Chapter 17Chapter 17Current and ResistanceCurrent and Resistance

Conceptual questions: 3,6,10,14

Quick quizzes: 1,3,4,5,6,7

Problems: 12,27,30,47

Electric CurrentElectric Current The current is the The current is the rate at which the rate at which the

charge flows through a surfacecharge flows through a surface The direction of current flow is the The direction of current flow is the

direction positive charge would direction positive charge would flowflow

The SI unit of current is Ampere (A)The SI unit of current is Ampere (A) 1 A = 1 C/s1 A = 1 C/s

QUICK QUIZ 17.1Consider positive and negative charges moving horizontally through the four regions in Figure 17.2. Rank the currents in these four regions, from lowest to highest.

Charge Carrier Motion in a Charge Carrier Motion in a ConductorConductor

The zig-zag black line The zig-zag black line represents the motion of represents the motion of charge carrier in a conductorcharge carrier in a conductor The net drift speed is smallThe net drift speed is small

The sharp changes in The sharp changes in direction are due to collisionsdirection are due to collisions

The net motion of electrons The net motion of electrons is opposite the direction of is opposite the direction of the electric fieldthe electric field

Electrons in a CircuitElectrons in a Circuit

The drift speed is much smaller The drift speed is much smaller than the average speed between than the average speed between collisionscollisions

Although the drift speed is on the Although the drift speed is on the order of 10order of 10-4-4 m/s the effect of the m/s the effect of the electric field is felt on the order of electric field is felt on the order of 101088 m/s m/s

Meters in a Circuit -- Meters in a Circuit -- AmmeterAmmeter

An ammeter is used to measure currentAn ammeter is used to measure current In line with the bulb, all the charge passing In line with the bulb, all the charge passing

through the bulb also must pass through the through the bulb also must pass through the metermeter

Meters in a Circuit -- Meters in a Circuit -- VoltmeterVoltmeter

A voltmeter is used to measure voltage A voltmeter is used to measure voltage (potential difference)(potential difference) Connects to the two ends of the bulbConnects to the two ends of the bulb

QUICK QUIZ 17.3Look at the four “circuits” shown below and select those that will light the bulb.

ResistanceResistance

The The resistanceresistance of the conductor of the conductor Units of resistance are Units of resistance are ohmsohms ( (Ω)Ω)

1 1 Ω = 1 V / AΩ = 1 V / A Resistance in a circuit arises due to Resistance in a circuit arises due to

collisions between the electrons collisions between the electrons carrying the current with the fixed carrying the current with the fixed atoms inside the conductoratoms inside the conductor

ΔVR=

I

Ohm’s Law; ohmic materials Ohm’s Law; ohmic materials ΔV = I RΔV = I R

Ohm’s Law is an empirical Ohm’s Law is an empirical relationshiprelationshipMaterials that obey Ohm’s Law are said Materials that obey Ohm’s Law are said

to be to be ohmicohmic

Non-ohmic materialsNon-ohmic materials

The current-voltage The current-voltage relationship is relationship is nonlinearnonlinear

A diode is a A diode is a common example common example of a non-ohmic of a non-ohmic devicedevice

QUICK QUIZ 17.4In the figure below, does the resistance of the diode (a) increase or (b) decrease as the positive voltage ∆V increases?

ResistivityResistivity The resistance of an ohmic The resistance of an ohmic

conductor is proportional to its conductor is proportional to its length, L, and inversely proportional length, L, and inversely proportional to its cross-sectional area, Ato its cross-sectional area, A

ρ is the constant of proportionality and ρ is the constant of proportionality and is called the is called the resistivityresistivity of the material of the material

See table 17.1See table 17.1

A

LR

Problem 17-12Problem 17-12

Suppose that you wish to fabricate Suppose that you wish to fabricate a uniform wire out of 1 g of copper. a uniform wire out of 1 g of copper. If the wire is to have a resistance If the wire is to have a resistance of R=0.500 Q, and if all of the of R=0.500 Q, and if all of the copper is to be used, what will becopper is to be used, what will be

A. the lengthA. the length

B. the diameter of that wire?B. the diameter of that wire?

QUICK QUIZ 17.5Aliens with strange powers visited Earth and doubled every linear dimension of every object on the surface of the Earth. A wire has the length and diameter twice their original values. Does the wire now have (a) more resistance than before, (b) less resistance, (c) the same resistance?

(Assume the resistivities of materials remain the same before and after the doubling.)

Temperature Variation of Temperature Variation of ResistivityResistivity

For most metals, resistivity increases For most metals, resistivity increases approximately linearly with approximately linearly with temperaturetemperature

ρρoo is the resistivity at some reference is the resistivity at some reference temperature Ttemperature Too

TToo is usually taken to be 20° C is usually taken to be 20° C is the is the temperature coefficient of resistivitytemperature coefficient of resistivity

see Table 17.1see Table 17.1

)]TT(1[ oo

Temperature Variation of Temperature Variation of ResistanceResistance

Since the resistance of a conductor Since the resistance of a conductor with uniform cross sectional area is with uniform cross sectional area is proportional to the resistivity, the proportional to the resistivity, the effect of temperature on resistance effect of temperature on resistance isis

)]TT(1[RR oo

Problem 17-27Problem 17-27

A 34.5 m length of copper wire at A 34.5 m length of copper wire at 20.020.0ooC has a radius of 0.25 mm. If a C has a radius of 0.25 mm. If a potential difference of 9.0 V is applied potential difference of 9.0 V is applied across the length of the wire, across the length of the wire, determine the current in the wire.determine the current in the wire.

