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# Chapter 21: Electric Current and Direct-Current Circuits

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What is electric current?
-a flow of electric charge from one place to another
Often, the charge is carried by...?
-electrons moving through a metal wire
What is the equation that defines electric current?
I = ΔQ/Δt
What are the units of current?
C/s or ampere (A)
What is an electric circuit?
-a system in which charge flows through a closed path and returns to its starting point
What are direct current (DC) circuits?
-circuits in which current always flows in the same direction
What are alternating current (AC) circuits?
-circuits with currents that periodically reverse their direction
What is an open circuit?
-a circuit in which there is no closed path through which electrons can flow
When a battery is disconnected from a circuit and carries no current, the difference in electric potential between its terminals is referred to as its...?
-electromotive force (emf)
What is a battery's electromotive force?
-the difference in electric potential between its terminals when it is disconnected from a circuit and carries no current
What are the units of emf?
-the same as electric potential-volts (J/C)
The emf of a battery is the ________ _________ it can produce between its terminals under _______ _________.
-The emf of a battery is the POTENTIAL DIFFERENCE it can produce between its terminals under IDEAL CONDITIONS
Is emf a force?
-no, it is a potential different (voltage)
Do electrons travel quickly or slowly through a typical wire?
-slowly
Why?
-they suffer numerous collisions with atoms in the wire, and hence their path is torturous and roundabout
By convention, the direction of current is given in terms of...?
-a positive test charge
Describe the direction in which a positive charge will flow in a circuit?
-a positive test charge will flow from a region of high electric potential (near the positive terminal of the circuit), to a region of low electric potential (near the negative terminal of the circuit)
And in doing so...?
-reduce their electric potential energy
Describe the direction in which a negative charge will flow in a circuit?
-a negative test charge will flow from a region of low electric potential (near the negative terminal of a circuit), to a region of high electric potential (near the positive terminal of the circuit)
What is the voltage difference across any contiguous piece of conductor?
-zero
Therefore, is an electric field present?
-no
-electrons are mobile but have no desire to do anything/go anywhere
Suppose a material has a higher voltage on one ened, and a lower voltage on the other. In what direction does current actually flow?
-electrons flow from lower potential/voltage to higher potential/voltage (seeking lower potential energy)
What do we actually pretend?
-that positive charges move from higher potential/voltage to lower potential/voltage
What is equation that describes electric current?
I = ΔQ/Δt
What are the units of current?
coulombs/second; aka ampere, "amp", or A
What is a significant notational change that occurs as we move into the circuits unit?
ΔV becomes simply V
What two key components does every battery have?
-a higher voltage plate and a lower voltage plate
In order to cause electrons to move against the resistance of a wire, it is necessary to...?
-apply a potential difference between its ends
For a wire with a constant resistance R, the potential difference V necessary to create a current I is given by what equation?
V = IR
What is this called?
-ohm's law
What are the SI units of V?
-volts
Materials that are well approximated by Ohm's law are said to be...?
-"ohmic" in their behavior
If one plots current versus voltage for an ohmic material, what is the result?
-a straight line
What is the slow of the line equal to?
1/R
Solving Ohm's law for resistance results in...?
R = V/I
From this expression, it is clear that the units of resistance are...?
-volts per amp
What is 1 volt per amp defined to be?
1 ohm (Ω)
What is a device for measuring resistance called?
-an ohmmeter
In an electrical circuit, a resistor is signified by a...?
-zigzag line
What do the straight lines in a circuit indicate?
-ideal wires of zero resistance
What is the equation that describes resistance in a given material of a given length and area?
R = ρ(L/A)
What is ρ?
-a measure of the resistivity of a given material
What are the units of ρ?
Ω * meter
As ρ increases, what is the effect on resistance?
-resistance increases
What is L?
-length of the material
As L increases, what is the effect on resistance?
-resistance increases
What is A?
-the area of the material
As A increases, what is the effect on resistance?
-resistance decreases
As a wire is heated, what is the impact on its resistivity?
-resistivity tends to increase
Why?
-because atoms that display increased thermal oscillation (due to a temperature increase) are more likely to colide with electrons and slow their progress through a wire
What is one type of materials that actually show a drop in resistivity as temperature is increased?
