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Electrical circuits and Ohm’s Law
Introduction
In this experiment, you will investigate the basic concepts and terminology associated with electrical
circuits and Ohm’s law.
Equipment and Materials
1.
2.
3.
4.
5.
6.
7.
Ammeter
Voltmeter
Decade resistance box (30 – 200 Ω)
Rheostat (20 Ω)
Battery or power supply (6 V)
Switch
Connecting wires
Important Concepts
Static Electricity and Current Electricity
Electric charge is a property of particles that may exist in one of two forms, positive or negative.
Uncharged particles are said to be neutral. Particles of the same charge exhibit repulsive forces and
particles of opposite charges exhibit attractive forces. In the space surrounding an electrically charged
particle, there exists an electric field. The electric field of one charged particle can affect another
charged particle, by either attracting or repelling it. Electric charge is symbolized by the letter q and is
given in units of coulombs C. An electron has a charge of -1.60 x 10-19 C. Electrons in insulators such as
glass and rubber cannot move readily; thus if an insulator has an excess of electrons, it is said to contain
a net charge and it constitutes static electricity. Conductors such as copper or aluminum have electrons
that can move readily. Under proper conditions conductors allow a flow of charge called electric current.
Most practical uses of electricity involve electrical current and not static electricity.
Voltage
A potential difference, also called a voltage causes electric charges to flow. In a battery, electric
charge is set to a higher potential due to chemical reactions, and it can do work as it flows through the
circuit. The symbol of voltage is V, and the unit is the volt, V. One volt is the work a battery has to do to
move one coulomb of charge. In a 5-V battery, the positive terminal would be assigned 5 V and the
negative terminal would be assigned 0 V.
Current
When a battery or other source of voltage is connected into a closed circuit (a conducting path with no
gaps), an electric field is set up in the circuit at almost the speed of light. In response to this electric field,
charge (electrons) begins to flow through the circuit, somewhat like water molecules move through water
pipes. This continuous flow of charge is called an electric current. (See Figure 1.) Current, symbolized
by I, is defined as the number of coulombs C of charge passing a given point in the circuit per second.
The unit of current is the ampere (A), often shortened to just amp; one amp is the flow of one coulomb of
charge each second. If all the circuit’s conductors are metallic, the current can be pictured as a steady
flow of electrons from the negative terminal of the battery, through the circuit, and back to the positive
terminal. A larger voltage speeds up the electrons, so the current increases as the voltage increases.
a)
b)
Figure 1: A battery causes a flow of charge (a current) in the circuit when the switch is closed.
a) The conventional current is always shown moving from + to –, but b) the electrons flow from – to +.
Before it was realized that electrons even existed, electric current was thought to be caused by the
movement of positive charge. When it was realized that is was the negatively charged electrons doing
the moving, the convention was not changed. Thus, the direction of current is always shown in a circuit
as if positive charges were coming from the positive terminal of the power source and going through the
circuit toward the negative terminal. (See Figure 1.) Although this conventional current is opposite to
the direction of electron flow, its use causes no problem.
A switch is the electrical equivalent of a valve in a water circuit, but electric charge flows only when the
switch is closed, while water flows only when the valve is open.
Resistance
It is a resistance (or load, or device, or resistor) that hampers the flow of charge and extracts energy
from it as the charge passes. Collisions of the moving charge (electrons) with atoms of the wire and other
loads hinder the motion of the charge, and this hindrance is called the electrical resistance, R.
Resistance is given in ohms (Ω, a capital Greek omega), where an ohm is a volt/amp. Inside a material
that has electrical resistance, the kinetic energy of the moving charges is transformed into heat energy. If
the resistance gets hot enough, it will glow like the filament of a light bulb. A current of one amp can raise
the tungsten filament of a light bulb to a temperature of 2500 *C, where it is white-hot. (Tungsten is used
because it has the highest melting point of any element.) Some devices, such as electric ranges and hair
driers, are designed to extract energy in the form of heat. Other devices, such as radios and motors, may
extract the energy in other forms in addition to heat.
