# Electric Circuits Review

### Part B: Multiple Choice

8. If an electric circuit was analogous to a water park, then the battery would be analogous to the ____.

a. pipes which carry the water through the water circuit

b. pump which supplies energy to move the water from the ground to a high elevation

c. the people which flow from the top of the water ride to the bottom of the water ride

d. the rate at which water is pumped onto the slide

e. the change in potential energy of the riders

f. the top of the water slide

g. the bottom of the water slide

h. the long lines which exist at the park

i. the speed at which riders move as they slide from the top to the bottom of the ride

 Answer: B A water ride at a water park is analogous to an electric circuit. First of all, there is an entity which flows -water flows in a water park and (in conventional terms) + charge flows in an electric circuit. In each case, the fluid flows spontaneously from a high energy location to a low energy location. The flow is through pipes (or slides) in a water park and through wires in an electric circuit. If the pipes or the wires are broken, then there can be no continuous flow of fluid through the circuit. A complete loop is required to establish the circuit. This flow of fluid - whether of water or charge - is possible when a pressure difference is created between two locations in the circuit. In the water park, the pressure difference is the difference in water pressure created by two locations of different heights. Water flows spontaneously from locations of high pressure (high altitude) to locations of low pressure (low altitude). In an electric circuit, the electric potential difference between the two terminals of a battery or energy source provides the electric pressure which presses on charge to move them from a location of high pressure (high electric potential) to a location of low pressure (low electric potential). Energy is required to move the fluid uphill. In a water park, a water pump is used to do work upon the water in order to raise it from the low height back up to the high height. The water pump does not supply the water; the water which is already in the pipes. Rather, the water pump supplies the energy to pump the water from the location of low energy and low pressure to the location of high energy and high pressure. In an electric circuit, the battery is the charge pump which pumps the charge through the battery from the location of low electric potential energy (the - terminal) to the location of high electric potential energy (the + terminal). The battery does not supply the electric charge; the charge is already in the wires. The battery simply supplies the energy to do work on the charge in pumping it uphill.

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9. If an electric circuit was analogous to a water park, then the positive terminal of the battery would be analogous to the ____.

a. pipes which carry the water through the water circuit

b. pump which supplies energy to move the water from the ground to a high elevation

c. the people which flow from the top of the water ride to the bottom of the water ride

d. the rate at which water is pumped onto the slide

e. the change in potential energy of the riders

f. the top of the water slide

g. the bottom of the water slide

h. the long lines which exist at the park

i. the speed at which riders move as they slide from the top to the bottom of the ride

 Answer: F (See Question #8 Discussion above.)

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10. If an electric circuit was analogous to a water park, then the electric current would be analogous to the ____.

a. pipes which carry the water through the water circuit

b. pump which supplies energy to move the water from the ground to a high elevation

c. the people which flow from the top of the water ride to the bottom of the water ride

d. the rate at which water is pumped onto the slide

e. the change in potential energy of the riders

f. the top of the water slide

g. the bottom of the water slide

h. the long lines which exist at the park

i. the speed at which riders move as they slide from the top to the bottom of the ride

 Answer: D (See Question #8 Discussion above.) Current is defined as the rate at which charge moves past a point on a circuit as measured in Coulombs of charge per second (or some comparable set of units). In our analogy, the fluid which flows is water and the rate at which the fluid passes any given point is the current.

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11. The potential energy possessed per unit of charge at any given location is referred to as the electric ___.

 a. current b. resistance c. potential d. power

 Answer: C This is the definition of electric potential - a concept you should internalize.

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12. One ampere is the amount of current that exists when ____ flows by a certain point in a conductor in ____.

 a. one watt; one second b. one joule; one hour c. one electron; one second d. one electron; one hour e. one volt; one second f. one volt; one hour g. one coulomb; one second h. one coulomb; one hour

 Answer: G An ampere is a unit of electric current. And electric current is defined as the rate at which charge moves past a point on a circuit as measured in standard units of Coulombs of charge per second).

