Chapter 18Chapter 18

Direct Current CircuitsDirect Current Circuits

General Physics

Current, Resistance, and PowerCurrent, Resistance, and Power

Ch 17, Secs 1–4, 6Ch 17, Secs 1–4, 6

DC Circuits and RC CircuitsDC Circuits and RC Circuits

Ch 18, Secs 1–3, 5Ch 18, Secs 1–3, 5

General Physics

Which of the 4 circuits Which of the 4 circuits will light the bulb?will light the bulb?

1 2 3 4

25% 25%25%25%

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

1.1. AA

2.2. BB

3.3. CC

4.4. DD

General Physics

Sources of emfSources of emf

The source that maintains the current in a The source that maintains the current in a closed circuit is called a source of closed circuit is called a source of emfemf• Any devices that increase the potential energy of Any devices that increase the potential energy of

charges circulating in circuits are sources of emfcharges circulating in circuits are sources of emf• Examples include batteries and generatorsExamples include batteries and generators

SI units are VoltsSI units are Volts• The emf is the work The emf is the work

done per unit chargedone per unit charge

General Physics

emf & Internal Resistanceemf & Internal Resistance A real battery has some A real battery has some

internal resistanceinternal resistance

The schematic shows the The schematic shows the internal resistance, rinternal resistance, r

The terminal voltage is not The terminal voltage is not equal to the emf because equal to the emf because voltage drops across the voltage drops across the internal resistanceinternal resistance

The terminal voltage is:The terminal voltage is:

ΔV = VΔV = Vbb-V-Vaa = ε – Ir = ε – Ir

Active Figure: A Real Battery

General Physics

Resistors in SeriesResistors in Series When two or more resistors are When two or more resistors are

connected end-to-end, they are connected end-to-end, they are said to be in said to be in seriesseries

The current is the same in all The current is the same in all resistors because any charge resistors because any charge that flows through one resistor that flows through one resistor flows through the othersflows through the others

The sum of the potential The sum of the potential differences across the resistors differences across the resistors is equal to the total potential is equal to the total potential difference across the difference across the combinationcombination

General Physics

Resistors in Series, contResistors in Series, cont The current is the same in all resistorsThe current is the same in all resistors

• II11 = I = I2 2 = I= I

The total potential difference is equal to The total potential difference is equal to the sum of the potential differences the sum of the potential differences across the resistorsacross the resistors• ΔΔVV11 + + ΔΔVV2 2 ==ΔΔV V

The resistors can be replaced with one The resistors can be replaced with one resistor with a resistance of resistor with a resistance of • RReqeq = R = R11 + R + R2 2 + …+ …

The equivalent resistor must have The equivalent resistor must have exactly the same external effect on the exactly the same external effect on the circuit as the original series resistorscircuit as the original series resistors

The equivalent resistance of a series The equivalent resistance of a series combination of resistors is greater than combination of resistors is greater than any of the individual resistorsany of the individual resistors

General Physics

Equivalent Resistance – Series: Equivalent Resistance – Series: An ExampleAn Example

Four series resistors are replaced with Four series resistors are replaced with their equivalent resistancetheir equivalent resistance

Active Figure: Resistors Connected in Series

General Physics

Resistors in ParallelResistors in Parallel

When two or more resistors are When two or more resistors are connected across each other, they connected across each other, they are said to be in parallel are said to be in parallel

The potential difference across each The potential difference across each resistor is the same because each is resistor is the same because each is connected directly across the connected directly across the battery terminalsbattery terminals

The sum of the currents through the The sum of the currents through the resistors is equal to the total current resistors is equal to the total current through the combinationthrough the combination

General Physics

Resistors in Parallel, contResistors in Parallel, cont The total current is equal to the sum of The total current is equal to the sum of

the currents in the resistorsthe currents in the resistors• II11 + I + I2 2 = I= I

The potential difference across the The potential difference across the resistors is the sameresistors is the same• ΔΔVV11 = = ΔΔVV2 2 ==ΔΔV V

The resistors can be replaced with one The resistors can be replaced with one resistor with a resistance of resistor with a resistance of • 1/R1/Reqeq = 1/R = 1/R11 + 1/R + 1/R2 2 + …+ …

The equivalent resistor must have The equivalent resistor must have exactly the same external effect on the exactly the same external effect on the circuit as the original parallel resistorscircuit as the original parallel resistors

The equivalent resistance of a parallel The equivalent resistance of a parallel combination of resistors is less than the combination of resistors is less than the smallest of the individual resistorssmallest of the individual resistors

General Physics

Equivalent Resistance – Parallel: Equivalent Resistance – Parallel: An ExampleAn Example

Three parallel resistors are replaced Three parallel resistors are replaced with their equivalent resistancewith their equivalent resistance

Active Figure: Resistors Connected in Parallel

General Physics

Problem-Solving Strategy, 1Problem-Solving Strategy, 1

Combine all resistors in seriesCombine all resistors in series• They carry the same currentThey carry the same current• If the resistors are different, the If the resistors are different, the

potential differences across them are potential differences across them are not the samenot the same

• The resistors add directly to give the The resistors add directly to give the equivalent resistance of the series equivalent resistance of the series combination: combination:

RReqeq = R = R11 + R + R22 + … + …

General Physics

Problem-Solving Strategy, 2Problem-Solving Strategy, 2

Combine all resistors in parallelCombine all resistors in parallel• The potential differences across them are The potential differences across them are

the samethe same• If the resistors are different, the currents If the resistors are different, the currents

through them are not the samethrough them are not the same• The equivalent resistance of a parallel The equivalent resistance of a parallel

combination is found through reciprocal combination is found through reciprocal addition: addition:

1/R1/Reqeq = 1/R = 1/R11 + 1/R + 1/R22 + … + …

General Physics

Problem-Solving Strategy, 3Problem-Solving Strategy, 3

A complicated circuit consisting of several A complicated circuit consisting of several resistors and batteries can often be resistors and batteries can often be reduced to a simple circuit with only one reduced to a simple circuit with only one resistorresistor• Replace any resistors in series or in parallel Replace any resistors in series or in parallel

using steps 1 or 2. using steps 1 or 2. • Sketch the new circuit after these changes Sketch the new circuit after these changes

have been madehave been made• Continue to replace any series or parallel Continue to replace any series or parallel

combinations combinations • Continue until one equivalent resistance is Continue until one equivalent resistance is

foundfound

General Physics

Problem-Solving Strategy, 4Problem-Solving Strategy, 4

If the current in or the potential If the current in or the potential difference across a resistor in the difference across a resistor in the complicated circuit is to be identified, complicated circuit is to be identified, start with the final circuit found in start with the final circuit found in step 3 and gradually work back step 3 and gradually work back through the circuitsthrough the circuits• Use ΔV = I R and the procedures in Use ΔV = I R and the procedures in

steps 1 and 2steps 1 and 2

General Physics

Equivalent Resistance – Complex CircuitEquivalent Resistance – Complex Circuit

General Physics

How bright will each light beHow bright will each light beafter adding one in parallel?after adding one in parallel?

1 2 3

33% 33%33%

10

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21 22 23 24 25 26 27 28 29 30

1.1. The same as beforeThe same as before

2.2. Brighter than beforeBrighter than before

3.3. Dimmer than beforeDimmer than before

General Physics

How bright will each light beHow bright will each light beafter adding one in series?after adding one in series?

1 2 3

33% 33%33%1.1. The same as beforeThe same as before

2.2. Brighter than beforeBrighter than before

3.3. Dimmer than beforeDimmer than before

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

General Physics

RC CircuitsRC Circuits

A direct current circuit may A direct current circuit may contain capacitors and contain capacitors and resistors – the current will vary resistors – the current will vary with timewith time

When the circuit is completed, When the circuit is completed, the capacitor starts to chargethe capacitor starts to charge

The capacitor continues to The capacitor continues to charge until it reaches its charge until it reaches its maximum charge (Q = Cε)maximum charge (Q = Cε)

Once the capacitor is fully Once the capacitor is fully charged, the current in the charged, the current in the circuit is zerocircuit is zero

General Physics

Charging Capacitor in an RC Charging Capacitor in an RC CircuitCircuit

The charge on the The charge on the capacitor varies with timecapacitor varies with time• q = Q(1 – eq = Q(1 – e-t/RC-t/RC))• The The time constanttime constant, , =RC=RC

The time constant The time constant represents the time represents the time required for the charge to required for the charge to increase from zero to increase from zero to 63.2% of its maximum63.2% of its maximum

Active Figure: Charging a Capacitor

General Physics

Notes on Time ConstantNotes on Time Constant

In a circuit with a large time In a circuit with a large time constant, the capacitor charges very constant, the capacitor charges very slowlyslowly

The capacitor charges very quickly if The capacitor charges very quickly if there is a small time constantthere is a small time constant

After t = 10 After t = 10 , the capacitor is over , the capacitor is over 99.99% charged99.99% charged

General Physics

Discharging Capacitor in an RC Discharging Capacitor in an RC CircuitCircuit

When a charged capacitor is When a charged capacitor is placed in the circuit, it can be placed in the circuit, it can be dischargeddischarged

The charge decreases The charge decreases exponentiallyexponentially• q = Qeq = Qe-t/RC-t/RC

At t = At t = = RC, the charge = RC, the charge decreases to 0.368 of Qmaxdecreases to 0.368 of Qmax• In other words, in one time In other words, in one time

constant, the capacitor loses constant, the capacitor loses 63.2% of its initial charge63.2% of its initial charge

Active Figure: Discharging a Capacitor

General Physics

Electrical SafetyElectrical Safety

Electric shock can result in fatal burnsElectric shock can result in fatal burns Electric shock can cause the muscles of Electric shock can cause the muscles of

vital organs (such as the heart) to vital organs (such as the heart) to malfunctionmalfunction

The degree of damage depends onThe degree of damage depends on• the magnitude of the currentthe magnitude of the current• the length of time it actsthe length of time it acts• the part of the body through which it passesthe part of the body through which it passes

General Physics

Effects of Various CurrentsEffects of Various Currents

5 mA or less5 mA or less• Can cause a sensation of shockCan cause a sensation of shock• Generally little or no damageGenerally little or no damage

10 mA10 mA• Hand muscles contractHand muscles contract• May be unable to let go a of live wireMay be unable to let go a of live wire

100 mA 100 mA • If passes through the body for just a few If passes through the body for just a few

seconds, can be fatalseconds, can be fatal

General Physics

Electrical Signals in NeuronsElectrical Signals in Neurons

Specialized cells in the Specialized cells in the body, called body, called neuronsneurons, , form a complex network form a complex network that receives, processes, that receives, processes, and transmits and transmits information from one information from one part of the body to part of the body to anotheranother

General Physics

Electrical Signals in Neurons, contElectrical Signals in Neurons, cont Three classes of Three classes of

neuronsneurons• Sensory neuronsSensory neurons

Receive stimuli from Receive stimuli from sensory organs that sensory organs that monitor the external and monitor the external and internal environment of internal environment of the bodythe body

• Motor neuronsMotor neurons Carry messages that Carry messages that

control the muscle cellscontrol the muscle cells

• InterneuronsInterneurons Transmit information from Transmit information from

one neuron to anotherone neuron to another

Electron microscope image of neurons in the brain

A simple neural circuit