Conductors made of different materials have different innate resistance, or resistivity. For example,
copper is a better conductor than iron. Not only does the resistance depend on the identity of the
material, it also depends on the configuration. For wires, if the length is doubled, the resistance is
doubled. If the wire’s cross-sectional area is doubled, the resistance is halved. Resistance also
increases as the temperature of the wire rises, because the increased vibration of the atoms makes it
harder for the electrons to move by. For those situations where heat or light production is desirable
(electric blankets, toasters, stoves, light bulbs, etc.), wires with low resistance are used, so that the higher
current flow will lead to greater heat production.
In summary, in order for a current (a flow of charge) to perform some practical task—light a bulb, cook
your toast, run your TV – three criteria are necessary:
1. A source of voltage (potential difference) such as a battery, generator, or solar cell.
2. A closed conducting path through which the charge can flow in response to this voltage. (If there is a
break in the path, it’s called an open circuit.)
3. A device, or load, in the circuit to do the task. The current transfers energy from the voltage source to
the device. (In Figure 1, the device is a light bulb.)
Drawing figures such as Figure 1 takes time, so shorthand notation, described in Figure 2, is commonly
used for circuits. The circuit in Figure 1 can be represented as shown in Figure 3.
Figure 2: Some Shorthand Symbols for Electrical Circuits. For the battery, the long line
represents the positive terminal and the short line represents the negative terminal.
Ohm’s Law
One of the most frequently applied relationships in current electricity is that known as Ohm’s Law. This
relationship, discovered by the German physicist Georg Ohm (1787-1854), is basic in the analysis of
electrical circuits. Current, voltage, and resistance are tied together by Ohm’s law. Specifically, current
equals voltage divided by resistance, or
I
Equation 1:
V
R
To increase the electrical current, you could increase the voltage, or decrease the resistance, or do both.
Given your knowledge of direct and inverse proportionalities, Equation 1 makes it obvious that such an
increase in voltage or decrease in resistance will, indeed, increase the current.
The resistance of many devices is constant. That is, as the voltage increases, the current increases by
the same factor. (See Figure 4.) They are referred to as ohmic devices. However, light bulbs are nonohmic devices. Their resistance increases when they operate at higher temperatures, and a graph of
current vs. voltage does not yield a straight line. (See Figure 5.)
Figure 3: A schematic
diagram of Figure 2.
Figure 4: A graph of current
vs. voltage gives a straight
line for an ohmic device.
Figure 5: For a non-ohmic
device, a straight line is not
obtained.
Even in non-ohmic devices, Ohm’s law will be qualitatively correct in predicting how a change in one of
the factors (V, I, or R) affects another. In addition, for both ohmic or non-ohmic devices, if the voltage and
current for that part of the circuit are known at a particular time, the resistance of that part can be
calculated correctly by using R = V/I.
Figure 6 Circuit diagram. The voltmeter is connected in parallel across the ammeter and the known
resistance Rs. Rh is a rheostat (a continuously variable resistor).
In an electrical circuit with two or more resistances and a single voltage source, Ohm’s law may be
applied to the entire circuit or to any portion of the circuit. When applied to the entire circuit, the voltage is
the terminal input voltage supplied by the voltage source, and the resistance is the total resistance of the
circuit. In the case of applying Ohm’s law to a particular portion of the circuit, the individual voltage drops,
currents, and resistances are used for that part of the circuit.
Consider the circuit diagram shown in Figure 6. The applied voltage is supplied by a power supply or
battery. Rh is a rheostat, which is a variable resistor that allows the voltage across the resistance Rs to be
varied. An ammeter measures the current through the resistor Rs, and a voltmeter registers the voltage
drop across both Rs and the ammeter. S is a switch for closing and opening (activating and deactivating)
the circuit.
Power
An electric current moves charge from a higher to a lower potential, and work is done as the electrical
energy is converted to another form. The rate at which work is done, or electrical energy used, is defined
as power, symbolized by P and given in watts, W. Electric power equals the amount of charge that flows
per second (I, the current) multiplied by the joules of work done per coulomb of charge (V, the voltage).
That is,
Equation 2:
P = IV
Since from Ohm’s law, V = IR, power can also be found from P = I2R.
Instructions
1. It is good practice to take measurements initially with the meters connected to the largest scales.
This prevents the instruments from being “pegged” (forcing the needle off scale) and possibly
damaged, should the magnitude of the voltage or current exceed the smaller scale limits. A scale
setting may be changed for greater sensitivity by moving the connection to a lower scale after the
general magnitude and measurement are known.