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13. If 6 coulombs of charge flow past point 'A' in a circuit in 4 seconds, then ____ coulombs of charge will flow past point 'A' in 8 seconds.

 a. 0.67 b. 1.5 c. 2 d. 3 e. 4 f. 6 g. 8 h. 12 i. 24

 Answer: H The current (I) is the quantity of charge flowing past a point (Q) in a given amount of time (t). That is, I = Q/t. So in this case, the current at point A is (6 C) / (4 s) or 1.5 amperes. Thus the Q/t ratio is 1.5 regardless of the time. So solve the equation 1.5 = Q / (8 s) for Q to obtain the answer.

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14. In which of the following situations will the light bulb light? List all that apply.

 Answer: DF For a circuit to be established, there must be a closed conducting loop from the positive terminal to the negative terminal. This would mean that circuits D, E and F would all be circuits. But in order for the light bulb to light, it must be included as part of the electric circuit. So in E, the bulb does not light since the loop does not extend up into and through the light bulb; charge would simple flow out of the + terminal battery and directly back into - terminal the battery.

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For questions #15-17:

A simple circuit containing a battery and a light bulb is shown in the diagram at the right. Use this diagram to answer the next several questions.

15. The current through the battery is ___.

 a. greater than that through the light bulb b. less than that through the light bulb c. the same as that through the light bulb d. greater than that through each wire e. less than that through each wire

 Answer: C Charge is a conserved quantity; it is never gained nor lost. In an electric circuit, the charge present in the wires and conducting elements is what moves through the circuit. This charge is enclosed in the wires and unable to escape (assuming there is no fault in the circuit). As the charge flows, it does not accumulate in a given location. And charged is not used up as thought it were a consumable quantity. Nor is charge transformed into another type of entity. Given all this reasoning, one would conclude that the current at one location in an electric circuit is the same as the current at any other location in an electric circuit.

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16. Charge flowing through this circuit is most energized at ____. Choose the one best answer.

a. the + terminal of the battery

b. the - terminal of the battery

c. just prior to entering the light bulb

d. just after exiting the light bulb

e. ... nonsense! The energy of the charge is the same everywhere throughout the circuit.

 Answer: A The + terminal of the battery is the high energy terminal of the battery.

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17. The role or purpose of the battery in this circuit is to ____. Choose three.

a. supply electric charge so that a current can exist

b. supply energy to the charge

c. move the charge from the - to the + terminal of the battery

d. transform energy from electrical energy into light energy

e. establish an electric potential difference between the + and - terminals

f. replenish the charge which is lost in the light bulb

g. offer resistance to the flow of charge so that the light bulb can get hot

 Answer: BCE To establish an electric circuit, charge must be moved from low energy to high energy. Once at high energy, the charge spontaneously flows through the conducting wires and other conducting elements of the circuit back down to the low energy terminal. A battery's role is to supply the energy which is required to move the charge from the - terminal to the + terminal of the battery. By placing a large quantity of like charge at one location, an electric pressure or potential difference is established, forcing the like charges to move away from this location to the location of opposite charge (the - terminal).

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18. A 12-Volt battery would supply ___. List all that apply.

a. 3 Coulombs of charge with 4 Joules of energy

b. 4 Coulombs of charge with 3 Joules of energy

c. 12 Coulombs of charge with 1 Joule of energy

d. 1 Coulomb of charge with 12 Joules of energy

e. 0.5 Coulombs of charge with 24 Joules of energy

f. 24 Coulombs of charge with 2 Joules of energy

 Answer: D Electric potential (or voltage) is defined as the electric potential energy per charge. It is the Joules of energy per coulomb of charge possessed by some quantity of charge at some location in an electric circuit. A 12 Volt battery moves some quantity of charge from the - terminal to the terminal, giving the charge energy. Each coulomb of charge would acquire 12 Joules of energy. The energy/charge ratio would be 12 J/C.

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19. The charges that flow through the wires in your home ____.

a. are stored in the outlets at your home

b. are created when and appliance is turned on

c. originate at the power (energy) company

d. originate in the wires between your home and the power company

 Answer: E This question targets a common misconception about electric circuits. The misconception presumes that the role of the electric outlet, the battery, or the power company is to provide the charge required to move through the home. But the power company is only the source of the energy required to set the charge in motion by the establishment of an electric potential difference. The charge itself is present in the wires and conducting elements of your home in the form of mobile electrons.

