chapter 25 electric currents and resistance - znzamzuhairusnizam.uitm.edu.my/phy097/slide/slide...

Chapter 25Electric Currents and

ResistanceResistance

Copyright © 2009 Pearson Education, Inc.

25-1 The Electric Battery

Volta discovered that electricity could be created if dissimilar metals were connected by a conductive solutionconductive solution called an electrolyte.

Thi i i lThis is a simple electric cell.


25-1 The Electric Battery

A battery transforms chemical energy into y gyelectrical energy.

Chemical reactions within the cell create aChemical reactions within the cell create a potential difference between the terminals by slowly dissolving them. This potential y g pdifference can be maintained even if a current is kept flowing, until one or the other terminal is

l t l di l dcompletely dissolved.


25-1 The Electric BatterySeveral cells connected together make a battery, although now we refer to a single cell as a battery as well.


25-2 Electric CurrentElectric current is the rate of flow of charge through a conductor:

The instantaneous current is given by:

Unit of electric current: the ampere, A:Unit of electric current: the ampere, A:

1 A = 1 C/s.


25-2 Electric Current

A complete circuit is one where current can flow all the way around Note that theflow all the way around. Note that the schematic drawing doesn’t look much like the physical circuit!p y


25-2 Electric Current

Example 25-1: Current is flow of charge.

A steady current of 2.5 A exists in a wire for 4.0 min.

(a) How much total charge passed by a given point in the circuit during thosegiven point in the circuit during those 4.0 min?

(b) How many electrons would this be?(b) How many electrons would this be?

Solution p654


p

25-2 Electric CurrentC t l E l 25 2 H t tConceptual Example 25-2: How to connect a battery.

What is wrong with each of the schemes shown for lighting a flashlight bulb with a flashlight b tt d i l i ?battery and a single wire?

S l i 6


Solution p655

25-2 Electric CurrentBy convention, current is defined as flowing from + to -. Electrons actually flow in the opposite direction but not all currents consistopposite direction, but not all currents consist of electrons.


25-3 Ohm’s Law: Resistance and ResistorsResistors

Experimentally, it is found that the current in a wire is proportional to the potential difference between itsthe potential difference between its ends:


25-3 Ohm’s Law: Resistance and Resistors

The ratio of voltage to current is called the

Resistors

The ratio of voltage to current is called the resistance:



In many conductors, the

Resistors

resistance is independent of the voltage; this relationship is calledrelationship is called Ohm’s law. Materials that do not follow Ohm’s lawdo not follow Ohm s law are called nonohmic.

fUnit of resistance: the ohm, Ω:


1 Ω = 1 V/A.


Conceptual Example 25-3: Current and potential.

Current I enters a resistor R as shown. (a) Is the potential higher at point A or at point B? (b) Is the current greater at point A or at point B?current greater at point A or at point B?

Solution p656



Example 25-4: Flashlight bulb resistanceresistance.

A small flashlight bulb draws 300 mA from its 1.5-V battery.from its 1.5 V battery.

(a) What is the resistance of the bulb?(b) If the battery becomes weak and the ( ) yvoltage drops to 1.2 V, how would the current change?

Solution p657



Standard resistors are

Resistors

Standard resistors are manufactured for use in electric circuits; they are color-coded to indicate their value

d i iand precision.



This is the standard resistor color code. Note that the colors from red to violet are in thethat the colors from red to violet are in the order they appear in a rainbow.



Some clarifications:Resistors

• Batteries maintain a (nearly) constant potential difference; the current varies.

• Resistance is a property of a material or device.

• Current is not a vector but it does have a direction.

• Current and charge do not get used up. Whatever charge goes in one end of a circuit


Whatever charge goes in one end of a circuit comes out the other end.

25-4 ResistivityThe resistance of a wire is directly proportional to its length and inversely

ti l t it ti lproportional to its cross-sectional area:

The constant ρ, the resistivity, is characteristic of the materialcharacteristic of the material.


25-4 ResistivityThis table gives the resistivity and temperatureThis table gives the resistivity and temperature coefficients of typical conductors, semiconductors, and insulators.


25-4 ResistivityE l 25 5 S k iExample 25-5: Speaker wires.

Suppose you want to connect your stereo to remote speakersstereo to remote speakers.

(a) If each wire must be 20 m long, what diameter copper wire shouldwhat diameter copper wire should you use to keep the resistance less than 0.10 Ω per wire?

(b) If the current to each speaker is 4.0 A, what is the potential difference or voltage drop acrossdifference, or voltage drop, across each wire?


Solution p659

25-4 Resistivity

Conceptual Example 25-6: Stretching changes resistance.changes resistance.

