### 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

### 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

### Why?

-they suffer numerous collisions with atoms in the wire, and hence their path is torturous and roundabout

### 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)

### 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)

### 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 a significant notational change that occurs as we move into the circuits unit?

ΔV becomes simply V

### 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 the equation that describes resistance in a given material of a given length and area?

R = ρ(L/A)

### 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 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!

### 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

### 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.

### 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

### 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...

### The sum of individual potential differences in a circuit is equal to...?

-the total potential difference for the entire circuit/the emf value

### 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 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

### 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

### 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

### 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

### What happens to the total current running through the circuit?

-the total current running through the circuit increases

### 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?

-the equivalent resistance of the circuit has decreased (keep in mind that we are discussing a series circuit)

### 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

### 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 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 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

### 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

### 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

### 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

### The junction rule follows from the observation that the current entering any point in a circuit must...?

-equal the current leaving that point

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### When the switch is closed on a circuit containing only batteries and capacitors, how quickly does the charge on capacitor plates appear?

-almost instantaneously

### 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)

### What is significant about this result?

-this is the charge Q the capacitor would have had from t=0 if there had been no resistor in the circuit

### Why is this term significant?

-this is the value current would have if the capacitor were replaced by an ideal wire

### 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)

### 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 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

### What will happen to the current across the resistor?

-the current across the resistor will decrease to zero

### 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

### 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 equation can be used to calculate the decrease in electric current provided by the dielectric?

E net = E external/k

### 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

### 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

### 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

### Why?

-to counteract the reductive effects of the dielectric -to ensure that the voltage drop across the capacitor can equal the emf

### 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

### 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 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

### 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

### 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

### 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 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

### 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

### 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 a voltmeter in parallel to a circuit at the appropriate points

### Which means?

-that the current flowing through the circuit is less than before the meter was connected

### 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

### 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