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20. Approximately how long would it take an electron to travel from the battery of a car to a head light and back (complete loop)?

 a. seconds b. hours c. years d. one-millionth of a second e. one-tenth of a second

 Answer: B Electric charge drifting through an electric circuit moves at a rather slow pace. Quite surprising to many, the distance traversed per unit of time is on the order of 1 meter per hour.

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21. The electric circuit shown at the right consists of a battery and three identical light bulbs. Which of the following statements are true concerning this circuit? List all that apply.

a. The current through point X will be greater than that through point Z.

b. The current through point Z will be greater than that through point Y.

c. The current will be the same through points X, Y and Z.

d. The current through point X will be greater than that through point Y.

e. The current through point Y will be greater than that through point X.

 Answer: C As discussed in Question #15 above, the current in an electric circuit is everywhere the same. So the current at these three locations is the same.

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22. The electric circuit shown at the right consists of a battery and three identical light bulbs. Which of the following statements are true concerning this circuit? List all that apply.

a. The electric potential difference between X and Y is more than that between Y and Z.

b. The electric potential difference between X and Z is more than that between Y and W.

c. The electric potential difference between X and Y is the same as that between Y and Z.

d. The electric potential difference between X and Z is the same as that between Y and W.

e. The electric potential difference between Y and W is more than that between X and Y.

 Answer: DE The electric potential difference across a light bulb (or any resistor) in an electric circuit is simply the product of the current at that bulb multiplied by the resistance of the bulb. Each bulb has the same resistance (since they're identical) and the same current (since the current is everywhere the same). So the electric potential difference across each bulb is the same. And the potential drop across any two consecutive bulbs is the same. And the potential drop across two bulbs would be greater than that across one bulb.

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23. The electric circuit shown at the right consists of a battery and three identical light bulbs. Which of the following statements are true concerning this circuit? List all that apply.

a. Conventional current is directed through the external circuit from point X to Y to Z to W.

b. Conventional current is directed through the external circuit from point W to Z to Y to X.

c. Conventional current is directed through the internal circuit from point W to point X.

d. Conventional current is directed through the internal circuit from point X to point W.

e. The point where charge possesses the least amount of electric potential energy is point W.

 Answer: ACE The battery is referred to as the internal circuit. Charge moves in the internal circuit from the - terminal to the + terminal (in the direction from W towards Z). The wires and light bulbs comprise the external circuit; charge moves through the external circuit from the + terminal to the - terminal (in the direction of X to Y to Z to W).

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24. Voltage ____ an electrical circuit.

 a. goes through b. is expressed across c. is constant throughout d. is the rate at which charges move through

 Answer: B Voltage or electric potential is not a thing which moves. Thus, choices A and D are not the answers since they imply movement of voltage. And the voltage or electric potential of a charge is not something which is constant throughout the circuit as choice C suggests. Voltage or electric potential is a measure of how energized a quantity of charge is at a given location relative to the - terminal. It is often expressed as a difference across two points. Perhaps you have noted this language of "the potential across ..." in several of the answers in this Review.

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25. Two or more of the following words and phrases mean the same thing. Identify them by listing their letters.

 a. Voltage b. Wattage c. Electric Potential Difference d. Rate at which charge flows e. Electric Pressure f. Energy

 Answer: ACE The voltage or electric potential difference are synonymous terms. Voltage is not synonymous with energy. While voltage (or electric potential difference) is a measure of how energized a quantity of charge is at a given location, voltage is expressed as the energy per charge (and not simply as energy). Drawing from the analogy between a water park and an electric circuit, voltage is a measure of the quantity of electric pressure placed upon a charge in inducing it to move from one location to another location. Wattage is synonymous with power. Current is synonymous with the rate at which charge flows.

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26. A high voltage battery can ____.

a. do a lot of work on each charge it encounters

b. do a lot of work over the course of its lifetime

c. push a lot of charge through a circuit

d. last a long time

 Answer: A Voltage refers to the energy/charge. A battery rated with a high voltage can do a lot of work per every Coulomb of charge which it encounters. It may or may not be able to do a lot of work over its lifetime, depending upon the size of the battery.

