Physics 201 Laboratory: Analog and Digital Electronics. I-0. Introductory Notes

Transcription

1 Physics 201 Laboratory: Analog and Digital Electronics -0. ntroductory Notes Definitions of circuit and current. Current is the flow of charge. We may think of electrons flowing through a wire as a current the movement of negative charges. By convention, the current is in the opposite direction to the electron flow. A complete circuit is a closed path around which current may flow. Definitions of conductors and insulators. A conductor conducts electricity: it is a material that allows for the easy flow of charge. An insulator inhibits this flow: it does not easily conduct electricity. Metal wires are conductors, whereas rubber is an insulator. Characteristics of electrical circuits. The current in a circuit is usually designated by ; the S unit for current is the Ampère (abbreviation: A). The quantity that induces the flow of charge is called voltage or potential, and is usually denoted by ; its units are olts (abbreviation: ). A characteristic of material that impedes the flow of charge is called resistance, labeled R, whose units are Ohms (abbreviation: Ω). Generally we are interested only in potential differences; that is, the point in our circuit we choose to be at zero potential is arbitrary. Ohm s Law. The relation between voltage, current and resistance for many materials is quite simple, and is known as Ohm s Law: = R. Materials for which this expression is valid are called ohmic. Circuit elements. An electrical circuit may contain active elements (sources of potential, e.g., batteries), which introduce electrical energy into the circuit, and passive elements or loads (e.g., light bulbs), which remove energy from the circuit. Typical loads are resistors, capacitors and inductors, to be described later. A wire is not a circuit element: it does not provide energy nor, ideally, does it remove it. Actually, wires have non negligible resistance (and will therefore heat up a little in a live circuit), but for our purposes this may be ignored. Wires, then, maintain a constant potential across their lengths and therefore provide for a

2 -0. ntroductory Notes p. 2 less cluttered circuit, but they may be removed or replaced by other wires without altering the circuit, provided the circuit is kept complete. Open and short circuits. Circuits which are not fully connected are called open circuits. No current flows through an open circuit. Two points connected by a wire, which offers no load (resistance), are said to constitute a short circuit. The ends of a source of potential should not be short-circuited, for Ohm s Law above would require an infinite current to provide a non zero voltage across the negligible resistance of the wire. Series and parallel circuits. A series circuit is one which is linear: current passing through a given component has no choice but to continue to pass through other components in series with it. A parallel circuit is a branch: current entering a parallel circuit will generally be divided between the various branches. Figures 1 and 2 show a series and a parallel circuit. n Figure 2, = R 1 R 2 1 R 1 2 R 2 Figure 1: Series circuit. Figure 2: Parallel circuit. Direct and alternating current. Direct current (DC) and alternating current (AC) are distinct types of current. Batteries, for instance, produce direct current: a constant potential difference is maintained between the nodes of the battery, so a circuit connected to it will draw a current equal to this voltage divided by the effective resistance of the circuit (by Ohm s Law). f this circuit is connected to the AC wall current, however, the input voltage will vary sinusoidally with time, so the current (= /R) will also be sinusoidal (alternating) since R is constant. Passive circuit elements. Passive circuit elements do not provide electrical energy to a circuit. The simplest type is the resistor, which is simply a cylinder of graphite which does not conduct electricity as easily as metal wires. t will heat up as current passes through it; this is the conversion of electrical energy to heat energy (Joule heating). Consequently, a resistor, when placed in a live circuit, will have a potential difference across it. n Figure 3, for example, an electron gains energy e (where e is the electron charge) when it goes through the battery and it loses energy e when it goes through the resistor R. Here, = R.

3 -0. ntroductory Notes p. 3 R Figure 3: A simple circuit Another passive circuit element is the capacitor, which may be thought of as two conducting plates separated by an insulator. When placed in a DC circuit, it will allow charge to build up (negative on one plate, positive on the other) until the current vanishes. A third type is the inductor, which is of interest in AC circuits, and will be described later. Circuit diagrams. We may represent electrical circuits schematically with a circuit diagram. Wires are represented by lines; more than two wires which connect are marked at intersection by dots. Figure 2 shows the symbols for common circuit elements. One must be careful to differentiate between a DC source and a capacitor. DC source (e.g., battery) AC source (e.g., wall current) Resistor ariable resistor (potentiometer or helipot) Capacitor nductor Figure 4: Circuit elements. Notes: The long bar in the DC source diagram is the higher potential side. We generally think of current as flowing from higher potential to lower potential. This may be remembered by associating current with water and potential with height: a battery will force current uphill (from the short bar to the long bar) and a resistor will allow it to drop. This analogy is only a model for electricity, however, and should be as such. Kirchhoff s Laws. There are two fundamental laws related to circuit analysis. One, the node law (or current law), derives from the principle of conservation of charge; the other, the loop law (or voltage law), from the principle of conservation of energy.