-semiconductors
SInce resistivity typically increases with temperature, what happens when a wire is cooled below room temperature?
-resistivity will decrease
What are superconducting materials?
-those materials that allow current to flow through them with zero resistance
When cooled below their critical temperature, superconductors not only lose their resistance to current flow but also exhibit _________ _________ _________ , such as the ability to _________ ____ _________ _________ _________ .
When cooled below their critical temperature, superconductors not only lose their resistance to current flow but also exhibit NEW MAGNETIC PROPERTIES, such as the ability to REPEL AN EXTERNAL MAGNETIC FIELD.
What is resistance?
-the opposition within any material to the movement of flow and charge
What are materials that offer low resistance called?
-conductors
What are those materials that offer very high resistance called?
-insulators
What are conductive materials that offer medium amounts of resistance called?
-resistors
What four factors is the resistance of a resistor dependent upon?
-resistivity of the conductive material
-length
-cross-sectional area
-temperature
What is the number that characterized the intrinsic resistance to current flow in a material called?
-the resistivity (ρ)
Does Ohm's law apply to a single resistor with a circuit, any part of a circuit, or to an entire circuit?
-all of the above!
As current moves through a resistor, does the voltage change?
-yes
As current moves through a resistor, does current change?
-no, it is constant
Is any charged gained or lost through the resistors?
-no
When a cell is not actually driving any current, what is its internal resistance equal to?
-zero
The longer that a material is, the ________ resistance it will display.
-The long that a material is, the MORE resistance it will display.
If we increase the cross-sectional area of a material, resistance will ____________.
-If we increase the cross-sectional area of a material, resistance will DECREASE.
True or false: All components of a circuit display resistance (excluding materials that are superconductors).
-true
-(its not just the resistor that displays resistance!)
If resistance exists, particles will not move unless...?
-there is a reward in the form of a drop in potential energy
This fact presents complications. As a result, what do we do?
-we consider all parts of a circuit that are not resistors to be ideal conductors
Therefore, the only location in which voltage will drop is...?
-through the resistor
A battery that produces a potential difference V is connected to a 5-W lightbulb. Later, the 5-W lightbulb is replaced with a 10-W lightbulb. In which case does the battery supply the greatest current? Why?
-according to the the equation P = IV, the battery delivers twice as much current when it is connected to the 10-W bulb
Which lightbulb has the greatest resistance? Why?
-according to the equation P = V^2/R, the resistance of the 5-W bulb is twice that of the 10W bulb
On a microscopic level, what is the power dissipated by a resistor the result of?
-incessant collisions between electrons moving through the circuit and the atoms making up the resistor
Power is proportional to a lightbulb's ___________.
Power is proportional to a lightbulb's BRIGHTNESS.
A 100 W lightbulb outputs _________ of potential electric energy _________.
A 100W lightbulb outputs 100J of potential electric energy per second.
A 50 W lightbulb outputs _________ of potential electric energy _________.
A 50W lightbulb outputs 50J of potential electric energy per second.
Is the resistance of a lightbulb inherent?
-yes
What is the effect on power if resistance is increased?
-power decreases
What is the effect on power if resistance is decreased?
-power increases
What are the three most basic types of circuits?
1. simple (with only one resistor)
2. series (with multiple resistors)
3. parallel (also with multiple resistors)
At what location within a circuit does a voltage drop occur?
-all voltage drop occurs across the resistor
Suppose you have a circuit with a resistor of 1 ohm attached to a lightbulb. Then, you replace the original resistor with a resistor of 2 ohms. Which resistor glowed brightest? Why?
-the first resistor glowed the brightest because it had the lowest resistance
Suppose you have a series circuit with two resistors. Describe the current at each resistor.
-the current at each resistor is equivalent
Suppose you have a circuit where V=12 V. Would the electric current increase or decrease if a 3 ohm resistor was replaced with a 2 ohm resistor?
-the electric current would increase
-->if resistance decreases, electric current will increase
When resistors are connected to each other end to end, what are they said to be in?
-series
Describe the current drawn by three resistors in series vs the current drawn by each independently (within the same circuit).