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27. Which one of the following occurs when a rechargeable battery is recharged?

a. The battery, which has run out of watts, has its wattage restored.

b. The battery, which has run out of amps, has current placed back into it.

c. The battery, which has run out of charge, has charge returned to it.

d. The battery, which has run out of chemical reactants, has its chemicals reformed.

 Answer: D Batteries perform their energy-supplying tasks by using the energy from an exothermic oxidation-reduction reaction to do work upon charge within the electric circuit. When a battery no longer works, its reactants are consumed to the point that the electric potential which the reactants are capable of producing is small compared to the overall resistance of the circuit. At such an instant in time, the ability to induce a current is limited to the point that the external circuit elements are no longer functional. Not all batteries are rechargeable. Those that are rechargeable can have the products transformed back into reactants. The recharger utilizes electrical energy from an outlet to reverse the previously exothermic reaction, turning its products back into reactants.

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28. Birds can safely stand on high voltage electric power lines. This is because ____.

a. they are at low potential with respect to the ground.

b. they offer no resistance to current.

c. they always choose power lines that are not in use.

d. the potential difference between their feet is low.

e. they are perfect insulators.

f. they are perfect conductors.

 Answer: D In order for charge to flow between two locations, there must be an electric potential difference established between those two locations. If a bird places its left foot on an electric power line and his right foot a few centimeters away on the same electric power line, then there is little to no difference in potential between his two feet. Without an electric potential difference, charge will not flow through the bird and the bird is safe.

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29. When the light bulb in your lamp no longer works, it is because the bulb has _____.

a. run out of energy and can no longer pump charge

b. run out of voltage and must be recharged

c. run out of electrons and so there is no more current

d. burned all of its watts and can no longer shine

e. tripped a circuit breaker and must be fixed at the fuse box

f. a broken filament which has resulted in an open circuit

g. ... nonsense! The bulb is fine; your family just needs to fully pay their power bill.

 Answer: F The most common cause for the inability of a light bulbs to light is a broken filament. A coiled wire of tungsten stretches between two vertical supports. If disturbed while hot or if overworn, the tungsten metal can break and leave a gap between the two vertical supports. This gap represents a break in the circuit; a closed conducting loop is no longer established and charge will not flow.

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30. A battery is needed in the circuit of your flashlight so that ____.

a. charge is provided to the wires

b. the energy of the light is balanced by the battery

c. an exothermic, light-creating reaction is possible

d. an electric potential difference is maintained across the circuit

e. electrons are supplied in order to light the bulb

 Answer: D One of the roles of a battery is to simply establish a difference in electric potential between its two terminals. Charge at the high potential will flow through the external circuit to the low potential location.

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31. When you turn on the room lights, they light immediately. This is best explained by the fact that ____.

a. electrons move very fast from the switch to the light bulb filament

b. electrons present everywhere in the circuit move instantly

 Answer: B Electrons move very slowly from one location to another location. But once a circuit is closed, they start moving immediately. While electrons move about a meter or in an hour, the actual signal which tells them to start moving can travel at the speed of light. So once the switch is turned on, a signal is circulated throughout the circuit to start the electrons marching. The electrons present in the filament of the circuit.

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32. The drift velocity of mobile charge carriers in electric circuits is ____.

a. very fast; less than but very close to the speed of light

b. fast; faster than the fastest car but nowhere near the speed of light

c. slow; slower than Michael Jackson runs the 220-meters

d. very slow; slower than a snail

 Answer: D Drift velocity is the distance which a charge moves per unit of time. This value is very small since electrons move very, very slowly. Moving at about 1 meter per hour, they are literally slower than a snail.

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33. Suppose that the current in a typical circuit (DC) is large. This is an indication that ____.

a. the mobile charge carriers are moving very fast

b. a large number of mobile charge carriers are moving forward per second

c. both a and b are true

 Answer: B Current (the rate at which charge moves past a point on the circuit) and drift velocity (the distance a charge moves in a second) should not be confused (and often are). If a current is large, one can be sure of only one thing: a lot of charges are moving forward past a point on the circuit every second.