Suppose a wire of resistance R could be stretched uniformly until it was twice itsstretched uniformly until it was twice its original length. What would happen to its resistance?its resistance?

Solution p659


25-4 Resistivity

For any given material, the resistivity increases with temperature:increases with temperature:

Semiconductors are complex materials, and may have resistivities that decrease with temperaturetemperature.


25-4 ResistivityExample 25-7: Resistance thermometer.

The variation in electrical resistance with temperature b d t k i t tcan be used to make precise temperature

measurements. Platinum is commonly used since it is relatively free from corrosive effects and has a high melting point. Suppose at 20.0°C the resistance of a platinum resistance thermometer is 164.2 Ω. When placed in a particular solution, the resistance is 187.4placed in a particular solution, the resistance is 187.4 Ω. What is the temperature of this solution?

Solution p660


25-5 Electric Power

Power, as in kinematics, is the energy transformed by a device per unit time:

or


25-5 Electric Power

The unit of power is the watt, W.

For ohmic devices, we can make the substitutions:


25-5 Electric Power

Example 25-8: Headlights.

Calculate the resistance of a 40-W automobile headlight designed for 12 V.

Solution p661


Solution p661

25-5 Electric Power

What you pay for on your electric bill is not power, but energy – the power consumption multiplied by the time.

We have been measuring energy in joules, but the electric company

it i kil tt h kWhmeasures it in kilowatt-hours, kWh:

1 kWh = (1000 W)(3600 s) = 3.60 x 106 J.


25-5 Electric Power

Example 25-9: Electric heater.

An electric heater draws a steady 15.0 A on a 120-V line. How much power does it req ire and ho m ch does itdoes it require and how much does it cost per month (30 days) if it operates 3 0 h per day and the electric company3.0 h per day and the electric company charges 9.2 cents per kWh?

Solution p661


25-5 Electric PowerExample 25-10: Lightning bolt.Lightning is a spectacular example of electric current in a nat ral phenomenon There is m ch ariabilit to lightningnatural phenomenon. There is much variability to lightning bolts, but a typical event can transfer 109 J of energy across a potential difference of perhaps 5 x 107 V during a time interval of about 0 2 s Use this information to estimateof about 0.2 s. Use this information to estimate

(a) the total amount of charge transferred between cloud and ground,

(b) the current in the lightning bolt, and

(c) the average power delivered over the 0.2 s.

Solution p662


Solution p662

25-8 Microscopic View of Electric Current: Current Density and Drift

Electrons in a conductor have large, random

Current: Current Density and Drift Velocity

Electrons in a conductor have large, random speeds just due to their temperature. When a potential difference is applied, the electrons also acquire an average drift velocity, which is generally considerably smaller than the th l l itthermal velocity.


25-8 Microscopic View of Electric Current: Current Density and DriftCurrent: Current Density and Drift

VelocityWe define the current density (current per unit area) – this is a convenient concept for relating the microscopic motions of electrons to the macroscopic current:

If the current is not uniform:If the current is not uniform:

.



VelocityThis drift speed is related to the current in the wire, and also to the number of electrons per unit pvolume:

dand



VelocityExample 25-14: Electron speeds in a wire.

A copper wire 3.2 mm in diameter carries a 5.0-A current. DetermineDetermine

(a) the current density in the wire, and

(b) the drift velocity of the free electrons.(b) the drift velocity of the free electrons.

(c) Estimate the rms speed of electrons assuming they behave like an ideal gas at 20°C. Assume that one electron per Cu atom is free to move (the others remain bound to the atom)free to move (the others remain bound to the atom).

Solution p667


Solution p667

25-8 Microscopic View of Electric Current: Current Density and Drift y

Velocity

The electric field inside a current-carrying wire can be found from the relationship b t th t lt d i tbetween the current, voltage, and resistance. Writing R = ρ l/A, I = jA, and V = El , and substituting in Ohm’s law gives:

l l

substituting in Ohm’s law gives:



VelocityExample 25-15: Electric field inside a wire.

What is the electric field inside the wire of Example 25–14? (The current density was found to be 6.2 x 105 A/m2.)

Solution p668


Summary of Chapter 25• A battery is a source of constant potential difference.

• Electric current is the rate of flow of electric charge.

• Conventional current is in the direction that positive charge would flow.p g

• Resistance is the ratio of voltage to current:


Summary of Chapter 25• Ohmic materials have constant resistance, independent of voltage.

• Resistance is determined by shape and material:

• ρ is the resistivity.


Summary of Chapter 25• Power in an electric circuit:

• Direct current is constant• Direct current is constant.

• Alternating current varies sinusoidally:


chapter 25 electric currents and resistance - znzamzuhairusnizam.uitm.edu.my/phy097/slide/slide...

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