-they draw the same current
What is the equation that describes the equivalent resistance for any number of resistors in a series...?
Req = R1 + R2 + R3 +R4...
As resistance increases, what happens to V?
-V increases
The sum of individual potential differences in a circuit is equal to...?
-the total potential difference for the entire circuit/the emf value
When are resistors in parallel?
-when they are connected across the same potential difference
What equation describes the equivalent resistance for resistors in parallel?
1/Req = 1/R1 + 1/R2 + 1/R3...
Describe the current through a series resistor when resistance is large
-current never changes through a series circuit, it is always the same
Describe the current through a series resistor when resistance is small
-current never changes through a series circuit, it is always the same
Describe the voltage drop across a series resistor when resistance is large
-the voltage drop is large
Describe the voltage drop across a series resistor when resistance is small
-the voltage drop is small
Describe the power produced by a series resistor when resistance is large
-a large amount of power is produced
Describe the power produced by a series resistor when resistance is small
-a small amount of power is produced
Suppose resistor 1 has a resistance of 1 ohm. Resistor 2 has a resistance of 2 ohms. Does resistor 1 glow more brightly in series, or on its own?
-on its own
Suppose resistor 1 has a resistance of 1 ohm. Resistor 2 has a resistance of 2 ohms. Does resistor 1 glow more brightly in series, or on its own?
-on its own
Suppose resistors 1 and 2 are in series. Will resistor 1 or resistor 2 glow more brightly?
-resistor 2
Why?
-because it has a resistance of 2 ohms, whereas resistor 1 only has a resistance of 1 ohm
What equation should be used to calculate power in a series circuit?
P = (I^2)(R)
Why should this equation be used?
-it is harder to go wrong using this equation because the currents will always be the same in a series circuit
What does a parallel circuit provide?
-two or more distinct routes for current to pass through
Compare the voltage across any resistors in a parallel circuit
-the voltage across any resistors in a parallel circuit will always be the same
Suppose resistor 1 has a resistance of 1 ohm. Resistor 2 has a resistance of 2 ohms. If the resistors are in a parallel circuit, will more current pass through resistor 1 or resistor 2?
-more current will pass through resistor 1
Why?
-because it is the path of least resistance
What will the total current in the circuit be equal to?
I total = I1 + I2
Suppose resistor 1 has a resistance of 1 ohm. Resistor 2 has a resistance of 2 ohms. If the resistors are in a parallel circuit, will more power be generated by resistor 1 or 2?
-more power will be generated by resistor 1
Why?
-because resistance is less
What equation should be used to calculate power within a parallel circuit?
P = V^2/R
For a pure parallel circuit, each resistor has...?
-the same behavior as if connected alone
For a pure parallel circuit, each _________ has the same behavior as if connected alone.
-for a pure parallel circuit, each RESISTOR has the same behavior as if connected alone
Suppose you have a parallel circuit with two resistors, R1 and R2. Initially, the circuit is set up in such a way that current does not flow to R2. Then, a trap door closes which allows current to flow to R2. What happens to the current running through R1?
-remains the same
Why?
-because opening up another branch does not change the resistance offered by this resistor
What happens to the current running through R2?
-the current running through R2 increases
What happens to the total current running through the circuit?
-the total current running through the circuit increases
Where does all of this current increase go to?
-R2
What happens to the voltage of R1?
-it remains the same
Why?
-a result of Ohm's law, V=IR
-since I and R remain the same, V will remain the same
What happens to the power produced by R1?
-it remains the same
Why?
-a result of Ohm's law, P = V^2/R
-since voltage and resistance stay the same, power is constant
Suppose you have a series circuit with two resistors, R1 and R2. Initially, the circuit is set up in such a way that current flows from R1 to R2. Then, a short circuit is created after R1. What happens to I2, V2, and P2?
-decreases to zero
Why?
-because there is no longer any incentive for current to move through R2
What is the impact on I1?
-increases
Why?
-the equivalent resistance of the circuit has decreased (keep in mind that we are discussing a series circuit)
Is current (I) the same for each resistor in series?
-yes
Is current (I) the same for each resistor in parallel?
-no
Is voltage (V) the same fore each resistor in series?
-no
As resistance increases, what happens to voltage?
