Download Ohm`s Law Lab Eli Bashwinger Lab Partners: Jennifer Morriesey

Ohm’s Law Lab
Eli Bashwinger
Lab Partners: Jennifer Morriesey,
Matthew De Waal Malefyt
OBJECTIVE: You will determine if certain resistors “obey” Ohm’s Law by making
measurements of voltage versus current. If the data fits Ohm’s Law, then a plot of V vs I
will be linear and pass through (0,0). Furthermore, the slope will equal the resistance. You
will also make predictions of voltage and current using Ohm’s Law, and see how resistors
combine in “series” and “parallel”.
A
R
Theory: Ohms’ law states that electric current through a conductor between two points is
proportional to electric potential difference, and inversely proportional to the resistance that the
current experience between these two points. In mathematically terms,
, where I is the
electric current, V is the electric potential difference, and R is the resistance a circuit,
This section of theory will be devoted to explaining constituents (electric current, electric
potential, electrical resistance) of Ohm’s Law in more detail:
Electric current is, when flow is steady, the rate at which charge flows between the two
points during a time interval (is this time interval the amount of time it takes the charge to flow
from one terminal to the next?):
, which is in units of amperes. Since electric current
does not always flow steadily, it’s better to state electric current more generally as
, the
infinitesimal unit of charge that flows (where is it flowing? Between the two points?) during an
infinitesimal time interval
Resistance is a measure of the inherent opposition a conductive material imparts to the
flow of charge. Electrical resistance depends on a few quantities: it depends on the physical
properties of the material used to make the electrical wire; it depends on the cross-sectional area
of the wire; and, finally, it depends on the length of the wire.
Electric potential, V, has many countenances, but its simplest form and most applicable
form, at least to our situation, is
, where the ratio can be thought of—not in a strict
and formal sense, mind you—as the potential energy a positive unitary charge possesses, as it is
moved an from a position of zero electric potential (this point can be chosen arbitrarily, and is
usually chosen at a point infinitely far away; but in the context of electric circuits, zero electric
potential is assigned to the negative terminal), to a point of interest. Electric potential is a
property of an electric field; it has a different scalar value at every point in the electric field
generated by a source charge distribution, given that you aren't comparing equipotential regions.
For instance, let’s take a simple example of a positive point source charge to help understand
electric potential. (Before we proceed, though, a little preliminary work is needed.) The electric
field due to a point charge can be obtained from Coulomb’s Law:
, where Fe is the electric force described by Coulomb’s Law, and q0 is a positive test
charge placed in the electric field, used to quantize the direction of the electric field and its
strength at a particular position. Substituting in our expressions and simplifying, the electric field
becomes,
, where q1 the positive source charge. Now, our we know the general
expression for electric potential is
, where a is some initial point and b is
some final point in the electric field created by the source charge. Through modification, our
expression becomes
, because the strength of the electric field at some
particular point only depends on the radial distance between that point and the source charge, and
so will our electric potential at some point I the electric field. Integrating and simplifying, we
arrive at an expression for the electric in some electric field due to a source charge, that only
depends on the radial distance:
, where we take Vi to be zero at r = infinity.
Now, suppose we have a positive point source charge, fixed at some position, whose charge is
+ 20 C. At a radial distance of 10 m, the electric potential due to the source charge’s field would
be 4.45e10 J/C. Now, let’s move a positive point charge of 1 C to this point, from its place at
infinity; as you can imagine, the charges will repel each other, so this going against the nature of
things, object’s in nature like to be in places of low potential energy, so this particle will have to
have an external force applied to it over a distance, thereby doing work, furthermore exhausting
the external agents energy and transferring it into the particle. What potential energy would this
particle possess at this point? 4.45e10 J. This justifies our notion that we can think of electric
potential as the amount of energy that would be put into a positive point charge of 1 C in moving
it from infinity to a point of interest in the electric field. What if we had a 2 C particle? Well, we
know that for every 1 C of a particle stationed at this point, it will possess 4.45e10 J of energy.
We have 2 C, so it would be twice as much, which is consistent with our mathematical formulas
and intuition.
The two points are usually taken to be the positive and negative terminal
current flows from high electric potential to low electric potential, during which it is resisted by
the inherent properties of the material through which the current is flowing; among these are
material type and geometric properties.