If the wire is heated to 30.0If the wire is heated to 30.0ooC while C while the potential difference is maintained, the potential difference is maintained, what is the resulting current in the what is the resulting current in the wire?wire?

A platinum resistance thermometer has resistances of 200.0 Ω when placed in a 0°C ice bath and 253.8 Ω when immersed in a crucible containing melting potassium. What is the melting point of potassium? (Hint: First determine the resistance of the platinum resistance thermometer at room temperature, 20°C.)

The resistance at 20.0°C is

Solving for T gives the temperature of the melting potassium as

0 1-30

200.0 217 1

1+ 3.92 10 C 0 C 20.0 C

RRT T

0 01R R T T

00 10 3

253.8 217 20.0 C

3.92 10 C 217

R RT T

R

63.2 C

Problem 17-30

SuperconductorsSuperconductors A class of materials A class of materials

and compounds whose and compounds whose resistances fall to resistances fall to virtually zero below a virtually zero below a certain temperature, certain temperature, TTCC

TTCC is called the is called the critical critical temperaturetemperature

The graph is the same The graph is the same above Tabove TCC, but suddenly , but suddenly drops to zero at Tdrops to zero at TCC

Electrical Energy and Electrical Energy and PowerPower

The rate at which the energy is lost The rate at which the energy is lost is the poweris the power

From Ohm’s Law, alternate forms From Ohm’s Law, alternate forms of power areof power are

VIVt

QP

R

)V(RIP

22

Electrical Energy and Electrical Energy and PowerPower

The SI unit of The SI unit of powerpower is Watt (W) is Watt (W) The unit of The unit of energyenergy used by electric used by electric

companies is the companies is the kilowatt-hourkilowatt-hour This is defined in terms of the unit of This is defined in terms of the unit of

power and the amount of time it is power and the amount of time it is suppliedsupplied

1 kWh = 3.60 x 101 kWh = 3.60 x 1066 J J

QUICK QUIZ 17.6A voltage V is applied across the ends of a nichrome heater wire having a cross-sectional area A and length L. The same voltage is applied across the ends of a second heater wire having a cross-sectional area A and length 2L. Which wire gets hotter? (a) the shorter wire, (b) the longer wire, (c) not enough information to say.

QUICK QUIZ 17.7For the two resistors shown here, rank the currents at points a through f, from largest to smallest.

The heating coil of a hot water heater has a resistance of 20 and operates at 210 V. If electrical energy costs $0.080/kWh, what does it cost to raise the 200 kg of water in the tank from 15 °C to 80 °C?

The kilowatt-hour is a measure of energy equal to

The energy needed to raise the temperature of 200 kg of water from 15 C to 80 C is

and the cost of operating the heater to produce this quantity of thermal energy is

(cost)= (energy used) (rate) = (15 kWh) ($0.080/kWh) = $1.20

Problem 17-47

3. Why don’t the free electrons in a metal fall to the bottom of the metal due to gravity? Charges in a conductor are suppose to reside on the surface – why don’t the free electrons all go to the surface?

6. Two lightbulbs are each connected to a voltage of 120V. One has a power of 25 W, the other 100 W. Which bulb has a higher resistance? Which bulb carries more current?

10. Some homes have light dimmers that operate by rotating a knob. What is being changed in the electric circuit when the know is being rotated?

14. Use the atomic theory of matter to explain why the resistance of a metal should increase as its temperature increases.

Conceptual questions

In the two cases shown here a battery is connected up to a box containing some resistors. The battery provides an EMF =V0.Which box will draw more current from the battery?1. They will draw the same amount.2. #1 will draw twice as much as #2.3. #1 will draw more than #2 but not twice.4. #2 will draw twice as much as #15. #2 will draw more than #1 but not twice.6. You can’t tell from the information given

MCATMCAT A positive charge q=1.1x10A positive charge q=1.1x10-11-11 C is located 0.01 C is located 0.01

m away from a negative charge of equal m away from a negative charge of equal magnitude. Point P is exactly between them. magnitude. Point P is exactly between them. What is the magnitude of the electric field at What is the magnitude of the electric field at point P?point P?a. 1000 N/Ca. 1000 N/C b. 2000 N/Cb. 2000 N/C

c. 4000 N/Cc. 4000 N/C d. 8000 N/Cd. 8000 N/C If a water molecule is placed between two If a water molecule is placed between two

plates of a capacitor, which orientation would plates of a capacitor, which orientation would it take to minimize its energy? The electric it take to minimize its energy? The electric field is upfield is up..

a. a. HH b. b. HH

OO OO

HH HH

c. Hc. H H H d. d. O O

OO H H H H

E

MCAT, cont.MCAT, cont. The ratio of the potential difference across a The ratio of the potential difference across a

conductor and the current moving through it is conductor and the current moving through it is called thecalled the

a. resistancea. resistance b. capacitanceb. capacitance

d. conductanced. conductance d. electric potentiald. electric potential In a solid metal conductor, electric current is the In a solid metal conductor, electric current is the

movement ofmovement ofa. electrons onlya. electrons only b. protons onlyb. protons onlyc. nucleic. nuclei d. protons and electronsd. protons and electrons

A 12 A 12 load is connected across a 6.0 V battery. load is connected across a 6.0 V battery. How much energy does the load use in ½ an How much energy does the load use in ½ an hour?hour?a. 1.5 x 10a. 1.5 x 10-3-3 kWh kWh b. 2.0 x 10b. 2.0 x 10-3-3 kWh kWh

c. 3.0 x 10c. 3.0 x 10-3-3 kWh kWh d. 12 x 10d. 12 x 10-3-3 kWh kWh