your answer in ohms)? You must show your work to get credit.
89
Part B: Current and Voltage in a Series Resistor Circuit
(1) Using the circuit diagram below, wire up in series a 6 V battery, switch, ammeter, a 300 
resistor and 1 k resistor. For now, leave the switch open.
(2) Suppose that you want to measure the voltage across the 300 resistor. Correctly sketch in
the multimeter and its wire connections on the above schematic. Show your instructor.
(3) Close the switch and fill in the following table of measured quantities
Measured value
uncertainty
voltage Vb across battery (V)
voltage Vs across switch (V)
voltage Va across ammeter (V)
voltage V300 across 300 resistor (V)
voltage V1000 across 1 k resistor (V)
Current I flowing in circuit (A)
(4) From your values in Part 3 above, deduce the resistance Ra of the ammeter. (you must show
your work to get credit).
Ra =
(5) (a) Find Rtot = R300+Ra+R1000 from your values measured above.
Rtot =
(b) Calculate Vb/Rtot and compare qualitatively to the current “I” you measured above.
90
Vb/Rtot =
(6) Suppose that you wanted to measure current flowing through the 300  resistor in the circuit
below. Sketch in and label the ammeter.
+
V
-
switch
300
100
1 k
300

(7) In the above circuit, how much current will flow through the switch when it is closed if the
battery voltage is 5 V? Show your work.
(8)
(a) A voltmeter has a low resistance ?
(b) An Ammeter has a low resistance ?
True or False
True or False
PART C: Generate and Measure ac Signals
(1) Using a BNC cable, plug the output from the function generator into channel 1 of the scope.
(2) Adjust the function generator and scope so that you have a nice stable display of a 250 kHz
square wave that is 1 Volt peak-to-peak. YOU MUST SHOW YOUR INSTRUCTOR TO GET
CREDIT.
(3) After your instructor has checked the above display, use the BNC cable to connect the
output from the black signal box into channel 1 of the oscilloscope.
(4) Adjust the oscilloscope controls to get a nice stable display of the waveform that the
instructor is generating. Again have one of your instructors check the display and settings. YOU
MUST SHOW YOUR INSTRUCTOR TO GET CREDIT.
91
(5) For the displayed wave, fill in the table.
UNIT
peak-to-peak voltage
mean value voltage
period
frequency
Measured value
uncertainty
Part D: Observing a Pulse at the far end of the Cable
(1) Arrange a circuit so that the scope has channel 1 plugged into the front end of the cable (see
Fig. 1). Set the function generator to generate square-wave pulses which swing between +2V
and -2V with a width of 500 ns at a rate of 100 kHz.
(2) Measure the reflected pulse height (second pulse on channel 1 and its uncertainty for
different settings of the resistor box (0, 20, 50, 200 ). Record resistances and pulse heights
and the pulse height uncertainties in your data table. Show your instructor.
(3) Plot a graph of the reflected pulse heights with error bars versus the resistance of the resistor
box.
oscilloscope
channel 1
BNC Tee
1000 foot cable
resistor
box
function
generator
Figure 1- Circuit arrangement for observing the voltage pulse at the near end of the cable.
QUESTION 1: Compare the reflected pulse for the cases when there is a low and a high
resistance at the end. What's the qualitative difference?
92
PART E: Error Analysis
1. For the plot below, find 2, the number of degrees of freedom v, and P(2,v). Assume that the
solid line is a theory that has been given to you and does not involve any fitting parameters.
Also discuss the significance of P(2,v).
2 =
v=
P(2,v) =
2. Let R = R1+R2. Write an equation for the uncertainty in R if there are uncertainties R1 in R1
and R2 in R2. SHOW YOUR WORK
3. Find the slope "m" and intercept "b" of the straight line that best fits the data shown below.
t (sec)
V (volts)
V (V)
0
1
2
3
4
-0.5
1.2
2.1
3.2
4.3
0.3
0.3
0.3
0.2
0.2
93
5
5.5
0.2
4. How many degrees of freedom v are there in the above fit?
v = "number of degrees of freedom" =
5. Plot the above best fit line and the data (with error bars).
6. Do the above data actually fit the line ? Explain below using 2 and P(2, v).
When you are all finished, email your work to yourself, send a copy to WebCT.
94
III. Homework - Twenty Extra Problems on Measuring Current and Voltage
1. Suppose that you wanted to measure the
current flowing through the 100  resistor in
the circuit below. Sketch in and label the
ammeter.
+
V
5. Suppose that you wanted to measure the
current flowing through the switch (when its
closed) in the circuit below. Sketch and
label the ammeter.
switch
-
300
100
+
V
1 k
300

3. Suppose that you wanted to measure the
voltage across the 100  resistor in the circuit
below. Sketch in and label the voltmeter.
+
V
V
300
100
-
switch
300
100
switch
-
300
100
1 k
300

6. Suppose that you wanted to measure the
voltage across the switch in the circuit
below. Sketch in and label the voltmeter.
2. An ammeter has a low resistance.
True or
False ?
+
-
switch
1 k
300

1 k
300

7. Suppose that you wanted to measure the
voltage across the 300  resistor in the circuit
below. Sketch in and label the voltmeter.
4. Suppose that you wanted to measure current
flowing through the 300  resistor in the
circuit below.
Sketch in and label the
ammeter.
+
V
+
V
-
switch
300
100
-
switch
300
100
1 k
300

8. A voltmeter has a low resistance.
True or False ?
95
1 k
300

9. Suppose that you wanted to measure the
current flowing out of the battery in the
circuit below when the switch is closed.
Sketch in and label the ammeter.
12. Suppose that you wanted to measure the
current flowing through the 100  resistor
in the circuit below. Sketch in and label the
ammeter.
1 k
1 k
+
V
switch
+
-
V
100 
1 k
V
-
switch
+
V
-
100 
13. Suppose that you wanted to measure the
current flowing through the switch in the
circuit below.
Sketch in and label the
ammeter.
1 k
10. Suppose that you wanted to measure the
voltage across the 1 k resistor in the circuit
below. Sketch in and label the voltmeter.
+
switch
100 
11. Suppose that you wanted to measure the
voltage across the 100  resistor in the
circuit below. Sketch in and label the
voltmeter.
switch
-
100 
14. Suppose that you wanted to measure the
current flowing through the 1000  resistor in
the circuit below. Sketch in and label the
ammeter.
1 k
+
V
-
1 k
switch
+
100 
V
96
-
switch
100 
15. The circuit below is wired correctly for
measuring the current through the 100
resistor, True or False?
+
V
18. The circuit below is wired correctly for
measuring the voltage across the 100
resistor, True or False?
100 
-
V
300
V
-
V
switch
+
V
100 
300
100 
-
300
V
A
17. The circuit below is wired correctly for
measuring the voltage across the 100
resistor, True or False?
V
300
19. The circuit below is wired correctly to
measure the voltage across the 100
resistor, True or False?
switch
-
+
100 
-
A
16. The circuit below is wired correctly for
measuring the voltage across the 100
resistor, True or False?
+
switch
+
switch
20. The circuit below is wired correctly to
measure current flowing out of the battery.
True or False?
switch
100 
+
300
V
A
97
V
-
switch
100 
300