chapter 21 electric current and direct- current...

Chapter 21

Electric Current and Direct-

Current Circuits

Units of Chapter 21

• Electric Current

• Resistance and Ohm’s Law

• Energy and Power in Electric Circuits

• Resistors in Series and Parallel

• Kirchhoff’s Rules

• Circuits Containing Capacitors

• RC Circuits

• Ammeters and Voltmeters

HW # 5

Pg. 754 – 759:

# 7, 8, 11, 19, 22, 28, 32, 44, 49, 73, 78

PHYS 1402.01

Due on Thursday, Oct. 10

PHYS 1402.02

Due on Thursday, Oct. 10

Practical resistors:

Example # 4

When a potential difference of 18 V is

applied to a given wire, it conducts 0.35 A

of current. What is the resistance of the

wire?

Resistance and Ohm’s Law

Two wires of the same length and diameter will

have different resistances if they are made of

different materials. This property of a material is

called the resistivity.


The difference between

insulators,

semiconductors, and

conductors can be clearly

seen in their resistivities:


In general, the resistance of materials goes up

as the temperature goes up, due to thermal

effects. This property can be used in

thermometers.

Resistivity decreases as the temperature

decreases, but there is a certain class of

materials called superconductors in which the

resistivity drops suddenly to zero at a finite

temperature, called the critical temperature TC.

Example # 5

Nichrome is a nickel –chromium alloy

used in heating applications like electric

toasters, because it has a relatively high

resistivity and heats up when current

passes through it. Suppose you have a

nichrome wire 0.20 mm in diameter and

75 cm long. ( a ) What’s its resistance?

( b) Find the current when a potential

difference of 120 V is connected across

the wire’s ends.

Energy and Power in Electric Circuits

When a charge moves across a potential

difference, its potential energy changes:

Therefore, the power it takes to do this is

Energy and Power in Electric Circuits

In materials for which Ohm’s law holds, the

power can also be written:

This power mostly becomes heat inside the

resistive material.

Consider a 60 W light bulb, connected to

a 120 V voltage source.

What is the current passing

through the wire in the bulb?

(A) 0.5 A (B) 1.0 A (C) 2.0 A

(D) 240 A

What is the resistance of the

wire in the bulb?

(A) 0.5 W (B) 1.0 W (C) 2.0 W (D)

240 W

Example # 6 (Your turn)

1. 0.5 A

2. 1.0 A

3. 2.0 A

4. 240 A

0%

0%

0%

0%

What is the current passing

through the wire in the bulb?

1. 0.5 A

2. 1.0 A

3. 2.0 A

4. 240 A

0%

0%

0%

0%

What is the resistant of the wire in

the bulb?

1. 5 -W

2. 10-W

0%

0%

A battery that produces a potential difference V is

connected to a 5-W lightbulb. Later the 5-W

lightbult is replaced with a 10- W lightbulb. (a) In

which case does the battery supply more current?

Conceptual Checkpoint 21 - 2

1. 5 -W

2. 10-W

0%

0%

A battery that produces a potential difference V is

connected to a 5-W lightbulb. Later the 5-W

lightbult is replaced with a 10- W lightbulb. (b)

Which lightbulb has the greater resistance?

Conceptual Checkpoint 21 - 2

1. 0.60 kW

2. 1.0 kW

3. 0.58 kW

4. 2.6 kW

0%

0%

0%

0%

Example # 7 pb. # 29 a) Find the power dissipated in a

25-Ω electric heater connected to a 120- V

outlet.

Energy Use: Energy and Power in

Electric Circuits When the electric company sends you a bill,

your usage is quoted in kilowatt-hours (kWh).

They are charging you for energy use, and kWh

are a measure of energy.

1. 2.1 kW

2. 1.0 kW

3. 1.1 kW

4. 2.6 kW

0%

0%

0%

0%

Example # 8 Electric utilities measure energy in kilowatt-hours (kWh),

where 1 kWh is the energy consumed if you use energy

at the rate of 1 kW for 1 hour. If your monthly electric bill

(30 days) is $100 and you pay 12.5c/kWh, what’s your

home’s average power consumption and average current,

assuming a 240-V potential difference between the wires

supplying your home?

1. 4.0 A

2. 4.6 A

3. 3.0 A

4. 2.6 A

0%

0%

0%

0%

Example # 8 Electric utilities measure energy in kilowatt-hours (kWh),

where 1 kWh is the energy consumed if you use energy

at the rate of 1 kW for 1 hour. If your monthly electric bill

(30 days) is $100 and you pay 12.5c/kWh, what’s your

home’s average power consumption and average current,

assuming a 240-V potential difference between the wires

supplying your home? Response for 2nd question

1. 9.0 A

2. 8.6 A

3. 9.03 A

4. 8.33 A

0%

0%

0%

0%

Example # 9 Several male students in the same dorm room want to

dry their hair. Having taken PHYS 1402 at UTPA, they

have set their hair dryers to the “low, “ 1000-W settings.

Assuming a standard 120-V how many hair dryers can

they operate simultaneously without tripping the 20-A

circuit breaker?

Resistors in Series

Resistors connected end to end are said to be in

series. They can be replaced by a single

equivalent resistance without changing the

current in the circuit.

Resistors in Series

Since the current through the series resistors

must be the same in each, and the total potential

difference is the sum of the potential differences

across each resistor, we find that the equivalent

resistance is:

Resistors in Series

Total potential difference from point A to point B

must be the emf of the battery ε

Veq = ε = V1 + V2 + V3 …….

