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OBJECTIVES

1. To learn how to make basic electrical measurements of current, voltage, and resistance using multimeters.

2. To study the relationship of Ohm's Law.

3. To learn the various methods of calculating power.

4.  To study the accuracy of electrical measuring insturments.

BACKGROUND & THEORY

Definitions for various electrical quantities is as follows:

a. Electric current (i or I) is the flow of electric charge from one point to another, and it is defined as the rate of movement of charge past a point along a conduction path through a circuit, or i = dq/dt. The unit for current is the ampere (A).  One ampere = one coulomb per second .

b. Electric voltage (v or V) is the "potential difference" between two points, and it is defined as the work, or energy required, to move a charge of one coulomb from one point to another. The unit for voltage is the volt (V).  One volt = one joule per coulomb.

c. Resistance (R) is the "constant of proportionality" when the voltage across a circuit element is a linear function of the current through the circuit element, or v = Ri.  A circuit element which results in this linear response is called a resistor. The unit for resistance is the Ohm(W).  One Ohm = one volt per ampere.  The relationship v = Ri is called Ohm's Law.

d. Electric power (p or P) is dissipated in a resistor in the form of heat. The amount of power is determined by p=Vi, p=i²R, or p=v²/R. The latter two equations are derived by using Ohms Law (v = Ri) and making substitutions into the first equation. The unit for power is the watt (W)  One watt = one joule per second.

Resistors come in many shapes and sizes, but in this class we will use small carbon film resistors. Some points to note about carbon film resistors are as follows:

a. The value of resistance is indicated by color coded bands around the body of the resistor. Color Code cards will be furnished in the lab.

b. The power rating of the resistor is determined by its physical size while the resistance value is determined by its internal composition.  A resistor which has a larger physical size has a larger surface area to transfer heat to the surrounding air and therefore can dissipate a larger power without over heating.  Most of the resistors used in our lab experiments will be 1/2w or 1/4w resistors.

c. Typical standard resistor values are 1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, 7.5, 8.2, and 9.1 multiplied by a power of 10.

Meters are used to make measurements of the various physical variables in an electrical circuit. These meters may be designed to measure only one variable such as a voltmeter or an ammeter.  Other meters called multimeters are designed to measure several variables, typically voltage, current and resistance.  These multimeters have the capability of measuring a wide range of values for each of these variables. Some multimeter operate on battery power and are therefore easily portable, but need battery replacement.  Others operate on a.c. power.

The read-out, or display, of value being measured on the multimeter may be of the digital type or the analog type. The digital type displays the measurement in an easy to read  form. The analog type has a pointer which moves in front of a marked scale and must be read by visually interpolating between the scale markings.

EQUIPMENT AND PARTS LIST

Digital Multimeter (DMM)
Adjustable DC power supply
Circuit breadboard
Resistors: 560 W, 1.2 kW, 5.6 kW
 

PROCEDURE

1. Identify the make, model no., and serial number of each piece of measuring equipment.  This will be required on all experiments.

2. Note the color code on each resistor and determine its nominal value from the color code cards provided.  The first two color bands give the two significant digits for the value.  the next band tells how many zeros to put after the first two digits.  The fourth band tells the tolerance specification for the resistor value.  No fourth band = 20%.  Silver = 10%.  Gold = 5%.  The color code cards show a third significant figure band, but this is only used for precision resistors with a tolerance of 1% or less.  We will not normally use precision resistors in this laboratory, but sometimes you may find a few in the resistor drawers.  You will recognize them by the fact that they have a total of five bands.

3. Measure and record the actual value for each resistor. The meter range should be set so that you obtain the most accurate possible value.  There should be at least three significant figures in each measurement.  Make a tabulation showing the marked or nominal value, the measured value, and the % difference ( 100[measured - nominal]/nominal).  Are they within the specified resistor tolerance?

4. Set the DMM to D.C. voltage. Turn on the D.C. power supply and adjust the power supply to its lowest value. Then measure and record the power supply output voltage. Then adjust the power supply for its maximum output value. Measure and record this value. Do this for all three outputs of the power supply.  Note the terminal marked COM is the common reference node for all three of the outputs.  The black terminal marked ground is connected only to the third prong safety ground of the ac line cord and is not internally connected to any of the three DC power supplies.  What is the range of output voltage for each of the power supply outputs?  Note the output labeled -20 is actually controlled by two controls.  The control knob above the +20 output controls both the +20 and the -20 outputs.  the ratio knob above the -20 output controls the ratio of the -20 output to the +20 output.  Experiment with changes in both controls and their effects.  The +6 output is controlled only by the control above it.  The meter built into the power supply can be switched to any one of the three outputs.  Check to see how close it comes to agreeing with the DMM.