-voltage increases
As resistance increases, what happens to power?
-power increases
What is the total resistance across several resistors in series equal to?
Req = R1 + R2 + R3 + ...
What is the relationship between the total resistance and the resistance of one individual resistor in series?
total resistance > resistance of an individual resistor in parallel
Is voltage (V) the same for each resistor in parallel?
-yes
Is current (I) the saem for each resistor in parallel?
-no
As R increases, what happens to current?
-current decreases
As resistance increases, what happens to power?
-power decreases
What is the total resistance across several resistors in series equal to?
1/Req = 1/R1 + 1/R2 + ...
What is the relationship between the total resistance and the resistance of one individual resistor in series?
total resistance < resistance of an individual resistor in parallel
Are objects connected to a power strip (such as a hair dryer and straightener) connected in series or in parallel?
-in parallel
What is often used to protect against a surge in power?
-fuse or circuit breaker
What does a fuse or circuit breaker do when there is a surge in power?
-fuse will blow when power is too high
-circuit breaker will mechanically cause a break in a circuit
What does an ammeter measure?
-current through itself
Using a high or low resistance?
-using a low resistance
What does a voltmeter measure?
-a voltage drop across itself
Using a low or high resistance?
-using a high resistance
What does a voltmeter take advantage of?
-the fact that in parallel, the voltage across two resistors is the same
How should a voltmeter be connected to a resistor that you are interested in measuring?
-voltmeter should be connected in parallel with the resistor you are interested in
Why?
-because the voltage across the voltmeter and across the resistor will be the same?
Why?
-because the voltmeter and resistor are connected in parallel
What will increase when an additional path is introduced?
-the total current
As such, what is the voltmeter given?
-a high resistance
Why?
-to reduce the desirability of its path
What does an ammeter take advantage of?
-the fact that current is the same through every element of a series resistor
As such, how is an ammeter connected to a circuit?
-ammeter is connected in series with the resistor that you are interested in
Ideally, will an ammeter have a very high or very low resistance?
-a low resistance
Why?
-to keep current flow the same through the device
What are three steps that can be used to obtain all of the information you need to know about resistors in a combination series/parallel circuit?
1. Combine individual resistances into Req
2. Use the equation I total = V total/R total (aka I total = E/Req) to calculate the total current flowing through the circuit
3. Break apart the circuit into individual currents and voltages, using the voltage schematic for organizing
What tools can you use to more easily combine individual resistances into Req?
-circle equipotential regions
-combine regions with the same current (these are in series)
-combine regions with the same voltage (these are in parallel)
The more resistors are connected in parallel, the ___________ the equivalent resistance.
The more resistors are connected in parallel, the SMALLER the equivalent resistance.
If any one of the resistors in a parallel connection is equal to zero, what is the equivalent resistance equal to?
-zero
What is this situation referred to as?
-a short circuit
Two identical lightbulbs are connected to a battery, either in series or in parallel. Are the bulbs in the series (a) brighter, (b) dimmer, or (c) the same brightness as the bulbs in parallel?
-the bulbs connected in series are dimmer than the bulbs connected in parallel
Why?
-both sets of lightbulbs are connected to the same potential difference V
-the power delivered to the bulbs is V^2/Req
-Req is twice the resistance of a bulb in the series circuit and half the resistance of a bulb in the parallel circuit
-as a result, more power is converted to light in the parallel circuit
What are the Kirchoff rules?
-simple ways of expressing charge conservation and energy conservation
What law expresses charge conservation?
-the junction rule
What law expresses energy conservation?
-the loop rule
The junction rule follows from the observation that the current entering any point in a circuit must...?
-equal the current leaving that point
What sign do we generally associate with currents entering a junction?
-a (+) sign
What sign do we generally associate with currents leaving a junction?
-a (-) sign
When using this notation, what can Kirchoff's junction rule be stated as?
-the algebraic sum of all currents meeting at any junction in a circuit must equal zero
We will know in all cases the direction of all currents meeting at a junction?
-no
When this happens, what must be done...?
-we must choose a direction for the unknown currents, apply the junction rule, and continue as usual
If the value we obtain is negative, what does it mean?
