Physics 111: Elementary Physics
Laboratory D
Electric Current, Potential and Power
1.
Introduction
Many of the ideas which one first encounters in physics, such as density, pressure, and speed are
familiar from our own direct experience. We have experiences with the uses of electricity which are as
familiar as the experiences related to these other quantities, but the uses are not as primitive conceptually,
so they are not at first as much of an aid. One speaks familiarly of electrical current, for instance, without
pausing to ask what it is that is flowing. One is familiar with the flow of water, for example, but electricity
and water are clearly not the same thing.
Pieces of matter have several intrinsic properties. One of these is mass. Another is electric charge.
It has been found that the smallest amount of charge found free in Nature is the amount present on a single
electron or proton (negative on the former and positive on the latter, both of the same magnitude). The size
of this elemental charge is so small in comparison to the amounts of charge transported in normal processes
that it appears that the large amount of charge is like a fluid, and we speak of its flow. The difference in
sizes becomes obvious when we note that the amount of charge which must be transferred in an electrolytic
cell to deposit one gram-atomic mass of a material is the charge called one faraday, or 96.49 x 10 3
coulombs (C). But the magnitude of the elemental charges on the electron or the proton is 1.602 x 10 -19 C.
If one divides the faraday by the elemental charge, one obtains Avagadro’s number, 6.023 x 10 23.
It is of great importance in handling electrical energy that in some materials, called insulators, the
motion of charge is greatly impeded, while in others, the metals, the resistance to transfer of electrical
charge is comparatively low. Thus by setting up networks of metal, the charges can be channeled from a
source into the region where they are needed to do work. In analogy with common fluids, we speak of the
moving charge as current. Specifically, if an amount of charge q, passes a given point of a conductor in a
given time ∆t, the current i, is the rate of flow,
i= q/∆t .
In order to specify electrical quantities, the basic unit added to the SI system of units is the unit of
current, the ampere (A). From the equation above, one could start with a unit of charge, but it is more
practical to establish accurate and reliable standards for measuring currents rather than charges, so the
universal practice is the use of the ampere as fundamental. Thus one coulomb is one defined as one
ampere.second,
1C = 1A.s.
Our experiences with charge tell us that the total amount of charge in the Universe is constant. The
condition of electrical neutrality does not necessarily imply that no charge is present. However, one only
becomes aware of charge on matter, when, as a result of mechanical actions such as rubbing, or chemical
activity such as in a so-called dry cell or in an electrolytic cell, positive and negative charges are separated.
Since the two unbalanced charges attract each other, it is necessary to do work on the charges in order to
separate them. As one would anticipate from the Conservation of Energy, it is to be expected that when the
separated charges come back together, they can do an amount of work equal to the work done to separate
them in the first place. Thus the existence of an unbalanced charge, positive or negative, represents a
situation in which potential energy exists.
The concept of electric potential is closely related to work. The electric potential difference ∆V,
between two points near a charge Q is the ratio of the work ∆W, done in moving a test charge between the
two points to the magnitude q, of the test charge,
∆V = ∆W/q.
The potential is positive if Q is positive and negative if Q is negative. The conventional unit for electric
potential is the volt (V). Since the unit of work is the joule (J), it is apparent that one can express the volt
in terms of joules per coulomb (1V = 1 J/C).
Power P, is the rate of doing work,
P = ∆W/∆t = q∆V/∆t = ∆V(q/∆t) = i∆V.
The power involved in moving a current i through a potential difference ∆V in an electrical circuit is
simply the product of the current and the potential difference.
Recall that, in the absence of a frictional force, a mass will continue to move indefinitely. In the
same manner, in the absence of a retarding force, a charge subject to the influence of an external electric
field should continue in the same state-of-motion. But if a power source is turned off, it does not continue
at the same rate. The electrical equivalent of friction occurs when the electrons (the most common carriers
of charge) encounter the nearly stationary lattice ions of the conductor and deliver to them the energy
which was obtained by the electrons from the electric potential. This electrical friction is usually called
simply the resistance of the circuit. Resistance is always defined by the expression R = ∆V/i. It is an
empirical fact, first studied by Ohm, that the resistance of a metallic conductor is a constant, independent of
the potential difference (V).
The resistance to current flow R, is large for an insulator in comparison to that which is observed for
a metal. The unit of resistance is the ohm (Ω). Not all conductors (the silicon based materials used in
transistors, for example) obey Ohm’s law, but all familiar metals do. When Ohm’s Law holds, the power
used to maintain the flow of a current i in a material of resistance R is given by
P = i∆V = i2R .
