ELECTRICITY: VOLTAGE, CURRENT, and OHM'S LAW
OBJECTIVE: To study the relation between voltage and current (Ohm's Law), to use Ohm's
Law to investigate resistance measurements, and to investigate the factors upon which the
resistance of a conductor and sets of conductors depends.
TERMINOLOGY:
symbols:
units:
meters
current (I)
amps [A]
conductor
voltage (V)
volts [V]
insulator
resistance (R)
ohms []
circuit
power (P)
watts [W]
THEORY:
Current is defined as the flow of electricity (flow of charges). It is measured in amps [A].
Voltage is defined as the energy per charge at a particular position and is measured in volts [V].
Current tends to flow from a place of high voltage to a place of low voltage - just like water
tends to flow from a place of higher elevation to a place of lower elevation. (Hence, elevation in
water flow is analogous to voltage in current flow.) Resistance is simply how much the material
resists the flow of charges and is measured in ohms []. (In our water analogy, water flowing
through large pipes encounters very little resistance, while water flowing through a sponge or
through sand encounters a higher resistance.) A voltage source (such as a battery or a power
supply) is like a water pump: a water pump can move water from a lower place to a higher
place; the voltage source moves the charge from a place of low voltage (negative terminal) to a
place of high voltage (positive terminal). A circuit is simply a path for the charges to flow from
the high voltage position to the low voltage position, just like pipes or rivers can form a "circuit"
for water flow.
The individual circuit elements are connected in such a way that the current flows through them,
usually giving up energy in the process. As the charges give up energy, the potential energy of
the charges (and hence the voltage) will decrease as they traverse the circuit. OHM'S LAW
states that for most common conductors the potential difference (V) across the conductor is
proportional to the current (I) that flows through the conductor:
V = IR .
(1)
The resistance is then simply the constant of proportionality and is a measure of how hard it is
to force the current through the conductor: the bigger the resistance, the more voltage is
needed to force a certain amount of current; or alternately, the bigger the resistance, the less
current will flow through the resistance for a certain voltage.
(NOTE: Although the formula should read V = IR, we often measure voltage like we measure
height: from some common reference level we label as 0, and hence V and V become the
same.)
In this experiment we will use the law to calculate the resistance of certain conductors, after
measuring the current and the potential difference. Since both the ammeter (for current
measurements) and the voltmeter (for potential difference measurements) have some
resistance, there will be certain errors in the measurements. Corrections would have to be
made for this in very accurate work.
Electricity: Voltage, Current, and Ohm's Law 2
There are two basic ways of connecting components into a circuit: series and parallel. In
SERIES, the same current must flow through each component. In PARALLEL, the current will
divide and different amounts will flow through the different components. The current in a series
circuit is the same throughout, so an ammeter is always connected in series. A voltmeter
measures the voltage difference between two points in a circuit, or across a particular part of a
circuit, and this means that a voltmeter is always connected in parallel.
In using D.C. instruments, care must be taken to connect them up with the proper polarity. The
terminal marked (+) should always be connected to the positive terminal of the power supply
and the terminal marked (-) to the negative terminal. They need not be connected directly, but
you should be able to trace back to the proper terminal. On many instruments only one terminal
is marked, and it is understood that the other is the opposite polarity. On meters with more than
one scale, the number on the terminal refers to the MAXIMUM value that can be measured on
that scale.
METHOD:
In Part One, the current in a resistor is varied by changing the applied voltage. The currents
and the corresponding voltages are measured. A voltage-current curve is plotted and the slope
of a straight line fitted to the points yields a value of a resistance which can be compared to the
known value.
In Part Two, we use a length of wire as our resistor. The potential difference across various
lengths of resistance wire are measured while the current is kept constant. A graph of
resistance versus length (which should yield a straight line) will illustrate the dependence of
resistance on length of conducting wire.
In Part Three, the resistance of several coils of wire of various sizes and materials are
measured by the voltmeter-ammeter method. From this data, the variation of resistance with
length, cross-sectional area and material is noted.
In Part Four, two light bulbs are used as resistors and the resistance of the different
combinations of the bulbs is analyzed.
*CAUTION: The power supply output should be turned down between readings to minimize
heating of the resistors. Heat causes the resistance to increase and this could decrease the
accuracy of your results.
Part 1. Ohm's Law: V = IR
PROCEDURE:
1. Connect the apparatus as shown in Fig. 1, using the 10 ohm resistor for R. Although this
resistor is stamped 10 , it will not be exactly 10 ohms when measured. Resistors are
guaranteed accurate only within a certain percent (10% in this case) which is usually
indicated on the resistor in some way. The power supply (PS) has a control so that by
rotating it the voltage across the resistor (and hence the current through the resistor) can be
varied from zero to some maximum value.
2. Adjust the voltage control on the PS so that about 0.5 A runs through the resistor. Then
take readings of voltage and current at about 0.1 A intervals as the current is decreased
from 0.5 A to zero.
Electricity: Voltage, Current, and Ohm's Law 3
+
+
PS
R
V
-
A
-
+
Fig. 1
REPORT:
1. Display your data (voltage vs. current) in tabular form.
2. Plot a graph of voltage (ordinate or vertical axis) and current (abscissa or horizontal axis).
3. Compute the slope of the best straight line through the points. Use a point on the line near
the top and one near the bottom to calculate the slope. (Recall that the slope is the change
in vertical quantity divided by the change in the horizontal quantity.)