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34. Which of the following statements represent correct unit equivalencies? List all that apply.

 a. 1 Ampere = 1 Coulomb / second b. 1 Joule = 1 Volt / Coulomb c. 1 Watt = 1 Joule • second d. 1 Watt = 1 Volt • Coulomb / second e. 1 Joule / Ohm = 1 Ampere • Coulomb f. 1 Joule • Ohm = 1 Volt2 • second

 Answer: ADEF This question requires a knowledge of both units for electrical quantities and the equations which relate those quantities. In choice a, an Ampere is a unit of current (I) and a Coulomb/second is a unit of charge per unit of time (Q/t). This is consistent with the equation I = Q/t. In choice b, a Joule is a unit of energy (E) and a Volt / Coulomb is a unit of voltage per unit of charge (V/Q). Since voltage is the energy per charge, we would expect that energy would be equivalent to voltage • charge. Thus, it is incorrect to equate units of energy to units of voltage per charge. In choice c, a Watt is a unit of power (P) and a Joule•second is a unit of energy (E) multiplied by a unit of time (t). But power is energy / time and not energy • time so this is not a correct unit equivalency. In choice d, a Watt is a unit of power (P). On the right side, a Volt is a unit of voltage (V) and a Coulomb / second is a unit of current (I). So since P = I • V, this is a correct unit equivalency. In choice e, a Joule / Ohm is a unit of energy per unit of resistance (E / R). An Ampere • Coulomb is a unit of current multiplied by a unit of charge (I • Q). Thus, the equation is suggesting that E / R = I • Q. This can be rearranged algebraically to say that E / Q = I • R. Since voltage is the energy per charge (E / Q), the equation can be rewritten as V = I • R. This is thus a correct unit equivalency. In choice f, a Joule• Ohm is a unit of energy multiplied by a unit of resistance (E • R). A Volt2 / second is a unit of voltage2 multiplied by a unit of time (V2 • t). So this equation is suggesting that E • R = V2 • t. This can be rearranged algebraically to say that E / t = V2 / R. The right side of the equation is equivalent to power, so the equation can be rewritten as P = V2 / R. Since this is a correct way of writing the power equation, the given unit equivalency is correct.

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35. Which of the following diagrams represents resistors connected in in series? List all that apply.

 Answer: B A and C represent parallel connections as shown by the branching which occurs before and after the resistors. There is no branching in choice B so it is a series connection of resistors.

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Questions #36-39:

The diagram at the right shows two identical resistors - R1 and R2 - placed in a circuit with a 12-Volt battery. Use this diagram to answer the next several questions.

36. These two resistors are connected in ____.

 a. series b. parallel c. neither

 Answer: A One can start at the positive terminal of the battery and begin tracing their finger along the wire. If there is ever a point where the wire comes to a junction and branches in two or more directions, then the circuit has a parallel connection. Otherwise, it is a series circuit. In this diagram, there is no branching. Thus, it is a series circuit.

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37. The electric potential difference (voltage drop) across each resistor is ___ Volts.

 a. 6 b. 12 c. 24 d. ... nonsense!. The electric potential difference is dependent upon the actual resistance of the resistors

 Answer: A Charge receives an increase in electric potential of 12 volts when moving through the internal circuit (the battery). So as a charge leaves the battery and traverses the external circuit, there must be a total drop in electric potential of 12 Volts. This drop in voltage occurs in a two-step fashion as the charge passes through each of the resistors. The charge will lose 6 volts in the first resistor and 6 volts in the second resistor, bringing it back to zero volts by the time it returns to the - terminal of the battery. The potential diagram at the right is a visual means of representing this important concept.

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38. If a third resistor (R3), identical to the other two, is added in series with the first two, then the overall resistance will ____ and the overall current will ____.

 a. increase, increase b. decrease, decrease c. increase, decrease d. decrease, increase e. increase, remain the same f. decrease, remain the same g. remain the same, increase h. remain the same, decrease i. remain the same, remain the same

 Answer: C Increasing the number of resistors in a series circuit will increase the overall resistance of that circuit and cause the current to decrease. (The opposite is true of a parallel circuit.)