A source of electrical power provides the energy per unit time which is expressed in the first of these
last equations. The latter of these equations is typical of the power losses, of the conversion of organized
energy into heat (called Joule heat) which occurs whenever current flows in a conductor obeying Ohm’s
law. If the current from the source flows into a divided network of conductors, the total current going into
the connecting point or node equals the total amount of current leaving the node since the total amount of
electrical charge must remain constant. In an isolated electrical network or circuit, just as in an isolated
mechanical system, total energy can be neither created nor destroyed. Thus the total Joule heat losses must
equal the amount of energy which is provided to the current by the power source.
2.
Procedure
You will set up a simple circuit involving a source of electrical power and three resistances which
will allow you to measure voltages, currents and resistances to test the proposition that the total power
losses in a circuit balance the power input. A sample circuit to be constructed with the equipment provided
is shown below.
The parallel bars, marked V, represent the power source, the
broken lines, marked R, represent the resistances and the
circled A’s represent current meters (ammeters). These
components are to be connected by wires, represented by the
straight lines on the diagram between the components.
Assemble the components and ask the Lab Instructor to check
your circuit before turning on the power supply.
The multimeter will allow you to measure the voltage
changes which occur across elements of the circuit. You can
also use this instrument to measure the resistance of the
various components. The Assistant will explain to you how to
use the multimeter to read voltage, current, and resistance. All
changes in the multimeter functions should be made with
power removed from the circuit.
The resistance boxes will let you set the resistances Ra
and Rb to about 500 ohms (Ω) and 1000 Ω respectively. The resistance R c is variable. Note that the
settings of the scales on the power supply are indicative of the magnitudes of the quantities involved, but it
cannot be assumed that any of these settings are carefully calibrated. Thus you should rely on the readings
which you make with the multimeter in the calculations which you make later. Set R c to approximately 500
Ω and record on the data sheet the values of the three resistances. After the circuit has been assembled and
checked, set the power source V to deliver about 6.0 volts to the circuit. With the multimeter set to read
DC voltage, record the voltages across the power source and each of the resistors. Enter the data on the
sheet on the next page. Use the ammeters in series with each of the resistors, as shown in the circuit
diagram above, to measure the current flowing in that resistance. Again record the data. Change the
variable resistor Rc, to approximately 2000 Ω and repeat the series of measurements.
Physics 111: Elementary Physics
Pre-Lab Exercise
Electric Current, Potential and Power
Name: ____________________________
Section: ___________
Some typical data from this type of experiment are given below. Note that 1mA = 10 -3 A.
1.
V = 10.0 V
Ra = 500 Ω
Rb = 1000 Ω
Rc = 750 Ω
ia =10.7 mA
ib = 4.6 mA
ic = 6.1 mA
Va = 5.4 V
Vb = 4.6 V
Vc = 4.6 V
Conservation of charge implies that at each branching point, or node, the current in should have
the same value as the current out. Use the data to test the statement.
ia = ib + ic .
2.
Conservation of energy tells us that the total energy provided to the circuit should balance the
Joule heat losses in circuit. The rate at which the energy is provided, the input power, must
therefore balance the rate at which the energy is converted to heat. Use the data to test the
following relationship equating the power in to the power out. [Since the values of voltage and
current above have been rounded to one decimal place your test of the equality below will not be
exact]
iaV = ia2 Ra + ib2 Rb + ic2 Rc
.
3.
Conservation of energy also tells us that the voltage rises around any given loop should equal the
voltage drops in the same loop. Use the data to test the following statements.
V = V a + Vb = V a + Vc .
4.
State briefly (100 words or less) the objectives of this experiment and the principles which are to
be tested.
Physics 111: Elementary Physics
Lab Report
Electric Current, Potential and Power
Investigators:
________________________ ,
_______________________
________________________ ,
_______________________
________________________
Date: _____________
Procedure: Describe briefly (200 words or less) the procedures used in this experiment.
Data:
1.
V = ___________
Ra = ___________
Rb = ___________
Rc = ___________
ia = ____________
ib = ____________
ic = _________
Va = ___________
Vb = ___________
Vc = _______
Repeat the calculations in questions 1, 2 and 3 of the Pre-Lab Exercises for the data above .
2.
V = ___________
Ra = ___________
Rb = ___________
Rc = ___________
ia = ____________
ib = ____________
ic = _________
Va = ___________
Vb = ___________
Vc = _______
Repeat the calculations in questions 1, 2 and 3 of the Pre-Lab Exercises for the data above .
Discussion:
Discuss the outcome of the experiment.
conservation laws tested ?
In particular, did the results validate the