Experiment

Experiment I : Ohm's Law

and Not Ohm's LawI. Purpose of this Experiment

The main purpose of this experiment is to review the measurement of voltage (V), current (I), and resistance (R) in dc circuits. In the first part, you will measure the internal resistance of a battery and examine the relationship between V and I in a resistor which obeys Ohm's law. In second part of the lab, you will measure the resistance of some electrical devices that do not obey Ohms law.II. References

Halliday, Resnick and Krane, Physics, Vol. 2, 4th Ed., Chapters 32, 33

Purcell, Electricity and Magnetism, Chapter 4

Taylor, An Introduction to Error Analysis, Second Edition

II. Equipment

Digital multimeters

Resistor board with 4, 5 10, and 20 ohm resistors

6-volt battery

knife switch

10 V Power Supply

diode board with switching diodes, LED and 40 ohm resistor

III. Introduction

This section contains background material on current, voltage and resistance that you should already know from your prior physics classes, including high-school physics, Physics 174, and Physics 272. A few days before your lab class starts, at the latest, take a quick look over this introduction. If you find you are already familiar with the material, then skip to the next section and go over the experiment. You probably will need to read the section on diodes, since this is usually not covered in beginning physics classes. If you are not familiar with the other material in the introduction, then you have missed or forgotten some very important and basic physics and you need to give this introduction a thorough and careful reading. You also should dig out your Physics 272 text, or one of the references above, and read over chapters on dc circuits. Voltage

When an electric charge moves between two points that have an electric potential difference between them, work is done on the charge by the source that is creating the potential. The amount of work that is done is equal to the decrease in the potential energy of the charge. The difference in potential energy is equal to the product of the difference in the electrical potential between the points and the magnitude of the electric charge. In the SI system of units, the unit of electrical potential difference is the volt (written as V). For this reason, almost everyone who work with circuits say "voltage difference" instead of "electrical potential difference". Voltages are measured using a voltmeter. Voltage differences are always measured between two points, with one lead of the voltmeter connected to one point and the second lead connected to another point. On the other hand, diagrams of circuits almost always show the voltage at individual locations in the circuit. If the voltage is given at one point, then this means that the second point was at "ground" potential or "zero volts" and this ground point is labeled on a circuit schematic using a special symbol (see Figure 1.2). Current

The rate at which charge passes through a surface is called the electrical current. Current is measured in Ampres, commonly called amps, with units written as A. One amp of current is defined as one Coulomb of charge passing through a cross-sectional area per second. Since an electron has a charge of -1.609x10-19 C, This is equivalent to about 61018 electrons passing per second. Current is measured using an ammeter which is placed in a circuit so that the current flows into the positive terminal of the ammeter and out the negative terminal. Since the current flows through the ammeter, and we do not want the ammeter to disrupt the current that is ordinarily flowing through a circuit, an ammeter has a low resistance. Never connect an ammeter directly across a battery (or other voltage source), since this will result in a large current flowing through the ammeter, possibly damaging it or the battery. Note that in contrast a voltmeter has a high resistance.Resistance and Ohm's Law

When current is driven through an ordinary electrically conducting material, such as a metal or semiconductor at room temperature, it encounters resistance. You can think of resistance as a sort of frictional drag. In a sample made of a good conductor, the current is directly proportional to the potential difference, i.e.

This relationship is called Ohm's Law and is usually written:

V=IRIn this relationship, I is the current flowing through the sample. The potential difference V is the difference in voltage between one end of the sample (where the current enters) to the other end (where the current leaves). Finally, R is the resistance of the sample. In the SI system of units, resistance has unit of ohms, which is written as .

