Resistors and Ohm's Law

•stor (Figure 1) is a component of an electrical circuit that resi~ts or A rest f 1 . al . , ' poses, the flow 0_ e ectnc current. The resistor is the load in a circuit oP d converts electncal energy to another form of energy, such as light a!l . y or heat energy. , ene1g f t c . . fbe unit o measuremen ior resistance is the ohm, which is denoted by

rnbol Q (the Greek letter "omega"). The amount of resistance offered . b

I a resistor depends on the type of matenal that makes up the resistor. Many

1 , wrs are made of carbon, a semiconductor. Other resistors are made of a ~~::al wire wrapped around ceramic_ ~r plastic tubing, and provide resistance Figure 1 Most eleg_dcal appliances

31 higher currents or volt~ges. In addi~ion to the type of material, the resistance have resistors in their circuits, of a resistor ?epends on_ its length, diameter, and temperature. The resistance 1c;Wlck-, I\ I\ j\__ fa resistor mcreases with length and decreases with diameter. An in.crease - V V

~1 temperature generally causes an increase in resistance. The circuit ·diag~am Figure 2 The circuit diagram symbol symbol for a resistor is shown in Figure 2. for a resistor

TRY THIS: Vo tage and Current in a Resistor

Skil!s Focus: observing, l easuring, interpreting data

In this ac: ivity, you wJll loo · at the relationship between voltage and cu rrent for carbon resi tors. Materials: 2 carbon resist~rs of different values, 5 D-cell~ in holders, switch, connecti \ g wires, ammeter and voltmeter (or multimeter)

1. Copy Table 1 into your ~otebook. ( ~)

Table 1 Voltage and Curre~t in a Res~ rJ

Number Voltage 1\ urr~n! Current Voltage of cells (V) (mA) I. (A) Cup:ent

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1 2

' 3 '

4 I

5 I I

( 2, Record the value of the resistance of the resistor. j 3. The cells should all have the same voltage. Use the voltmeter

to check the voltage of the cells.

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4. Use one of the resistors to construct a circuit like the circuit shown in Figure l Record the voltage and current in your table. Note that if the ammeter measures current in milliamperes, you will need to convert to amperes.

Figure 3

5.' Modify your circuit using two, three, four, and five cells in series."Record the voltage and current for each setup. $ 6. Create another table like Table 1, and repeat steps 2 and 3 using another resistor with a different value. .

A. On the same graph, plot voltage versus current for both / resistors. Draw a line of best fit through each set of data. l)!f"

B. In the last column of yo~r tables, calculate and record the ,-1 , value of the voltage divided by the current (in A). What do you notice about the values for each resistor?

c. How does the value in the last column compare with the value of the resistor? 1-

10.4 Resistors and Ohm's Law

Did You 0 KNOW I'

The Colour of Resistance Colour-coded bands on a resistor indicate the value of that resistor. Each colour represents a number as shown. The first two bands represent the first two digits and the third band is the number of zeros to be added. For example, the colour bands on a 68 Q resistor are blue, grey, and black; the bands on a 100 Q resistor are brown, black, and brown; and the bands on a 150 Q resistor are brown green, and brown. '

black . brown "' red -orange -yellow IT] green -blue -violet -

grey -white / 9 /

LEARNING TIP------Use Table 2 and Figure 4 to explain to a partner why the relationship between voltage and current in a resistor is called linear (relating to a straight line).

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,J• ·, Unit C Electricity

Voltage, Current, -and Resistors In Section 10.3, we looked at a water circuit that contained a pump and a water wheel (refer to Figure 4'on page 311) . If there was a load on the water wheel, such as a-millstone-to -grind corn, the water wheel would turn rnor slowly- ltdd less water would'flow through the circuit. In this case, the wat:r pump is the energy source andj t increases the voltage, the water whee] de~reases the voltage, the t urrent is similar to the rate of water flow, and the resistance is the load, or the millstone.