-that the direction we chose was wrong; current actually flows in the opposite direction
In general, how can Kirchoff's loop rule be stated?
-the algebraic sum of all potential differences around any closed loop in a circuit is zero
In general, does it matter in which direction we choose to go around a loop?
-no
If you move from a low voltage plate to a high voltage plate, what will the change in ε be equal to?
ε will be positive
If you move from a high voltage plate to a low voltage plate, what will ε be equal to?
ε will be negative
If you move from a low voltage to a high voltage across a resistor, will IR be positive or negative?
IR will be positive
If you move from high voltage to low voltage across a resistor, will you IR be positive or negative?
IR will be negative
What role do capacitors serve?
-capacitors store energy for later
What is the only type of capacitors we will be studying?
-parallel plate capacitors
Describe how charge is built up on a capacitor
-positive charges flow from a battery, and collect on the first/top plate of a capacitor
-the positive charges on the opposite side of the plate are repelled, negative charges remain
-eventually, the amount of charge stored on each plate is equal in magnitude but opposite in charge
Does a capacitor fill quickly or slowly?
-the capacitor fills quickly
Once a capacitor is completely filled, describe the current that flows through the circuit
-the current that flows through the circuit decreases to zero
Describe the voltage difference that separates a capacitor when it is completely filled
-when the capacitor is completely filled, it has the same voltage difference as the battery
When a capacitor is empty of charge, what voltage difference separates its plates?
-the voltage difference is equal to zero
What is the most general equation that describes capacitance?
Q = CV
What does Q represent?
-stored charge
What does C represent?
-capacitance
What does V represent?
-voltage difference
If a greater voltage difference is applied across a circuit, what will happen to the charge that is stored on the capacitor?
-the charge stored on the capacitor will increase
What is capacitor's rating related to?
-the physical properties of the device
What equation can be used to calculate the rating of a parallel plate capacitor?
C = εo*A/d
What does εo represent?
-permissivity of free space
What is this value equal to?
8.85e10^-12
What does A represent?
-the area of each plate
What does d represent?
-the distance that separates each plate
If we increase the area of the plates that make up a capacitor, what will happen to its capacitance?
-capacitance will increase
If we decrease the area between two plates, what will happen to its capacitance?
-capacitance will increase
Why?
-because the decreased distance helps charges to remain on the capacitor
What is the PE of a capacitor equal to?
PE = 1/2(QV)
When the switch is closed on a circuit containing only batteries and capacitors, how quickly does the charge on capacitor plates appear?
-almost instantaneously
Is this the case in circuits that also contain resistors?
-no
Why?
-the resistors limit the rate at which charge can flow
What is the simplest example of a circuit that contains a resistor and a capacitor?
-an RC circuit
Suppose you have a circuit. Initially, the switch is open, and there is no current in the resistor or charge on the capacitor. At t=0, the switch is closed, and current begins to flow. If the resistor was not present, what charge would the capacitor take on?
Q = Cε or Q = CV
What is the effect of the resistor on the charging process?
-the resistor slows the charging process down
-->the larger the resistance, the longer it takes for the capacitor to charge
What equation is used to show the charge on the capacitor as it varies with time?
q(t) = Cε(1-e^-t/τ)
In this expression, what is e?
-euler's number, 2.718
What is τ?
-the time constant of the circuit
What equation is used to calculate τ?
τ = RC
What can τ be thought of?
-a characteristic time for the behavior of an RC circuit
Per the equation q(t) = Cε(1-e^-t/τ), what is the charge on the capacitor at t = 0?
-0
Per the equation, what is the charge on the capacitor at t = ∞?
Cε or CV
-this is the charge Q the capacitor would have had from t=0 if there had been no resistor in the circuit
What is the equation for current within an RC circuit?
I(t) = (ε/R)*e^-t/τ
At time t = 0, what is the current equal to?
ε/R or V/R
Why is this term significant?
-this is the value current would have if the capacitor were replaced by an ideal wire
At t approaches ∞, what does the current approach?
-zero
In this limit, the capacitor behaves like...?
-an open switch
Is current constant in an RC circuit?
-no
What is current initially?
-ε/R
What is current finally?
