Circuits and Resistivity “Look for knowledge not in books but in things themselves.” W. Gilbert 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. Circuits An electrical circuit is a collection of components connected together with wires to perform a desired function. The physical realization of the circuit can vary enormously, as long as the connections between components are correct. For this reason, circuits are usually represented by schematic diagrams whose geometry need not resemble that of the physical circuit at all. An amplifier, for example, might equally well be assembled from several centimeter-sized components connected by pieces of solid copper wire, or from a micron-scale pattern of thin metal and semiconductor films on the surface of a silicon wafer. Details of the geometry only become important when the wavelength of the signals becomes comparable to the circuit size, typically at frequencies of a few gigahertz. A typical schematic diagram is shown in Fig. 1, along with a picture of one possible realization. If you wanted to construct a circuit you would first identify the various components AV+-+-AmpsVolts Fig. 1 Circuit for measuring the I-V characteristic of a light bulb, drawn as a schematic and as a pictorial.Circuits and Resistivity 2 and their connection points, using the manufacturers' data sheets if needed. You would then use wires to systematically join each component to the others according to the lines in the schematic drawing. The relative positions of the components need not resemble the schematic layout, but the circuit will work if the connections are correct. In discussing circuits, there are two general arrangements that are referred to by name, as drawn in Fig. 2 using resistors. In the series circuit the currents IAB and ICD must always be the same, since charge cannot accumulate between the components. The electric potential difference between A and B, VAB, will not be the same as VCD unless the elements are identical. For the parallel connection, the reverse is true: VAB = VCD because they are connected by a resistanceless wire, but the currents IAB and ICD are generally different. The distinction is useful if, for example, you want the same current to flow in two coils to generate a magnetic field. Connecting them in series guarantees that this will occur, regardless of the characteristics of the individual coils. Conversely, a group of devices which require the same voltage, such as light bulbs, would be connected in parallel with the power source. Electrical meters The potential difference between two points in a circuit can be measured with a voltmeter connected in parallel between the points, as shown in Fig. 3. An ideal voltmeter would have infinite resistance so that current flow in the circuit will not be affected by the additional path between the measuring points. Practical voltmeters, or the voltage input to a computer interface, have resistances of 1 - 10 M!, which may affect measurements in circuits with other large resistances. Current flow through a specified part of the circuit is measured by inserting an ammeter in series at the desired location, as shown in Fig. 3. An ideal ammeter would have zero resistance so the circuit would not be affected by insertion of the meter. Depending on their design and sensitivity, practical ammeters will add their internal resistance of 1 -10 ! into the circuit, which +-IIABCDABCD+-IABICDABCD(a) (b) Fig. 2 (a) Series connection of DC supply and two resistors. Here IAB = ICD, but VAB ! VCD unless the resistances are equal. (b) Parallel connection of two resistors across a DC supply. Now VAB = VCD, but IAB ! ICD unless the resistances are equal.Circuits and Resistivity 3 may disturb low-resistance circuits. Incidentally, their low resistance also means that if an ammeter is connected directly across a source of voltage, such as a battery, a very large current will flow. This is likely to damage both the source and the meter. Meters are also available to determine DC resistance. They typically apply a known voltage to the component to be tested and measure the resulting current, displaying the ratio as the resistance in ohms. The component must be disconnected from the rest of the circuit to avoid interference from currents or voltages not supplied by the meter. I-V characteristics and 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 later experiments it will be 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