Consider a circuit that has a resistor, a switch, an electric cell, a voltrnet and an ammeter. Figure 3 ( on page 315) shows the circuit diag; am for thi;r, circuit. An experi~ent is performed to determine how the v~ltage of an electric cell, the resistance of a resistor, and current are related in a circuit. The resistor has a value of 68 Q and is connected to a 1.2 V electric cell. When the switc~ is closed, the voltmeter measures the voltage across the resistor as 1.2 V and -the ammet~r measures the current as 18 mA ( or 0.018 A) . We could add electri~ cells in series to increase the voltage. If we measured the voltage across th~ re,sistor usi!}g the voltmeter and measured the current in the resistor using the ammet~~ each. time we added an electric J:ell, we would obtain the data given in Table 2. Note that, since al) ammeter usually measures current in mill)qmperes, and amp_eres, the table contains current measurements in milliqmperes a!}d in amperes. Figure 4 shows a graph of the relationship between yoltage :and current Since the relationship is linear, we can draw a straight line (line of best .fit) through the data. ·

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Table 2 Voltage and Current in a 'Resistor

·Number. - , . ". 1 -· .. •• .

of electric Voltage · 1 Cur.rent Cur.rent ,-cells (V) (mA) (A)

1.2 18 0.018 2 2.4 35 0.035 3 3.6 53 0.053 4 4.8 71 0.071 5 6.0 88 0.088

8 Voltage versus Current

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2

0.02 0.04 0.06 008 0.1 Current (A)

Figure 4 The straight line, or line of best fit, through the data from Table 2 shows that there is a positive correlation between voltage and current: as current increases, voltage increases.

Note that the variable that is controlled i . . on the x-axis. However fo th' . n an expenment IS usually placed

, r Is expenment the 11 d is placed on the y-axis and . 1 ' contra e variable, voltage, . current Is paced on the x-axis

As you can see, there Is a direct relationsh. . as the current increases the v lt . Ip between current and voltage: d

. tl , o age mcreases In oth d irec y related to current. · er wor s, voltage is

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ohl11's Law 1111sz7, German mathematician and physicist Ge9rg.Simon Ohm determined that the ratio of ~oltage to current was constant for a, g~~eµ co~duct@r.,He call,ed this ratio the res1st~nce of the conductor. The resi~tM1ce (R) of a conductor . defined as the ratio of the voltage across a conq.uctor to the curren1: through is Th 1 . h' ,, the condu~tor. e re ation~ 1p between voltage: current, and. resistance of a conductor 1s known as Ohms Law and can be wntte11 as the following equation:

R = V 1' I,·

I where R is resi~tance (in ohms), Vis the voltage (in volts), and J is the urrent (in amperes). This equation is usually written as: '

C , ,

V= IR

The resistance is a measure of how much the material of a conductor stows down, or resists, the flow of the current. Since the flow of current in a conHuctor is related to the movement of the electrons, the re'sistance is related to the· collisions between the electrons and the atoms in the conductor. 'The collisions transform some of the electron's energy into heat energy· in the tonductor.

Almost all conductors exhibit some resistance. However, not all conductors obey Ohm's law. The resistance of a material depends on its temperature: resistance tends to increase with increasing temperature. So,·• although Ohm's law forms -the basis for the definition of resistance, it is not a law in the usual scientific sense because it does not ipply in all situations. You may assume that the conductors you will study in ~~is course obey Ohm's law. ~ --- , , ·· .

The following sample problems illustrate how we can use different forms of Ohm's law to determine resistance, voltage, and current.

.,. . PLE PROBLEM 1

Determine Resistance , \ , The starter motor of a car is connected to a 12 V battery. If the starter motor ,hasJS A of

. h ~h/ .t t ,_ -~ Ft the car what is the resistance of the starter motor? cu rrent going t roug I o SLa · - 4_

Solution ",h "--

Substitute the values into the equation for Ohm's law and--Solvt.~

R=}!_ I

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Did You " KNow r Georg Ohm: .

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The Man and His Work /,"

Growing up in Germany, Georg Ohm ( 1787-1854) dreamed about working as a scientist at a German university. While teaching at a college, he experimentally showed the relationship between resistance, current, and voltage, and.published his work in 1827. He received so much criticism that he was forced to resign his teaching position. After 15 years of living in poverty, Georg was recognized for his discovery by the Royal Spciety. In 1849, five years before his death, Georg's childhood dream was realized when he became a professor at the University of Munich.

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To learn more about Ohm's law, go to

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12 V '\ /'_.,. , r- '-,,. v" . '--

= 75A R=0.16Q

The resistance of the starter motor is 0-16 Q.

Practice ' , . A flashlight uses two 1.5 V cells in series. Hie current in the bulb is 280 mA. What is the

resistance of the bulb? \ \ I 1

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( 10.4 Resistors anq Ohm's Law

Did You fl KNow r Superconductors Superconductors are materials that have little or no resistance to electric current. The first superconducting materials displayed this effect only at temperatures near absolute zero (- 273 °C). Scientists are researching materials that are superconducting at much higher temperatures. Superconductors are used to make extremely strong electromagnets, such as those used in magnetic resonance imaging (MRI) machines. Supercond1:Jctors may one day be developed for use In motors transformers, and transmission ' lines at normal temperatures.

