Chapter 18Chapter 18
Direct Current CircuitsDirect Current Circuits
Electric CircuitsElectric Circuits
An An electric circuitelectric circuit is a path through is a path through which charges can be conducted.which charges can be conducted.
A A loadload is any element in a circuit is any element in a circuit that dissipates energy (eg battery, that dissipates energy (eg battery, resistor, bulb). Wires have negligible resistor, bulb). Wires have negligible resistance so we will not classify resistance so we will not classify them as a loadthem as a load
Closed and Open CircuitsClosed and Open Circuits
In a In a closed circuitclosed circuit there is a closed- there is a closed-loop path for electrons to follow. A loop path for electrons to follow. A closed circuit must be present for closed circuit must be present for continuous current to exist.continuous current to exist.
In an In an open circuitopen circuit there is not a there is not a complete path and therefore no complete path and therefore no charge flow nor current.charge flow nor current.
Sources of emfSources of emf
The source that maintains the The source that maintains the current in a closed circuit is called a current in a closed circuit is called a source of source of emf (electromotive force)emf (electromotive force)– Any devices that increase the potential Any devices that increase the potential
energy of charges circulating in circuits energy of charges circulating in circuits are sources of emfare sources of emf
– Examples include batteries and Examples include batteries and generatorsgenerators
emf and Internal Resistanceemf and Internal Resistance
A real battery has A real battery has some internal some internal resistanceresistance
Therefore, the Therefore, the terminal voltage is terminal voltage is not equal to the not equal to the emfemf
More About Internal More About Internal ResistanceResistance
The schematic The schematic shows the internal shows the internal resistance, rresistance, r
The terminal The terminal voltage, ΔV = Vvoltage, ΔV = Vbb-V-Vaa
ΔV = ε – IrΔV = ε – Ir IR = ε – IrIR = ε – Ir For the entire For the entire
circuit, ε = IR + Ircircuit, ε = IR + Ir
Resistors in SeriesResistors in Series
When two or more resistors are When two or more resistors are connected end-to-end, they are said to connected end-to-end, they are said to be in be in seriesseries
The current is the same in resistors The current is the same in resistors because any charge that flows through because any charge that flows through one resistor flows through the otherone resistor flows through the other
The sum of the potential differences The sum of the potential differences across the resistors is equal to the across the resistors is equal to the total potential difference across the total potential difference across the combinationcombination
Resistors in Series, contResistors in Series, cont Potentials addPotentials add
– ΔV = IRΔV = IR11 + IR + IR22 = I = I (R(R11+R+R22))
– Consequence of Consequence of Conservation of EnergyConservation of Energy
Equivalent Resistance – Equivalent Resistance – SeriesSeries
RReqeq = R = R11 + R + R22 + R + R33 + … + … The equivalent resistance of a series The equivalent resistance of a series
combination of resistors is the combination of resistors is the algebraic sum of the individual algebraic sum of the individual resistances and is always greater resistances and is always greater than any of the individual resistancethan any of the individual resistance
Equivalent Resistance – Equivalent Resistance – SeriesSeries
An ExampleAn Example
Four resistors are replaced with their Four resistors are replaced with their equivalent resistanceequivalent resistance
Ex. 1Ex. 1
A 5 ohm, 10 ohm, and 15 ohm A 5 ohm, 10 ohm, and 15 ohm resistor are connected in series.resistor are connected in series.
A)A) Which resistor has the most current in Which resistor has the most current in it?it?
B)B) Which resistor has the largest potential Which resistor has the largest potential difference?difference?
C)C) What is the equivalent (or total) What is the equivalent (or total) resistance of the circuit?resistance of the circuit?
A 5 ohm, 10 ohm, and 15 ohm resistor A 5 ohm, 10 ohm, and 15 ohm resistor are connected in series to a are connected in series to a
batterybattery. . Which resistor has the Which resistor has the
most current passing through it?most current passing through it?