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39. If a third resistor (R3), identical to the other two, is added in series with the first two, then the electric potential difference (voltage drop) across each of the three individual resistors will ____.

 a. increase b. decrease c. remain the same

 Answer: B Using the same reasoning as in question #37, we can say that the charge will acquire 12 Volts in moving through the battery. It will have to lose this 12 volts in three steps as it passes through the external circuit. Since there are now three voltage drops in the external circuit instead of the original two, each drop must be smaller than before. So there will be a 4-Volt drop through each resistor (instead of the original 6-Volt drop).

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Questions #40-43:

The diagram at the right shows two identical resistors - R1 and R2 - placed in a circuit with a 12-Volt battery. Use this diagram to answer the next several questions.

40. These two resistors are connected in ____.

 a. series b. parallel c. neither

 Answer: B One can start at the positive terminal of the battery and begin tracing their finger along the wire. If there is ever a point where the wire comes to a junction and branches in two or more directions, then the circuit has a parallel connection. Otherwise, it is a series circuit. In this diagram, there is some branching. Once the charge reaches the branching point, it will either pass through the resistor in the left branch (R1) or through the resistor in the right branch (R2). Thus, it is a parallel circuit.

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41. The electric potential difference (voltage drop) across each resistor is ___ Volts.

 a. 6 b. 12 c. 24 d. ... nonsense!. The electric potential difference is dependent upon the actual resistance of the resistors

 Answer: B Charge receives an increase in electric potential of 12 volts when moving through the internal circuit (the battery). So as a charge leaves the battery and traverses the external circuit, there must be a total drop in electric potential of 12 Volts. This drop in voltage occurs in a single step since the charge will only pass through a single resistor on its path back to the battery. So since the charge chooses either the left or the right branch (and not both), either branch must provide the 12-Volt drop in voltage. In parallel circuits, the the electric potential difference across the battery is equal to the electric potential difference across either branch. The potential diagram at the right is a visual means of representing this important concept.

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42. If a third resistor (R3), identical to the other two, is added in parallel with the first two, then the overall resistance will ____ and the overall current will ____.

 a. increase, increase b. decrease, decrease c. increase, decrease d. decrease, increase e. increase, remain the same f. decrease, remain the same g. remain the same, increase h. remain the same, decrease i. remain the same, remain the same

 Answer: D Adding an identical resistor in a separate branch will provide more pathways by which charge can traverse through the loop of the circuit. This would be the equivalent of adding another booth at a toll station on a tollway in parallel with an existing booth. Opening up another lane for traffic will reduce the overall resistance and cause an increase in the car flow rate. The same occurs with charge in parallel circuits. More branches means less resistance and an increased current.

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43. If a third resistor (R3), identical to the other two, is added in parallel with the first two, then the electric potential difference (voltage drop) across each of the three individual resistors will ____.

 a. increase b. decrease c. remain the same

 Answer: C The electric potential difference across any branch is equal to the voltage of the battery. Adding a new branch can alter the overall resistance and the overall current, but it does not alter the electric potential difference across the battery nor across the branches.

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44. The resistance of a charge-carrying conducting wire will increase as the ____. Choose all that apply.

a. length of the wire is increased

b. cross-sectional area of the wire is increased

c. temperature of the wire is increased

d. voltage impressed across the ends of the wire is increased

e. wire is placed closer and closer to the + terminal of the circuit

 Answer: AC Resistance of a wire increases with increasing length and (to a smaller extent) with increasing temperature. Increasing wire length increases the number of atom-charge collisions and thus the amount of resistance. Increasing the temperature increases the resistivity of the material and thus increases the overall resistance.

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45.   When plugged into a 120-Volt outlet, a light bulb consumes 300 joules of energy over a 5 second time period. The power of the light bulb is ____ Watts.

 a. 0.0167 b. 0.50 c. 2.0 d. 2.50 e. 60 f. 600 g. 1500 h. 7200

 Answer: E Power is simply the rate at which energy is supplied to a circuit or transformed by a circuit. In this case, the power is the energy consumed per time. P = (300 J) / (5 seconds) = 60 Watts

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46. A certain electrical circuit contains a battery, wires and a light bulb. If potential energy is gained by charges at the battery location, then charges lose potential energy ____.

a. in the wires only

b. in the bulb only

c. equally in the wires and the bulb

d. mostly in the wires but a little in the bulb

e. mostly in the bulb but a little in the wires

f. nowhere

 Answer: E Charge will lose energy as they pass through locations of resistance. When in series, locations of greatest resistance will transform electrical energy into other forms at a greater rate. So energy will be lost in the light bulb and in the wires to a much lesser extent.