In many materials the resistance does not change with the amount of voltage applied or the current passing through it, over a large range of both parameters, so it is a constant to a very good approximation. The resistors used in this lab are made of thin metal films or carbon (a semiconductor). You should find that they obey Ohms Law very well. Metals are examples of good conductors. They have a high density of electrons that are relatively free to move around, so that connections made with metal tend to have a low resistance. In an electrical insulator, the electrons are more tightly bound and cannot move freely. In a semiconductor, most of the electrons are tightly bound, but there is a small fraction (compared to a metal) that are free to conduct current. The small density of carriers in semiconductors makes them more resistive than metals, and much more conducting than insulators. It also gives them many other unusual properties, some of which we will see in this lab. Batteries and EMF

There are a variety of ways to generate a voltage difference. Batteries produce an electrical potential difference through chemical reactions. If the plus (+) and minus (-) leads of a battery are connected across a resistor, a current will flow out of the positive terminal of the battery (which has a more positive potential than the negative terminal), through the resistor and into the negative terminal. In other words, the positive current flows from the positive to the negative terminal of the battery. Inside the battery, chemical reactions drive a current flow from the more negative region to the more positive region. As a result, a battery can be thought of as a charge pump that is trying to push positive charge out of the + terminal and suck positive charge into the - terminal.

In physics and EE textbooks, one also encounters the terms electromotive force or EMF. The term EMF comes from the idea that a force needs to be exerted on charges to move them through a wire (to overcome the resistance of the piece of wire to the flow of the current). The battery can be thought of as the source of this force. However, the EMF of a battery is just the voltage difference generated across the terminals of the battery and is measured in volts. So EMF is not actually a force, despite its name. In Physics 276, we will not make distinctions between the EMF, the voltage difference, and the electrical potential difference, but use these terms interchangeably.

Part of this experiment is to measure the EMF and internal resistance of a battery. When a current flows inside a battery it is also encounters resistance and the battery is said to have an internal resistance. Batteries with low internal resistance, such as the 12 V lead-acid batteries commonly found in cars, can deliver a lot of current. They need to be treated with caution; shorting together the terminals of a battery (or other voltage source) with a low internal resistance could lead to melted wires, a fire, or the battery exploding. On the other hand, batteries with high internal resistance cannot deliver much current and show significant loss of voltage when current is supplied. Electrical Symbols

Components used in electrical experiments have standard symbols. Those required in this experiment are shown in Fig. (1.2). You should understand what each symbol represents and use them when drawing schematics of your own circuits.

Figure 1.2. Some common symbols used in electrical circuits.

Figure 1.3 Simple circuit with a battery and two resistors showing direction of positive current flow I.

Electrical Circuits

An electrical circuit is formed by using wires to connect together resistors, batteries, switches, or other electrical components into one or more connected closed loops. Where three or more wires meet, the current will split between the different paths. However each new path for current flow that is created at these junctions must rejoin another channel at some other point, so that all loops close. All loops that are created must be closed so that current can flow.

Kirchhoff's Rules

There are two very useful rules for analyzing electrical circuits and finding the currents and voltages at different points in a circuit.

Rule 1: In going round a closed loop the total change in voltage must be zero.

Rule 2: The current flowing into any junction where wires meet is equal to the current flowing out of the junction.

For example, applying the first rule to Fig.1.3 and assuming that the conductors joining the components have zero resistance, we find the potential differences between the lettered points in the circuit are given by:

Summing all the differences we get:

which can be rewritten:

.

As another example, we can apply rule 2 to Fig. 1.3. Considering the nodes at points P and Q in the circuit, we get

At P:

Current in = I

At Q:

Current in = I1 and I2

Current out = I1 + I2

Current out = IBoth points yield the equation I = I1 + I2.

Figure I-3

Figure I-4: (a) Connecting resistors R1 and R2 in series produces a resistance. (b) Connecting resistors R1 and R2 in series produces a resistance.Series and Parallel Resistors

In Physics 174, you measured the resistance of two resistors when they were connected in series (see Fig. 1.4 a) and in parallel (see Fig. 1.4 b). For the series connection, one finds , i.e. the resistance adds. For the parallel connection, one finds.

These elementary results can be derived by applying Kirchoff's rules. For example, consider the series connected resistors. Since current is conserved, the current I in R1 must be the same as the current I in R2. Hence the voltage drop across R1 is and the voltage drop across R2 is . Thus we can write. This is equivalent to writing where and , i.e. two resistors connected in series are equivalent to one resistor whose value is equal to their sum. This argument can be generalized to n resistors in series, and one finds .