-0
Is the charge on the capacitor (Q) constant in an RC circuit?
-no
What is Q initially?
-0
What is Q finally?
-Q full
Is the voltage across the capacitor constant in an RC circuit?
-no
What is the voltage across the capacitor initially?
-0
What is the voltage across the capacitor finally?
Is voltage across the resistor constant in an RC circuit?
-no
What is the voltage across the resistor initially?
What is the voltage across the resistor finally?
-0
An empty capacitor has the same behavior as a...?
-short circuit
Why?
-because there is no voltage difference between the plates
-in theory, current can go onto the capacitor and off of the capacitor for free (although in actuality charges accumulate on the plates)
A fully charged capacitor has the same behavior as...?
-an open/broken circuit
Why?
-because no charge is able to flow through it
How long does it fully take to charge a capacitor?
-always ∞
Because this is not a very useful measurement, what is used as an additional benchmark?
τ
When a time τ has passed, how much of the current through an RC circuit remains?
-37%
How much has been depleted?
-63%
When at time τ has passed, how much of a capacitor within an RC circuit has been charged?
-63%
How much as yet to be charged?
-37%
Suppose we have a charged capacitor that is only connected to a battery. How do we discharge it?
-by connecting it to a resistor
How/why will this cause the capacitor to be discharged?
-the energy that had built up in the capacitor will dissipate through the resistor to the environment as heat
What happens to the Q of the capacitor?
-Q will dissipate to zero
What will happen to the voltage drop of the capacitor?
-the voltage drop of the capacitor will decrease to zero
At the time of initial discharge, will the voltage drop across the capacitor always equal the emf?
-no
Why not?
-there might have only been the opportunity to partially charge the capacitor
What will happen to the current across the resistor?
-the current across the resistor will decrease to zero
Why?
-because all of the stored charge within the capacitor will eventually be depleted
What will be the initial voltage drop across the resistor?
-the initial voltage drop across the resistor will be equal to IR
What will be the final voltage drop across the resistor?
-the final voltage drop across the resistor will be zero
Why?
-because all of the stored charge within the capacitor will eventually be depleted
What is one way to think of a battery?
-as a capacitor that never runs out
What is the equation that describes the current in a discharging RC?
I(t) = Ie^-t/τ
What is this the same as?
-the current for a charging RC
What is the equation that describes the charge within a discharing RC?
Q(t) = Qe^-t/τ
When a capacitor is full, what does it act like?
-an open circuit
When a capacitor is empty, what does it act like?
-a short circuit
What is the most useful property of a capacitor that you can remember?
-when a capacitor is completely empty , it acts like a short circuit; when it is full, it acts like an open circuit
What do dielectrics help to improve?
-the performance of a capacitor
What term is dielectric synonymous with?
"insulator"
What provides a dielectric with its ability to improve performance?
-its shielding abilities
When an electric is inserted between a capacitor, exists between the two plates?
-an electric field
In what direction does it point?
-from the positive plate to the negative plate
What happens to the atoms within a dielectric?
-the reorient themselves
In what direction?
-electrons point towards positive plate
-protons point towards negative plate
What results?
-charge polarization
Which creates?
-an induced electric field
In what direction does this induced electric field point?
-from positive to negative
Does partial or full electric shielding result?
-partial electric shielding
This reduces?
-the net electric field between the plates
What equation can be used to calculate the decrease in electric current provided by the dielectric?
E net = E external/k
What is k?
-the dielectric constant
-a rating of how effective the dielectric is at shielding
What will always be the relationship between Enet and Eexternal when a dielectric is used?
-Enet will always be less than Eexternal
Suppose a capacitor is connected to a battery. Then, the capacitor is disconnected from the battery, and a dielectric is inserted. What is the effect on the electric field (E)?
-the electric field is reduced
The electric field is equal to what?
initial electric field/k
What is the effect on voltage (V)?
-the voltage is reduced
The voltage is equal to what?
initial voltage/k
What is the effect on charge stored (Q)?
-there is no effect on charge stored
What is the effect on capacitance (C)?
-capacitance increases
Why?
-because it is not as hard to store charge on the capacitors now
Why?