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47. A high resistance light bulb and a low resistance light bulb are connected in series to a 6-Volt pack of batteries. Which of the two light bulbs will shine the brightest?

a. They will have the same brightness.

b. The low-R bulb will shine more brightly.

c. The high-R bulb will shine more brightly.

d. There is no way to make such a prediction since bulb brightness is independent of bulb resistance.

 Answer: C Since the two light bulbs are in series, the same current (i) is experienced by each. The power will be given by the i2•R product. Since i is the same for each light bulb, the bulb with the greatest resistance will have the greatest power. So the high-R light bulb will transform electrical energy into light energy at the greatest rate and thus shine most brightly.

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48. A high resistance light bulb and a low resistance light bulb are connected in parallel and powered by a 6-Volt pack of batteries. Which of the two light bulbs will shine the brightest?

a. They will have the same brightness.

b. The low-R bulb will shine more brightly.

c. The high-R bulb will shine more brightly.

d. There is no way to make such a prediction since bulb brightness is independent of bulb resistance.

 Answer: B Since the two light bulbs are in parallel, the same voltage drop (V) is experienced by each. The power will be given by the i2•R product. Since V is the same for each light bulb, the bulb with the greatest resistance will have the lest current. Current is of the greatest importance in determining the power of the light bulb since it is squared in the equation. So the low-R light bulb will have the greatest current and thus transform electrical energy into light energy at the greatest rate; it will shine most brightly.

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49. Three identical light bulbs are connected to a battery as shown at the right. Which adjustments could be made to the circuit that would increase the current being measured at X? Include all that apply.

a. increase the resistance of one of the bulbs

b. increase the resistance of two of the bulbs

c. decrease the resistance of two of the bulbs

d. increase the voltage of the battery

e. decrease the voltage of the battery

f. remove one of the bulbs

 Answer: CDF The current in a series circuit (both total current and current through individual resistors) is directly dependent upon the battery voltage and inversely dependent upon the total circuit resistance. This current can be increased by increasing the battery voltage. It can also be increased by decreasing the total resistance. Removing a bulb would decrease the total resistance and decreasing the resistance of any individual bulb would decrease the total resistance.

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50. Three identical light bulbs (labeled X, Y and Z) are connected to a battery as shown at the right. Which adjustments could be made to the circuit below that would increase the current at point P? List all that apply.

a. increase the resistance of one of the bulbs

b. increase the resistance of two of the bulbs

c. decrease the resistance of two of the bulbs

d. increase the voltage of the battery

e. decrease the voltage of the battery

f. remove one of the bulbs

 Answer: CD Point P represents the location where the total current of this parallel circuit can be measured. The total current would vary directly with the total voltage and inversely with the total resistance. Increasing the battery voltage would increase the current at location P. Decreasing the total resistance would increase the current at location P. The total resistance can be decreased by adding another resistor in a separate branch or by decreasing the resistance of any of the branches.

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51. Three identical light bulbs (labeled X, Y and Z) are connected to a battery as shown at the right. Which adjustments could be made to the circuit below that would decrease the current in bulb Z? List all that apply.

a. increase the resistance of bulb X

b. decrease the resistance of bulb X

c. increase the resistance of bulb Z

d. decrease the resistance of bulb Z

e. increase the voltage of the battery

f. decrease the voltage of the battery

g. remove bulb Y

 Answer: CF The current in bulb Z is dependent upon the voltage drop across bulb Z and the resistance of bulb Z. In equation form, IZ = VZ / RZ An increase in battery voltage would increase the voltage drop across bulb Z (VZ) and thus provide a greater current through the bulb. A decrease in the resistance of bulb Z would also increase the current through the bulb. However, making a change in bulb X or Y would have no effect on the VZ / RZ ratio.

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