- Voltage and Current
The voltages and currents measured in this lab generally take on the form
-
v(t) = B + Asinwt volts where
- B is the DC component of v(t) called the DC offset or just offset
- Asinwt is the AC component of v(t). Note that the AC component is a periodic function of time. The AC component has three parts: Shape (sin implies a sinusoidal shape); Amplitude (A is the zero-to-peak amplitude); Frequency (in this example the frequency would be radian frequency.
Recall these useful terms:
Radian frequency w = 2pif where f is frequency in Hertz (i.e. cycles/second)
Period T = 1/f = 2pi /w
Zero-to-Peak Amplitude = A for a sinusoidal function
Peak-to-Peak Amplitude = 2A for a sinusoidal function
RMS Amplitude = A /21/2 for a sinusoidal function
There are controls on the DMM that allow you to measure each of the parts of v(t) (B, A RMS, and frequency) very accurately. Note that each key has two (or more) options. To select the function printed on a key just press the key. To select the function printed just above the key you must first press the blue Shift key and then the function key. For example, if you wish to measure DC current then you must press the Shift key and then the DC V key to put the DMM into DC I (DC current) measuring mode. Note that you may only measure one quantity at a time. You must select either the DC V or AC V key to measure DC or AC voltages respectively.
- B is the DC component of v(t) called the DC offset or just offset
- Range Setting
The are two range modes: Auto ranging (the default mode) and Manual ranging. You may toggle between the two ranges by pressing the Auto/Man key. Pressing an arrow key puts the DMM into manual ranging mode and allows you to select a higher (arrow up) or lower (arrow down) range. If a range is to low for a value being measured then the meter goes into an overload condition indicated by OVLD printed to the display. To get out of overload simple select a higher range or select auto ranging. The most accurate rage is the lowest possible range that does not put the meter into an overload state.
- Terminals
For voltage and resistance measurements use the two upper right hand terminals just below the Omega V diode symbols. HI is the positive (+) terminal and LO is the negative (-) terminal for the voltage measurement. Use the two lower right hand terminals I and LO for current measurement. The I terminal is the positive terminal for the current measurement. The most common mistake made in the lab will be forgetting to move the positive connection from HI to I when going from a voltage measurement to a current measurement.
- How to measure current, voltage, and resistance
Your Teaching Assistant will explain to you how to use DMM to measure currents, voltages, and resistances. However, note the following:
- To measure voltages, you only need to attach the leads of the DMM
to two points of the circuit, select the DC V or AC V function, and select a meter range. The meter reading gives the voltage of the point connected to the
HI terminal (use a red cable) with respect to the point connected to the LO
terminal (use a black cable.) Voltage readings are the easiest
type to take.
- To measure currents, you must break the circuit at the point
where the unknown current flows, and re-route the current through the
meter, entering at the I terminal (use a red cable) and leaving at the LO
terminal (use a black cable.)
Then you must select the DC I or AC I function, and select the appropriate range.
- To measure resistance, you must disconnect at least one side of
the resistor from the circuit before attaching it to the DMM terminals or
leads. If you leave the resistor in the circuit and try to measure it in
place, you are likely to get bizarre results. This is because the DMM sends
current through the resistor to perform the measurement, and it assumes that
the current flows only through that single resistor. If the resistor is still
connected to the circuit, the current from the DMM might go through other
paths, with unpredictable results. Press the key labeled Omega 2W.
2W stands for the "two wire" measurement. Now select a range.
- To measure voltages, you only need to attach the leads of the DMM
to two points of the circuit, select the DC V or AC V function, and select a meter range. The meter reading gives the voltage of the point connected to the
HI terminal (use a red cable) with respect to the point connected to the LO
terminal (use a black cable.) Voltage readings are the easiest
type to take.
Set up the circuit in Figure 1 using the DC supply for VS and a 3.3K resistor for R. Adjust the DC voltage supply until the DMM, used as an ammeter, shows that the current is 1.00 mA. Then remove the DMM from the circuit (don't forget to re-connect the bottom of R to VS) and use it, now as a voltmeter, to measure the voltage across the resistor. Last, disconnect the resistor from the circuit and use the DMM to measure its resistance. Do the three readings verify Ohm's Law? Record the measurements and the percent error observed between R measured directly, and R calculated by R = V/I. Compare both of these values with the value of the resistor read from its color code (the so-called "nominal" value) and see whether or not the value is within the stated percentage tolerance.
Figure 1.
Set up the circuit in Figure 2 with
R1 = 20K
R2 = 33K
R3 = 47K
V6 = 8 Volts (use the +25 - COM terminals of the DC supply with the current limit set to 100mA. Remember that you are setting the maximum
current that the generator will be able to deliver and not the actual value that is being delivered - you will measure that value.)
Figure 2.
Measure all six voltages with the voltmeter (the DMM set on the DC voltage setting.) Using your DATA, make a table indicating the percent inaccuracy, according to your measurements (i.e. your DATA), in these three Kirchoff voltage law relationships:
V1 + V2 = V4
V2 + V3 = V5
V1 + V2 + V3 = V6
Do the data values on the left sum to the data on the right? That is the inaccuracy error that you are checking.
Measure the three resistors with the DMM and make a table indicating the percent inaccuracy, according to your measurements, in the relationships
V3 /R3 = V2 /R2 = V1 /R1 = I
We have not measured I yet. But each of the above ratios should equal the same value of I since the same I is flowing in all three resistors. Are the currents the same?
Now remove the DC supply from the circuit and insert the function generator as VS. Set VS = 4sin(3000pit) volts. The DC offset should be set to zero. Now repeat the above experiment making AC voltage measurements.
There are two ways to measure currents: (1) directly, using an ammeter, and (2) indirectly, using a voltmeter (or a scope) to measure the voltage across a resistor and then calculating the current by use of Ohm's Law. The second method, of course, is only accurate if you have an accurate value for the resistor.
Set up the circuit in Figure 3 with
R1 = 20K
R2 = 33K
R3 = 47K
VS = 8 Volts (use the +25 - COM terminals of the DC supply with the current limit set to 100mA.)
Figure 3.
Measure the indicated currents directly by inserting the ammeter (the DMM set on the DC I setting) into the circuit at the locations indicated by "I1", "I2", etc. Record your observations in a table and indicate the percent inaccuracy, according to your measurements, in the Kirchoff's current law relationships
I1 + I2 = I4
I3 + I4 = I5
Now measure the indicated currents indirectly (by measuring the voltages, measuring the resistances, and using Ohm's law) and repeat the above calculations of inaccuracy.
We will not do AC current measurements in this experiment.