5. Mount the 560 Ohm resistor on the circuit bread board so that the wires from each end of the resistor are not put in holes which are connected. Then connect the power supply output to the two ends of the resistor using jumper wires. Your circuit should look like the schematic diagram shown below.

The breadboards have a set of holes spaced 0.1 inches apart and arranged in a pattern similar to that shown above.  At the top and bottom edge of the board are two horizontal lines with several groups of five holes in each line.  All the holes in each of these lines are electrically connected together as shown by the red and blue lines.  In the center section of the board are two sets of vertical lines with five holes in each line.  There is a 0.3 inch space between the top and bottom set to match the standard spacing of pins on integrated circuit (IC) chips.  All the holes in each group of five are connected as shown by the black lines.  There is no connection across the central channel.  the holes will accept the solid wire leads of most electronic components.  The picture above shows a 2.2 kW resistor with its leads inserted into the middle holes of two different lines of five holes.  To connect the DC power supply to the resistor, the common lead from the power supply must be inserted into one of the other four holes of the line at one end of the resistor and the +V lead must be inserted into one of the holes of the line at the other end of the resistor.

The common lead of the meter voltmeter should go to the common side of the resistor.  The Volt lead of the meter should go to the other side of the resistor to measure the voltage across the resistor.

6. In the circuit above, adjust the voltage source, V, to approximately 4.3 V D.C., using the DMM to measure voltage.  You should have at least three significant figures in your measurements.

7. Next break the circuit and insert the DMM to measure and record the current through the series circuit above right. Keep the setting of the voltage the same as in 6. (Be sure to check the DMM for proper selection of ranges, variable, and position of the leads).  Do you have three significant figures in your measurement?

The mA meter should be connected between the +V side of the power supply and the side of the resistor where the power supply lead was previously connected.  The meter and its leads act as the connection from the power supply and the resistor so that all the current flowing through the resister must flow through the meter to get to the resistor.  This allows the meter to measure the same current that is flowing through the resistor.  To get the proper sign for the current into the positive terminal of the resistor, the positive terminal of the power supply must be connected to the mA terminal of the meter and the com terminal must be connected to the resistor.

8. Repeat the procedure in 6  and 7 above with each of the other two resistors.

9. Repeat the procedure in 6, 7, and 8 above for V = 10 V D.C. and V = 15 V D.C.

CALCULATIONS AND GRAPHS

1. Calculate the maximum expected error in each of your measurements using the information from the meter specification sheet.

2. Check Ohm's Law, by comparing your measured values of voltage (V) to the product of your measured resistance (R), measured current (I), and see if the two sides of the equation match within the expected measurement accuracy.  Is V_Measured = I_Measured * R_Measured ± the maximum value due to the accumulations of errors in the three measurements?  (|V_Measured -  I_Measured * R_Measured | < the maximum value due to the accumulation of errors in the three measurements)  See the supplement on measurement errors analysis at Measurement Errors.

3. Make a graph of current (y axis) versus voltage (x axis) for your 1 kOhm resistor. Does the current increase linearly with the voltage? On the same graph, compare to a theoretical line of constant R.  I recommend using a computer spreadsheet to plot the graphs.

4. Using Ohm's Law, calculate current (I) with a constant voltage of 10 V D.C. for each of the three nominal resistances (1.0 KW, 2.2 KW, 4.7 KW). Does the current decrease linearly with resistance? Make a graph of current (y axis) versus resistance (x axis) to show your calculated and your measured results.  If you use a spreadsheet you can easily calculate extra data points between the values of the resistances used in the experiment and then plot a much smoother curve.  Try this using steps of 0.1 kW from 1 kS to 5 kS.  Plot this theoretical curve with a line between points and no symbols.  Plot the experimental data on the same graph using symbols but no line.

5. Using the experimental measurements, calculate the power dissipated in each of the three resistors at each of the three voltages using all three methods, P=IV, P=I²R, and P=V²/R. 

6.  Make a graph of power (y axis) versus resistance (x axis) using your calculated results from step 4 above.  Does the power decrease linearly with resistance?

CONCLUSIONS  - Scientific conclusions supported by the data obtained in the experiment.

Last updated 02/03/2006