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Experiment 7 DC Circuits and Instruments
“Look for knowledge not in books but in things themselves.” William Gilbert (1544-1603)
OBJECTIVES To learn the use of several types of electrical measuring instruments in DC circuits. To observe the I-V characteristics of some devices. To see how resistivity is measured.
THEORY Because electrical devices and measurements are so pervasive, some knowledge of them is essential to all technical disciplines. In this experiment we will introduce several instruments and use them to measure the electrical characteristics of some common components and circuits. We will also measure a fundamental property of materials, the resistivity. One of the most basic properties of any electrical device is the amount of current I which flows when a known voltage V is applied to the device. A plot of the current as a function of the voltage is usually called the "I-V characteristic" of the device. The I-V characteristic is often a complicated curve, which may change as the temperature of the device changes, as light hits the device and so on. Sometimes these changes are used to sense temperature, light level or some other variable, but at other times any change is a nuisance. Whatever the I-V curve looks like, it is customary to define the ratio V/I as the resistance, R , of the device at a particular current, temperature, light level etc. When V is in volts and I in amperes, R is in ohms. There are many situations in which the I-V curve is simply a straight line through the origin. In other words, V = IR , where R is a constant. Such devices are said to obey Ohm's Law, or to be "ohmic". If the curve is also reasonably independent of external influences the device becomes particularly useful in electronics, and is simply called a "resistor". For example, in some situations it is convenient to use the voltage across a known resistor to infer the current in a circuit. Resistance depends on both the geometry of the device and the material of which it is made. The resistivity is a more fundamental property of the material, since it is independent of the geometry of a particular specimen. Resistivity, , is defined by
= E/J (7-1)
where J is the current density in response to an applied electric field E. More practically, the measured resistance of a sample of length L and area A is related to the resistivity by
R = L/A (7-2)
This relationship assumes that the material has been shaped into a uniform cross-section and that the current is uniformly distributed across the area. Turning now to circuits, it is clear that any combination of ohmic resistors is also ohmic, and could be replaced by an equivalent single resistor. Your text works out the effective resistance of series and parallel combinations of resistors R 1 and R 2 , arriving at
Reff = R 1 + R 2 (series) (7-3)
and
1 Reff
R 1
R 2
(parallel) (7-4)
More complicated combinations can be worked out by successive applications of these two results. Figure 7-1 displays two representations of a circuit for measuring the voltage across a light bulb and the current through the bulb. On the left is a schematic diagram, as usually seen in text books. It shows the connecting wires, represented by solid lines between the various devices, each of which is represented by a special symbol. On the right is a pictorial representation of the same circuit as it might appear in the lab. Since the schematic is much easier to draw, it is usually used in preference to a pictorial representation. The mechanical details of the circuit are then left to the ingenuity of the experimenter. We will almost always work with schematics, so it is important for you to learn to translate them into hardware easily and correctly. Recall that current is defined as the amount of charge that flows through a point in a specified time. To measure the current, we must therefore break the circuit and insert our ammeter at the point where we want to know the current. We can then think of current flowing in the original circuit up to the desired point, taking a detour through the ammeter, and being returned to the
A
V + - + -
Amps (^) Volts
Fig. 7-1 Circuit for measuring the I-V characteristic of a light bulb, drawn as a schematic and as a pictorial.
The digital multimeter or DMM can be used as an AC or DC ammeter or voltmeter, or as an ohmmeter. With the instrument in front of you, the set-up procedure is reasonably logical. As an example, we want to use the DMM as a DC voltmeter for our first measurements. Simply set the large knob to point at the "V" with the straight line beside it (the other symbol denotes AC voltage) and connect the circuit to the terminals labeled “V” and “Com” on the meter. The DMM automatically chooses a range and displays the voltage. Other functions are set up in a similar fashion. (The left-most input is used only for the current ranges, which we will not need for the moment.) The first experiment you should try is the measurement of the I-V characteristic of a resistor. Wire up the circuit of Fig. 7-1, replacing the light bulb with a 150 resistor and the battery with the power supply. Use the DMM to measure the voltage across the resistor. By varying the output of the power supply you will vary the current through the resistor. Plot current vs voltage as you go along to avoid the tedium of tabulating and then plotting data. Is the inverse of the slope of your line reasonably close to 150? When you finish with the resistor, replace it with the light bulb, and make a similar plot. The resistance of the bulb varies with the temperature of the filament and the temperature varies with the current, so we might expect some strange things to happen. Is the lamp ohmic?
Color Digits Multiplier Black 0 100 Brown 1 1 10 1 Red 2 2 102 Orange 3 3 103 Yellow 4 4 104 Green 5 5 105 Blue 6 6 106 Violet 7 7 107 Gray 8 8 108 White 9 9 109
Fig. 7-2. The resistor color code. The last band specifies the relative accuracy of the value: Gold ±5%; Silver ±10%; No band ±20%. A 51k, 10% resistor would be marked Green-Brown- Orange-Silver.
Next you should use the ohmmeter capability of the DMM to check the rules for series and parallel combinations of resistors, Eq. 7-3 and 7-4. Disconnect the power supply and dismantle the previous circuit. Switch the DMM to resistance measurement by turning the large knob to point at the "" symbol and connecting leads to the same terminals you used for voltage. Pick any two resistors from the left-hand column on the panel to be R 1 and R 2. Measure their values with the
DMM. Are they within the specified tolerance of their marked values? Using the measured values, calculate the effective resistances for the series and parallel combinations of the two resistors. Connect the resistors as in Fig. 7-3 and measure the actual series and parallel resistances. Do the measurements agree with the calculation? As a last exercise, we will determine the resistivity of some Play-Doh™. Because it does not come with wires attached, we will need to make our own connections. This is a bit complicated because chemical reactions between metal and Play-Doh may cause the contact resistance to change as current flows. To get around this problem, we will make a "4-probe" measurement as follows. Roll out a circular cylinder of Play-Doh, keeping the diameter as uniform as possible, and press the ends onto the two copper plates provided. Make the specimen long and skinny so the voltage will be big enough to measure easily. Connect the copper plates in series with the ammeter and power supply so you can pass current through the sample. Measure the voltage between two points a convenient distance apart on the cylinder surface. Changes in resistance at these contacts cannot affect the voltmeter reading since there is no current flow through the voltage contacts. Knowing the current, voltage and geometry you can derive the resistivity from Eq. 7-2. Try several shapes and areas to see if the resistivity as defined in Eq. 7-2 is indeed a constant of this material. Is Play-Doh ohmic?
REPORT This lab has many small bits of data and scattered questions. The write-up will be shorter than usual, but be sure all the pieces of your work can be identified by the instructor.
R 1 R 2
R 2
R 1
Fig. 7-3. Series and parallel connections of two resistors