Next, consider the parallel connected resistors. The potential difference V between O and O must be the same whether we go along OABO or OCDO . Also conservation of current requires that , where:

is the current through R1 and

is the current through R2. Substituting these expressions for I1 and I2 into our equation for I gives:

. This is equivalent to writing where . This argument can be generalized to n resistors connected in parallel and one finds .Diodes

Not everything obeys Ohm's law, i.e. current is not necessarily proportional to voltage. In this lab you will also measure the characteristics of a common type of electrical device called a diode. A diode consists of a junction of an n-type semiconductor and a "p-type" semiconductor. The current in n-type semiconductors is carried by negative charges (the electrons), while in p-type semiconductors the current is best thought of as being carried by positive charges (called "holes" that are due to missing electrons). When n and p materials are brought together, a few electrons will drift from n to p and some holes will drift from p to n. This charge transfer between n and p regions generates an internal electrical potential at the junction which opposes further transfer of electrons and holes between the two sides. It is possible to drive current from p to n (i.e. holes from the p region to n and electrons from the n region to the p) only if this potential barrier is overcome by applying a sufficiently large voltage difference across the diode. For current to flow, the p region must be positive with respect to the n. Applying a positive voltage to n and a negative voltage to p produces only a very small leakage current. Thus the diode acts like a one-way valve with low resistance to current flowing in the direction of the arrow, and high resistance to current flowing in the opposite direction. If too much voltage is applied in either direction, the diode will be destroyed.

The symbol for a diode is shown in Fig. 1.1 (a). The tip of the triangle points in the direction that current can flow with low resistance. The characteristics of an IN914 switching diode are shown in Table 1.1. This is one of the diodes that you can measure in the lab. A light emitting diode (LED) has also been provided. In an LED, the current flow causes emission of light with a fairly well-defined wavelength or color. LEDs are efficient, reliable and long-lived, provided you don't apply too much voltage across them. A red, yellow or green LED can typically withstand about 3 V and about 5V for a blue LED.

Figure 1.1: (a) Electrical symbol for a diode. (b) When Vb > Vg+Va, current flows through the diode, from b (the p-type region or anode) to a (the n-type region or cathode). Here Vg is the threshold voltage that needs to be reached before significant forward conduction occurs. When Vb < Vg+Va the flow of current is blocked. In particular, when Vb10 M

C50 pF

mV dc320.0 mV0.1 mV0.03 mV(0.3% of reading) + (0.1 mV)R>10 M

C50 pF

V ac3.200 V

32.00 V

320.0 V

750 V0.001 V

0.01 V

0.1 V

1 V0.0003 V

0.003 V

0.03 V

0.3 V(2% of reading) + (0.002 V)

(2% of reading) + (0.02 V)

(2% of reading) + (0.2V)

(2% of reading) + (10 V)R>10 M

C50 pF

320.0 3.200 k32.00 k320.0 k

3.200 M32.00 M0.1 0.001 k0.01 k0.1 k0.001 M0.01 M0.03

0.0003 k

0.003 k

0.03 k

0.0003 M

0.003 M(0.5% of reading) + (0.2 )

(0.5% of reading) + (1 )

(0.5% of reading) + (10 )

(0.5% of reading) + (100 )

(0.5% of reading) + (1 k)

(2% of reading) + (10 k)not applicable

A ac32.00 mA

320.0 mA10.00 A0.01 mA

0.1 mA0.01 A0.003 mA

0.03 mA

0.003 A(2.5% of reading) + (0.02 mA)(2.5% of reading) + (0.2 mA)

(2.5% of reading) + (0.02 A)6 6

0.05

A dc32.00 mA

320.0 mA10.00 A0.01 mA

0.1 mA0.01 A0.003 mA

0.03 mA

0.003 A(1.5% of reading) + (0.02 mA)

(1.5% of reading) + (0.2 mA)

(1.5% of reading) + (0.02 A)6

6

0.05

Example: If a reading of 20 V is measured on the 32.00 V dc range setting, the resolution is 0.01 V, the instrumental uncertainty is v = 0.003 V, and the accuracy is 0.3% of the measurement plus 0.01 V, i.e. the accuracy (systematic error) of the measurement is:

0.3%*20 V + 0.01 V = (0.3/100)*20 V + 0.01 V = 0.06 V + 0.01 V = 0.07 V.

electrical

ground

( V = 0 )

P

Q

O'

O

(a)

(b)

(b)

(a)

anode cathode

a

b

I

(c)

EMBED Equation.3

S

voltage

source

Vo

IN914

RL = 40

134

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