LEARN/N(rTJP .... ~---Your success in solving problems depends on you\ibility to understand what the problem is asking you to do. Ask yourself, the key words?

·,-, \· I What equation ·neeas to be applied to solve this problem?"

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Unit C Electricity

SAMPLE PROBLEM 2

Determine Voltage 'A 92 n resistor has a current of 78 mA flowing through it. What is the voltage in the resistor?

Solution First, convert the current into amperes.

78 mA = 0.078 A Substitute the values into the Ohm's law equation and solve.

V = IR = (0.078 A)(92 Q)

.;I V=7.2V

i he voJtage across the resistor is 7.2 V.

,; Pri ctice . ' A current of 150 mA flows through a 64 n resistor. What is the voltage across the resistor?

SAMPLE PROBLEM 3

Determine Current ' A flashlight has a filament with a resistance of 10. 7 Q. The batteries provide 2.8 V.

What is the current through the filament?

Solution \

Change the form of_Ohm's law,equation to solve for/. Then substitute the values into the equation and solve.

V = JR

I= Y._ R 2.8V

10.7 Q /

I= 0.26A The current through the filament is 0.26 A.

Practice

A 22 n _resistor has a,yol~ ge of 3.5 V. What is the current in the resistor? Give your answer in mA. / • J

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CHECK YOUR Understanding

1 Write definitions of "resistanc ,, d " . i · · / · e an res1sto " in your own words. r ' Table 3 Voltage and Current in a Resistor

2 An electric hot plate in a scien 1 b · ce a uses a current of 8.5 A when it is plugg d . Jlf

Voltage (V) 2 3 4 5 6

Current (mA) 7 13 20 27 33 40 Wh

• e mto a 120 V outlet. at 1s the resistance of th h (-e ot plate<

I. The 2.4 Q headlight of an autom b'l · j JJ• f o 1 e uses \'i-a current o 5 A. What is the volt . h .tj) . (b) Using Ohm's law, calculate the current . agem t e F , headlight? _ through ~ e resistor if she raised the voltage 7

/. (a) The resistance of dry skin

1· b D o\41'1 to 1000 V. What do you think would happen , 1- '--

. s a out 500 000 Q ' . . . · How much current would h · to the r,es1stor with this current? got rough you ifi £ . · . . you touched the terminals of a

9 V b v ,, M~ny 01dable electrical fires (Figure 6) can be

. h d h attery . ------t d . wit ry ands? .. ___ ____ - . ce to improper use of extension cords. If you (b) The resistance of wet skin is about 1~00

Q opera~e t~o many devices from an extension cord, How much current would go th h ·. . the w1re m the extension cord may become hot.1-you touched the terminals of

9roVubg · you if /) Why does this happen? · -

a r

/.J!-'Jt:~~~ r . with wet hands? (Remember that electric

currents can be_ dangerous, and it is possible D\ fl,~ to cause heart fibrillation with a current of

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;.a: ,...· . ~~ -K-~_:-~ -·;9 _ . less than 100 mA.) . /s. A toaster uses _a current of 4_A. If the resistance {lJ.J.

of the toaster 1s 27 Q, what 1s the voltage in

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,-:--~: ·L .~ the toaster? , j6. Figure 5 shows a light bulb connected to two

· 1.2 V cells. When the switch is closed, an a~er J:_. measures the current as 252 mA. What is the resistance of the bulb? \, 1~ .... 1.(i-~ .··

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Figure 5 7. If resistance is doubled and voltage is halved, '·

what is the effect on the current? r 8. (a) A student varied the voltage through a resistor

and measured the current through the resistor. J- ·

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Figure 6

(a) A 100 W light bulb is designed for use in North America where the voltage is 120 v: .../J · The resistance of the filament of the bulb is · P 144·Q. Calculate the current in the bulb. r, %3)\~

(b) If the bulb is taken to Europe where the voltage is 240 V, what do you think will happen to the brightness of the bulb? Expl~in your answer.

She recorded the information in Table 3. Draw a voltage-current graph of the data. Use the data to calculate the resistance of the resistor. (Hint: Remember tci-,convert mA to A first.)

p. l'.Jsing Ohm\ law as an example, describe the difference between a theory and a law.

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10.4 Resistors and Ohm's Law I 319