Physics 201 Laboratory:
Analog and Digital Electronics
I-0. Introductory 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
I; the SI 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 V; its units are Volts
(abbreviation: V ). 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:
V = IR.
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
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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.
In Figure 2, I = I1 + I2 .
I
R1
V
I
R2
Figure 1: Series circuit.
V
I1
R1
I2
R2
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). If this circuit is connected to the AC wall current, however, the input voltage
will vary sinusoidally with time, so the current I (= V /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. It 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. In Figure 3, for
example, an electron gains energy eV (where e is the electron charge) when it goes through
the battery and it loses energy eV when it goes through the resistor R. Here, V = IR.
I-0. Introductory Notes
p. 3
V
I
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
Variable resistor (potentiometer or helipot)
Capacitor
Inductor
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.
I-0. Introductory Notes
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Kirchhoff ’s Node Law. Simply stated, the current entering a node must equal the current
coming out of the node. In the water analogy, all the water entering a pipe junction must
leave that junction. Mathematically,
Iin = Iout
at any node in a circuit. In Figure 2, for example, I = I1 + I2 .
Kirchhoff ’s Loop Law. If 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:
∆Vclosed 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 (I), but we may have chosen the other direction for I; 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. In 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 (+V ) and a potential decrease at the resistor
(−IR). Thus, V − IR = 0 here. If the loop were chosen in the other direction, convince
yourself that the loop law would yield −V + IR = 0, the same equation as before. Convince
yourself further that changing the direction we assign to the current (and calling it I 0 ) will
yield V + I 0 R = 0, which is the same equation as that above if we assign I 0 = −I, i.e.,
the new current is of the same magnitude as I 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 V = 10 Volts and R = 5Ω, the first loop would
I-0. Introductory Notes
p. 5
have given I = V /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 I 0 = −V /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.
Voltmeter 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, I1 R1 = I2 R2 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. Voltages 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. In ohmmeter mode, the DMM produces a tiny current and uses Ohm’s
Law to compute a resistance from a measured voltage. In 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.