4. Compute the percent difference between the slope and the nominal value of 10  for the
resistor. Is it less than 10%?
Part 2. Resistance vs Length
PROCEDURE:
1. Connect the slide wire to the power supply as shown in Fig. 2. Adjust the power supply
voltage so that a current of 0.5 Amps or less flows through the circuit.
2. Record the voltages and currents for lengths, ,of the wire of 20, 40, 60, 80, and 100 cm.
Simply move one of the alligator clips of the voltmeter to change the length.

wire
+
V
+
PS
+
A
-
-
Fig. 2
REPORT:
1. Report your data (voltage vs. current for each length) in tabular form.
2. Calculate the resistances of the various lengths of wire (using V=IR).
3. Plot a graph of resistance against length. As best as you can, fit a straight line to the points.
4. Describe or express in some way the relation between the resistance of a conductor and its
length as illustrated by your graph.
Electricity: Voltage, Current, and Ohm's Law 4
Part 3. Resistance: R = /A
The board in this part has five coils of wires. The coils on the board are labeled according to
their size (determined by the gauge number which is related to the diameter of the wire),
material (described by , the resistivity of the material), and the length of wire () connected
between the pairs of terminals.
A #28 gauge wire has a diameter of 0.032 cm and a #22 gauge wire has one of 0.064 cm.
Recall that the cross-sectional area of a cylindrical object, such as a wire, is given by A = r2
where the radius r is half of the diameter. The resistivity of copper is  = 1.72x10-6 -cm. That
of German silver is  = 33x10-6 -cm.
PROCEDURE:
1. Connect the apparatus as shown in Fig. 3.
resistor coils
. 1 . 2 . 3 . 4 . 5 .
+
-
+
V
+
A
PS
-
-
Fig. 3
2. Measure the current and voltage across coil #1. Calculate the resistance for this coil of wire
using Ohm's law.
3. Repeat this procedure for coils #2, 3, 4, and 5. Be sure to write down the specifications of
the wires connected between each pair of terminals.
REPORT:
1. Report your data (V and I for each coil) in tabular form.
2. For wires of the same material and cross-sectional area, is your relation between resistance
and length in part 2 confirmed?
3. For wires of the same material and length, is the resistance bigger for the thicker or the
thinner wire? How would you describe the dependence of resistance on area: is R A or is
R 1/A?
4. For coils 1 and 5 the length and thickness are the same but the material is different. Does
the material affect the resistance? This is described by a quantity called the resistivity for
which the symbol  (Rho) is used. Taken together, the resistance of a conductor of
cross-sectional area A and length  is given by the equation R =  / A. Do your results
support this?
Electricity: Voltage, Current, and Ohm's Law 5
Part 4. Resistance in Series and Parallel
PROCEDURE:
WARNING: Do NOT go above 5 volts across any one light bulb or you may burn the bulb out!
1. Using your voltmeter and your ammeter, determine the resistance of each light bulb twice:
once when the filament is relatively cool (measure I when V = 1 volt and note brightness of
bulb) and again when the filament is very hot (measure I when V = 5 volts and note
brightness of bulb). In the case of a light bulb, the filament is designed to get very hot (
5000 F) so that it glows when 5 volts is placed across it. Determine whether the resistance
of the light bulb (essentially that of the filament) stays constant as the temperature goes up.
2. Replace the one light bulb with two light bulbs connected in series. (In other words, make
the current flow through both resistors - do not give it a choice). Now set the voltage of the
PS to 5 volts and note both the current and the brightness of both bulbs. Are they the same
brightness as when you placed five volts across each separately? Is the same current going
through each as when you had 5 volts across them separately? Is the current indicated by
the ammeter the same as the current flowing through light bulb #1 only, #2 only, both, or the
sum of the currents through #1 + #2 ? What do you have to do to the voltage to make both
light bulbs bright? What happens to the current when you do this (particularly, compare the
current to that for the single bright light bulb of step 1) ?
3. Unhook the two light bulbs and re-hook them in parallel. (In other words, give the current a
choice of flowing either through light bulb #1 or light bulb #2.) Now set the voltage of the PS
to 5 volts, measure the current, and note how bright each light bulb is. Are they the same
brightness as when you placed five volts across each separately? Is the same current going
though each as when you had 5 volts across them separately? Is the current indicated by
the ammeter the same as the current flowing through light bulb #1 only, #2 only, both, or the
sum of the currents through #1 + #2 ?
REPORT:
1. Answer the questions asked in the procedure part above.
2. By placing more resistance in the circuit in a series fashion, does the overall (effective)
resistance increase, decrease, or stay the same. Is this consistent with the results of part 2
which indicated that R   ?
3. By placing more resistance in the circuit in a parallel fashion, does the overall (effective)
resistance increase, decrease, or stay the same. Is this consistent with the results of part 3
which indicated that R  (1/Area) ?
4. Since voltage is defined as energy per charge and current is charge per time, voltage times
current gives energy per time or POWER. Power is measured in Watts [W], so 1 VA = 1W.
a) For having both bulbs bright, which circuit (parallel or series) takes more power?
b) For the same voltage, which circuit generated the most light from the light bulbs?
c) In your household wiring, do you connect appliances in series or parallel to the outlet?