4 -0. ntroductory Notes p. 4 Kirchhoff s Node Law. Simply stated, the current entering a node must equal the current coming out of the node. n the water analogy, all the water entering a pipe junction must leave that junction. Mathematically, in = out at any node in a circuit. n Figure 2, for example, = Kirchhoff s Loop Law. f we pick an arbitrary point on a circuit diagram and follow the circuit around until we return to the original point, counting potential increases as positive and potential drops as negative, the total must be zero. This is required by the definition of electric potential. Another expression of this is the statement that we cannot associate two different potential values to the same point in a circuit. This is embodied by the loop law: the sum of the potential differences encountered when traversing a closed loop in a circuit must be zero: closed loop = 0. This rule is not without its share of confusing sign conventions, but it is remarkably versatile in that the direction of current in a branch need not be known. By way of illustration, consider Figure 3, in which a single loop containing a battery and a resistor are connected. The current flows as shown (), but we may have chosen the other direction for ; this will not yield erroneous results upon using the loop law provided the following sign convention is followed: after choosing the direction of the loop you wish to follow, independent of the direction of the current(s), consider the traversal of a battery (or other DC source) as an increase in potential (positive potential difference) only in the event that you are passing from the short bar (negative side) to the long bar (positive side), and negative otherwise, and consider the traversal of a resistor as a decrease in potential (negative potential difference) only if passing with the current, and positive if passing against the current. The direction of the current here may be artificially chosen. n this example, if we choose the direction of our loop to be clockwise, starting from a point just below the battery, we encounter a potential increase at the battery (+ ) and a potential decrease at the resistor ( R). Thus, R = 0 here. f the loop were chosen in the other direction, convince yourself that the loop law would yield + R = 0, the same equation as before. Convince yourself further that changing the direction we assign to the current (and calling it ) will yield + R = 0, which is the same equation as that above if we assign =, i.e., the new current is of the same magnitude as but in the opposite direction as that we have (incorrectly) chosen. Currents are physical, so their directions must not depend on the conventions of the loop law. For instance, if = 10 olts and R = 5Ω, the first loop would

5 -0. ntroductory Notes p. 5 have given = /R = +2 Ampères as the current, whereas the second loop (whose direction is the opposite of that of the first loop) would have resulted in = /R = 2 Ampères, in the opposite direction. The two situations are physically identical: a positive current in one direction is identical to a negative current in the opposite direction. Measuring devices. Your lab bench contains a digital multimeter (DMM) which has modes to measure potential differences (voltmeter mode), currents (ammeter mode), and resistances (ohmmeter mode). The DMM may operate in only one mode at a time. oltmeter mode. Kirchhoff s Loop Law will allow you to prove easily that two branches of an electrical circuit, connected at either end to each other, have the same potential difference across them. For example, 1 R 1 = 2 R 2 in Figure 2. Thus voltages may be measured by placing a voltmeter in parallel with the circuit element(s) around which the potential difference is to be measured. oltages should be measured across part of a live circuit (viz., one in which current is flowing) to be meaningful. Ammeter mode. Kirchhoff s Node Law will allow you to see that the current in any part of a series circuit is constant, so currents should be measured in series with the circuit path to be tested. Unlike the voltmeter mode, using the DMM in the ammeter mode will require you to disconnect part of the circuit and force the current to run in series through the ammeter. Ohmmeter mode. n ohmmeter mode, the DMM produces a tiny current and uses Ohm s Law to compute a resistance from a measured voltage. n this mode, then, any auxiliary current will render the reading useless (and may even damage the DMM). To measure the resistance of a (set of) circuit element(s), disconnect the element(s) in question entirely from the circuit and place the DMM leads on each end. Never use the DMM in ohmmeter mode while testing a live circuit. Notes on this lab: The tray of circuit elements, etc., and the breadboard, which you will receive at the start of the first lab, is yours alone for the duration of the semester. Feel free to leave circuits on the breadboard from week to week; no one will pirate the components or remove the breadboard from your bench. The lab book you will use during the course of this semester is meant to be a diary of your experiments. This means that anything and everything you feel is pertinent to the lab should be written into it. You need not use rulers and fancy colored pencils unless you wish to do so: a primary goal in recording an experiment is to be able to easily understand what you did one year from now.