-because the charges are bound more tightly as a result of the charge polarization: positive charges are now closer to negative charges; negative charges are now closer to positive charges
The capacitance is equal to what?
initial capacitance * k
What is the effect on PE when the dielectric is inserted?
-PE decreases
Why?
-charge has not changed
-however, voltage has been reduced
-therefore, PE is reduced
What is PE equal to?
initial PE / k
Suppose that the capacitor and dielectric are re-connected to a battery. What happens to the voltage?
-voltage increases to the emf
Why?
-because the voltage change across a capacitor must always equal the emf of the battery it is connected to
What happens to the electric field?
-the electric field increases to the original amount
Why?
-because voltage increases
What happens to the stored charge (Q)?
-stored charge increases
Why?
-to counteract the reductive effects of the dielectric -to ensure that the voltage drop across the capacitor can equal the emf
What is the stored charge equal to?
initial stored charge * k
What is the effect on the capacitance?
-capacitance does not change
Why not?
-because the dielectric is already present
To review, what is the capacitance equal to?
initial capacitance * k
What is the effect on PE?
-PE increases
Why?
-due to the increase in Q
What is PE equal to?
initial PE * k
In terms of Q, PE, and V, what does a dielectric provide you with?
-a dielectric provides you with maximum Q and PE for a given voltage
This allows a capacitor to store charge more...?
-calmly
What would happen to the charge on a capacitor if a dielectric is put in place while it is charging?
-charge would approach Q initial * k
What would happen to voltage if a dielectric was removed from a capacitor while it was charging?
-the voltage value would rapidly increase to V initial * k
What is the master equation for capacitance?
C = kEoA/d
According to the equation, what happens if you increase plate area?
-you increase capacitance
What happens if you decrease the distance between the plates of a capacitor while a dielectric is in place?
-capacitance is increased
What is one impact that toying with the distance between the plates of capacitor may have?
-the strength of the electric field may be altered
The difference between insulators and conductors is largely an...?
Every dielectric material has an ____________ that it cannot withstand before it is torn apart.
Every dielectric material has an ELECTRIC FIELD that it cannot withstand before it is torn apart.
If the electric field becomes greater than the dielectric strength, what may happen?
-the insulator may become a conductor
What is this phenomenon known as?
-dielectric breakdown
Dielectric breakdown is responsible for which natural phenomenon?
-lightning
When does lightning strike?
-when the dielectric strength of air is exceeded
Suppose you are given two capacitors, C1 and C2, which are connected in parallel connected to one or more batteries. How long does it take the capacitors to charge?
-the capacitors are charged instantaneously
C2 > C1. Compare the voltages of the capacitors.
-the voltage of both of the capacitors is equal
If voltage is the same, what is the charge of the capacitors (Q) directly proportional to?
-the charge of the capacitors is directly proportional to capacitance
Suppose C2 > C1. Compare the charges on the capacitors.
Q2 > Q1
What is the equivalent capacitance of the two capacitors equal to?
C equivalent = C1 + C2 + ...
Compare C equivalent to C indvidual
C equivalent > C individual
Suppose that two capacitors are connected in series to a battery. C2 > C1. Compare Q1 to Q2.
Q1 = Q2
Why?
-the charges on capacitors in series must always be equal
-whatever one plate does, all the rest of the plates must do as well
If Q is fixed, compared V1 to V2.
V2 > V1
Why?
-larger capacitors have smaller voltage drops
-smaller capacitors have larger voltage drops
Why is this the case?
-charges have more area to spread out on on a larger capacitors, whereas they are squished together on a small capacitor
-smaller areas result in greater voltage hills and deeper voltage valleys
What is C equivalent for capacitors in series?
1/C equivalent = 1/C1 + 1/C2 + ...
Compare C equivalent to C individual for capacitors in series
C equivalent < C individual
Conceptually, explain why this is the case
-the middle segment of capacitors in series is not doing much
-in fact, theoretically it could be removed and the capacitor could function the same
-if this was done, the distance separating the plates would be obviously large
-if d is large, capacitance will be low
What is an ammeter designed to do?
-to measure the flow of current through a particular portion of a circuit
How is this accomplished?
-by connecting the ammeter in series between a particular circuit segment
What is an ideal ammeter?