The same current ( I ) must flow through each of

the resistors:

Ieq = I1 = I2 = I3

ε = I Req

Resistors in Series

1. A

2. B

3. C

4. D

0%

0%

0%

0%

Example # 10 Two resistors, one having half the resistance of the

other, are connected to a battery as shown on the white

board. What is the voltage across the bigger resistor?

2/bV

3/bV

2/3 bV

3/2 bV

1. A

2. B

3. C

4. D

0%

0%

0%

0%

Example # 11 Two resistors, one having half the resistance of the

other, are connected to an emf battery as shown on the

board. What is the emf of the battery?

2/IR

3/IR

2/3IR

3/2IR

Resistors Parallel

Resistors are in parallel

when they are across the

same potential

difference; they can

again be replaced by a

single equivalent

resistance:

Resistors in Parallel

Using the fact that the potential difference

across each resistor is the same, and the total

current is the sum of the currents in each

resistor, we find:

Note that this equation gives you the inverse of

the resistance, not the resistance itself!

Resistors in Parallel

The potential difference across each resistor

will be the same.

Veq = ε = V1 = V2 = V3

The equivalent current will be the sum of all the

currents.

Ieq = I1 + I2 + I3

Example # 12 Two resistors are connected ( a ) in parallel, and ( b ) in

series, to a 24.0 V battery. See the diagraph on the white

board. What is the current through each resistor and

what is the equivalent resistance of each circuit?

Resistors Parallel

If a circuit is more complex, start with

combinations of resistors that are either purely

in series or in parallel. Replace these with their

equivalent resistances; as you go on you will be

able to replace more and more of them.

Kirchhoff’s Rules

More complex circuits cannot be broken down

into series and parallel pieces.

For these circuits, Kirchhoff’s rules are useful.

The junction rule is a consequence of charge

conservation; the loop rule is a consequence

of energy conservation.

Kirchhoff’s Rules

The junction rule: At any junction, the current

entering the junction must equal the current

leaving it.

Kirchhoff’s Rules

The loop rule: The algebraic sum of the potential

differences around a closed loop must be zero (it

must return to its original value at the original

point).

Kirchhoff’s Rules

Using Kirchhoff’s rules:

• The variables for which you are solving are the

currents through the resistors.

• You need as many independent equations as

you have variables to solve for.

• You will need both loop and junction rules.

Circuits Containing Capacitors

Capacitors can also be connected in series or in

parallel.

When capacitors are

connected in parallel,

the potential difference

across each one is the

same.

21-6 Circuits Containing Capacitors

Therefore, the equivalent capacitance is the

sum of the individual capacitances:


Capacitors connected in

series do not have the

same potential difference

across them, but they do

all carry the same charge.

The total potential

difference is the sum of the

potential differences

across each one.


Therefore, the equivalent capacitance is

Capacitors in series combine like resistors in

parallel, and vice versa.

Note that this equation gives you the inverse of

the capacitance, not the capacitance itself!

21-7 RC Circuits

In a circuit containing

only batteries and

capacitors, charge

appears almost

instantaneously on the

capacitors when the

circuit is connected.

However, if the circuit

contains resistors as

well, this is not the case.

21-7 RC Circuits

Using calculus, it can be shown that the charge

on the capacitor increases as:

Here, τ is the time constant of the circuit:

And is the final charge on the capacitor, Q.

21-7 RC Circuits

Here is the charge vs. time for an RC circuit:

21-7 RC Circuits

It can be shown that the current in the circuit

has a related behavior:

21-8 Ammeters and Voltmeters

An ammeter is a device for measuring current,

and a voltmeter measures voltages.

The current in the circuit must flow through the

ammeter; therefore the ammeter should have

as low a resistance as possible, for the least

disturbance.

21-8 Ammeters and Voltmeters

A voltmeter measures the potential

drop between two points in a circuit.

It therefore is connected in parallel;

in order to minimize the effect on

the circuit, it should have as large a

resistance as possible.

Summary of Chapter 21

• Electric current is the flow of electric charge.

• Unit: ampere

• 1 A = 1 C/s

• A battery uses chemical reactions to maintain a

potential difference between its terminals.

• The potential difference between battery

terminals in ideal conditions is the emf.

• Work done by battery moving charge around

circuit:


• Direction of current is the direction positive

charges would move.

• Ohm’s law:

• Relation of resistance to resistivity:

• Resistivity generally increases with

temperature.

• The resistance of a superconductor drops

suddenly to zero at the critical temperature, TC.


• Power in an electric circuit:

• If the material obeys Ohm’s law,

• Energy equivalent of one kilowatt-hour:

• Equivalent resistance for resistors in series:


• Junction rule: All current that enters a

junction must also leave it.

• Loop rule: The algebraic sum of all potential

charges around a closed loop must be zero.

• Inverse of the equivalent resistance of

resistors in series:


• Equivalent capacitance of capacitors connected

in parallel:

• Inverse of the equivalent capacitance of

capacitors connected in series:


• Charging a capacitor:

• Discharging a capacitor:


• Ammeter: measures current. Is connected in

series. Resistance should be as small as

possible.

• Voltmeter: measures voltage. Is connected in

parallel. Resistance should be as large as

possible.

chapter 21 electric current and direct- current...

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