Also, attention should be given to the proper polarity (+ and -); otherwise, the meter will be
“pegged” into the opposite direction. Connect + to + and – to --.
2. Set up the circuit shown in the circuit diagram (Figure 6) with the switch open. A standard
decade resistance box is used for Rs. Set the rheostat resistance Rh for maximum resistance
and the value of the Rs to 10000000 Ω (or 10 MΩ). Have the instructor check the circuit
before closing the switch. The voltmeter can be set to the 200 V scale and the ammeter can be
set to the 200 mA scale.
3. After the instructor has checked the circuit , close the switch and turn on the power supply until
the voltmeter reads about 6 V. This is the terminal voltage Vt. Record the value in the data table.
Avoid adjusting the knob for the rest of the experiment.
A. Variation of Current with Voltage (Rs constant)
4. Set the decade resistance box to 100 Ω. Close the switch and read the voltage and current on
the meters. Open the switch after the readings are taken and record them in Data Table 1. Slide
the rheostat to vary the resistance Rh and vary the circuit. Close the switch and read the voltage
and current. Record the values in Data Table 1. Repeat this procedure for a total of five
successively lower rheostat settings along the length of the rheostat.
The switch should be closed only long enough to obtain the necessary readings. This prevents
unnecessary heating in the circuit.
5. Repeat procedure 3 for another value of Rs (about 200 Ω).
6. Plot the results for both resistances Vs versus Is and draw straight lines that best fit the sets of
data. (You will have two graphs.) Determine the slopes of the lines and compare them with the
constant values of Rs of the decade box by computing the percent errors. According to Ohm’s
law, the respective values should be equal.
B. Variation of Current and Resistance (Vs constant)
7. This portion of the experiment uses the same circuit arrangement as before. In this case, the
voltage Vs is maintained constant by adjusting the rheostat resistance Rh when the Rs is varied.
Initially, set the rheostat near maximum resistance and the resistance Rs of the decade box to
about 100 ohms. Record the value of Rs in Data Table 2.
Close the circuit and read and record the ammeter and voltmeter measurements in the data table.
The voltmeter reading is to be taken as the constant voltage Vs. Open the circuit after making the
readings.
8. Reduce the value of Rs to 80 Ω. Close the switch, and adjust the rheostat until the voltage is the
same as in part 7.
9. Repeat this procedure for Rs values of 60 Ω, 50 Ω, and 40 Ω. Keep the voltage across Rs
constant for each setting by adjusting the rheostat resistance Rh.
10. Plot the results on an Is versus 1/Rs graph and draw a straight line that best fits the data.
Determine the slope of the line and compare it with the constant value of Vs by computing the
percent error. According to Ohm’s law, these values should be equal.
Prelab Sheet for “Ohm’s Law”
Section:
Your Name:
1. Substances having electrons that can move readily are called _________________; other
substances are called _________________.
2. Electri charge flows in a circuit because of a ______________ ________________.
3. Give 4 synonyms for “a thing that hampers the flow of charge”.
4. Name the four factors on which resistance depends.
5. In order for electrical current to perform a practical task, what three criteria are necessary?
6. A 6 V battery is wired to a resistor, and an ammeter gives a reading of 0.30 A in the circuit. What
is the resistor’s resistance? Show setup.
7. How much power is used by the resistor in question 6? Show setup.
8. Which one of the graphs below shows a directly proportional relationship between
X and Y? The arrows on the axes point in the direction of increasing values.
a.
(a)
(b)
(c)
9. As the current in a wire increases, the wire gets _________________.
(d)
Data Sheet for “Hooke’s Law”
Section ______ Partner’s Last Name _____________________ Your Name ____________________
A. Variation of Current with Voltage (Rs constant)
DATA TABLE 1
Reading
Terminal voltage, Vt ___________
Constant Rs
Voltage, Vs (V)
Constant Rs
Current, Is (mA)
Voltage, Vs (V)
Current, Is (mA)
1
2
3
4
5
Calculations
(show work)
Slopes of lines
______________
Percent error from Rs
_________________
_______________
_________________
B. Variation of Current and Resistance (Vs constant)
DATA TABLE 2
Reading
Constant voltage, Vs ___________
Current, Is
(
)
Resistance, Rs
(
)
1/Rs
(
)
1
2
3
4
5
Calculations
(show work)
Slope of line
__________________
Percent error from Vs ____________