5 ohm
10 ohm
15 ohm
All have th
e s...
0% 0%0%0%
1.1. 5 ohm5 ohm
2.2. 10 ohm10 ohm
3.3. 15 ohm15 ohm
4.4. All have the All have the same currentsame current
A 5 ohm, 10 ohm, and 15 ohm resistor A 5 ohm, 10 ohm, and 15 ohm resistor are connected in series to a are connected in series to a
batterybattery. . Which resistor has the Which resistor has the largest potential difference across largest potential difference across
it?it?
5 ohm
10 ohm
15 ohm
All have th
e s...
0% 0%0%0%
1.1. 5 ohm5 ohm
2.2. 10 ohm10 ohm
3.3. 15 ohm15 ohm
4.4. All have the All have the same potential same potential differencedifference
When you add the potential When you add the potential differences across each resistor, differences across each resistor,
what is the relationship to the total what is the relationship to the total voltage?voltage?
Individual
vol...
Individual
vol...
Individual
vol...
0% 0%0%
1.1. Individual Individual voltages are voltages are greatergreater
2.2. Individual Individual voltages are all voltages are all equivalentequivalent
3.3. Individual Individual voltages add to voltages add to equal the totalequal the total
A 5 ohm, 10 ohm, and 15 ohm resistor A 5 ohm, 10 ohm, and 15 ohm resistor are connected in series to a are connected in series to a
batterybattery. . What is the equivalent What is the equivalent
resistance of the circuit?resistance of the circuit?
5 ohms
10 ohms
15 ohms
30 ohms
40 ohms
0% 0% 0%0%0%
1.1. 5 ohms5 ohms
2.2. 10 ohms10 ohms
3.3. 15 ohms15 ohms
4.4. 30 ohms30 ohms
5.5. 40 ohms40 ohms
Ex. 2Ex. 2
Find the current and potential Find the current and potential difference across each of the difference across each of the resistors in the following circuits:resistors in the following circuits:
A)A) A 2 ohm and a 4 ohm resistor wired in A 2 ohm and a 4 ohm resistor wired in series with a 12V sourceseries with a 12V source
B)B) A 4 ohm and a 12 ohm resistor wired in A 4 ohm and a 12 ohm resistor wired in series with a 12V sourceseries with a 12V source
C)C) A 150 ohm and a 180 ohm resistor A 150 ohm and a 180 ohm resistor wired in series with a 12V sourcewired in series with a 12V source
Resistors in ParallelResistors in Parallel
Analogy: Students leaving an assembly –Analogy: Students leaving an assembly –paths equal doors open, charges equal paths equal doors open, charges equal studentsstudents
The more doors that are open, the less the The more doors that are open, the less the total resistance istotal resistance is
The more doors that are present mean that The more doors that are present mean that less students pass through each door.less students pass through each door.
The potential difference across each resistor The potential difference across each resistor is the same because each is connected is the same because each is connected directly across the battery terminalsdirectly across the battery terminals
Kirchoff’s LawKirchoff’s Law
Kirchoff’s Law: Kirchoff’s Law: The current, I, that enters The current, I, that enters a point must be equal to the total current a point must be equal to the total current leaving that pointleaving that point– I = II = I11 + I + I22
– The currents are generally not the sameThe currents are generally not the same– Consequence of Conservation of ChargeConsequence of Conservation of Charge
Equivalent Resistance – Equivalent Resistance – Parallel, ExamplesParallel, Examples
Equivalent resistance replaces the two original Equivalent resistance replaces the two original resistancesresistances
Household circuitsHousehold circuits are wired so the electrical are wired so the electrical devices are connected in paralleldevices are connected in parallel– Circuit breakers may be used in series with other Circuit breakers may be used in series with other
circuit elements for safety purposescircuit elements for safety purposes
Equivalent Resistance – Equivalent Resistance – ParallelParallel
Equivalent Equivalent ResistanceResistance
****The equivalent ****The equivalent resistance is resistance is always less than always less than the smallest the smallest resistor in the resistor in the groupgroup
321eq R
1
R
1
R
1
R
1
Ex. 3Ex. 3
Find the current and potential Find the current and potential difference across each of the difference across each of the resistors in the following circuits:resistors in the following circuits:
A)A) A 2 ohm and a 4 ohm resistor wired in A 2 ohm and a 4 ohm resistor wired in parallel with a 12V sourceparallel with a 12V source
B)B) A 4 ohm and a 12 ohm resistor wired in A 4 ohm and a 12 ohm resistor wired in parallel with a 12V sourceparallel with a 12V source
Ex. 4Ex. 4
Find the equivalent resistance, the Find the equivalent resistance, the current in each resistor, and the current in each resistor, and the current drawn by the circuit load for current drawn by the circuit load for a 9.0V battery connected in parallel a 9.0V battery connected in parallel to the following resistors.to the following resistors.