-an ammeter with zero resistance
Why?
-if an ammeter offered resistance, it would alter the current it is intended to measure
What does a voltmeter measure?
-the potential drop between any two points in a circuit
How is this accomplished?
-by connecting a voltmeter in parallel to a circuit at the appropriate points
A real voltmeter always allows some...?
-current to flow through it
Which means?
-that the current flowing through the circuit is less than before the meter was connected
As a result, the measured voltage is altered from its...?
-real value
What then would an ideal voltmeter be?
-one in which the resistance is infinite, so that the current it draws from the circuit is negligible
What is the direction of the electric current produced by an electron that falls toward the ground?
-electric current is in the opposite direction to the motion of negative charge, therefore the electric current of the falling electron is upward
Suppose you charge a comb by rubbing it through tour hair. Do you produce a current when you walk across the room carrying the comb?
-no
-by rubbing the comb through your hair, you have transferred charge from your hair to the comb
-however, the net charge of you and the comb together is still zero
-therefore, no current is produced when you walk
Give an example of how four resistors of resistance R can be combined to produce an equivalent resistance of R.
-connect the four resistors in a parallel arrangement with two branches, each branch containing two resistors connected in series
What physical quantity do resistors connected in series have in common?
-resistors connected in series have the same current flowing through them
Explain how electrical devices can begin operating almost immediately after you throw a switch, even though individual electrons in the wire may take hours to reach the device.
-each electron in the wire affects its neighbors by exerting a force on them, causing them to move
-thus, when electrons beging to move out of a batter, their motion sets up a propagating influence that moves through the wire at nearly the speed of light
-this causes electrons everywhere in the wire to begin moving
Explain why birds can roost on high-voltage wire without being electrocuted.
-a potential difference is required for their to be a flow of current
-the bird is in contact with essentially the same high voltage in two different places, which doesn't lead to a potential difference
What physical quantity do capacitors connected in parallel have in common?
-voltage/potential difference
What physical quantity do capacitors connected in series have in common?
-charge
A given car battery is rated as 250 amp-hours. Does this rating indicate the amount of energy, power, charge, voltage, or current that can be drawn from the battery?
-recalling that 1 A = 1 C/s, it follows that an amp-hour has the dimensions of charge
-hence, 250 amp-hours are a measure of the amount of charge that can be drawn from the battery
A conducting wire is quadrupled in length and tripled in diameter. (a) does its resistance increase, decrease, or stay the same? (b) by what factor does its resistance change?
-the length L of the wire increases by a factor of 4, and its cross-sectional area increases by a factor of 3^2 (9)
-the resistance, which is proportional to L/A, decreases because the larger area more than makes up for the greater length
-the factor by which the resistance changes is 4/9
Two cylindrical wires are made of the same material and have the same length. If wire B is to have nine times the resistance of wire A, what must be the ratio of their radii, Rb/Ra?
1/3
An electric heater has a power rating of 500W when connected to a given voltage V. If two of these heaters are connected in series to the same voltage, is the power consumed by the two heaters greater than, less than, or equal to 1000W? Explain.
-when the two heaters are connected in series, the equivalent resistance increases to 2R
-the heaters are connected to the same potential difference, however, and therefore they draw half the original current
-from P = I^2R, we can see that each heater now dissipates one quarter the power of the single heater, for a total power consumption of one-half the original value
Two lightbulbs operate on the same potential difference. Bulb A has four times the power output of bulb B. Which bulb has the greater current passing through it?
-bulb A has greater current passing through it
What is the ratio of the current in bulb A to the current in bulb B?
-bulb A has four times greater current than in bulb B
A dozen lights are to be connected to a given emf. Will the lights be brighter if connected in series or parallel?
-in parallel
-->this is due to the fact that the equivalent resistance will be lower in parallel
Two resistors, R1 = R and R2 = 2R are connected to a battery. Which resistor dissipates more power when they are connected to the battery in series?
R2
When they are in parallel?
R1
Two capacitors are connected in series. If a third capacitor is connected in series with the other two, does the equivalent capacitance increase, decrease, or stay the same?
-the equivalent capacitance decreases due to the fact that the effective separation between the plates increases