A) two 30 ohm resistorsA) two 30 ohm resistors B) three 30 ohm resistorsB) three 30 ohm resistors C) five 30 ohm resistorsC) five 30 ohm resistors
Ex. 5Ex. 5
Sketch as many different circuits as Sketch as many different circuits as possible involving a battery and possible involving a battery and three bulbs of equal resistance.three bulbs of equal resistance.
How many different circuits would How many different circuits would exist with four bulbs?exist with four bulbs?
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
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 complicated circuit is to be identified, start with the final circuit identified, start with the final circuit found in step 3 and gradually work found in step 3 and gradually work back through the circuitsback through 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
QUICK QUIZ 18.3With the switch in this circuit (figure a) open, there is no current in R2. There is current in R1 and this current is
measured with the ammeter at the right side of the circuit. If the switch is closed (figure b), there is current
in R2. When the switch is closed, the reading on the ammeter (a) increases, (b) decreases, or (c) remains the
same.
QUICK QUIZ 18.3 ANSWER
(a). When the switch is closed, resistors R1 and R2 are in parallel, so that the
total circuit resistance is smaller than when the switch was open. As a result,
the total current increases.
QUICK QUIZ 18.4You have a large supply of lightbulbs and a battery. You start with one lightbulb connected to the battery and notice its brightness. You then add one lightbulb at a time, each new bulb being added in
parallel to the previous bulbs. As the lightbulbs are added, what happens (a) to
the brightness of the bulbs? (b) to the current in the bulbs? (c) to the power
delivered by the battery? (d) to the lifetime of the battery? (e) to the terminal
voltage of the battery? Hint: Do not ignore the internal resistance of the
battery.
QUICK QUIZ 18.4 ANSWER
(a) The brightness of the bulbs decreases
(b) The current in the bulbs decreases
(c) The power delivered by the battery increases
(d) The lifetime of the battery decreases
(e) The terminal voltage of the battery decreases
Equivalent Equivalent Resistance – Resistance –
Complex Complex CircuitCircuit
Electrical SafetyElectrical Safety
Electric shock can result in fatal burnsElectric shock can result in fatal burns Electric shock can cause the muscles Electric shock can cause the muscles
of vital organs (such as the heart) to of 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 the part of the body through which it
passespasses
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 1 second or less, if passes through the body for 1 second or less,
can be fatalcan be fatal
Ground WireGround Wire
Electrical Electrical equipment equipment manufacturers use manufacturers use electrical cords electrical cords that have a third that have a third wire, called a wire, called a groundground
Prevents shocksPrevents shocks
Ground Fault Circuit Ground Fault Circuit Interrupters (GFCI)Interrupters (GFCI)
Special power outletsSpecial power outlets Used in hazardous areasUsed in hazardous areas Designed to protect people from Designed to protect people from
electrical shockelectrical shock Senses currents (of about 5 mA or Senses currents (of about 5 mA or
greater) leaking to groundgreater) leaking to ground Shuts off the current when above this Shuts off the current when above this
levellevel