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Physics Unit: Current Electricity Worksheet 1: Electric Potential Electric Potential Energy = PEE and is measured in Joules (J). Electric Potential = V and is measured in Joules per coulomb (JIC also known as a volt but more on that later) Electric Charge = q and is measured in coulombs (C) p

V

—

—

‘

E

q

Electric potential measures the amount of potential energy per amount of charge at a particular point. Any of these can be negative but none of them are vectors. The negatives simply mean less than zero for electric potential or potential energy.

1. a. What electric potential exists at a point if + 4 mC of charge has 80 mJ of potential energy at that point? b. What potential energy would a +2 mC charge have at the same point? c. What potential energy would a -2 mC charge have at the same point? 2. How much positive charge would need to be placed at a potential of 12 V to accumulate a total of 252 Joules of electrical potential energy? 3. Would a charge of -3.0 C have more potential energy at a potential of 10 J/C or 20 J/C? Explain. A dropped rock moves to lower its gravitational energy (try it at home). A ‘dropped’ charge moves to lower is electrical potential energy. 4. a. A charge of+ 4 C is released at a point of electric potential 30 J/C. Would it begin to naturally move towards a potential of 20 J/C or 40 JIC? b. The charge in the last problem moves because an electric field exerts a force on it. Based on the last problem, does the electric field point towards higher potential or lower potential? In reality, the electric potential is an arbitrary value (as is gravitational potential energy). It is referenced from an arbitrary choice of zero. All that really matter in these problems is not the potential but the potential difference. Potential difference should really be written as AV but, confusingly, is generally written as V. I’ll use AV until you get used to it. So.. Potential Difference = AV and is measured in J/C. 1 JIC is known as a volt and for this reason potential difference is often referred to as voltage. Continued on next page

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IXPEE

=

qt\V

or

PEE —PEE

=

q(Vf

j 0 _V

5. A charge of +3.5 C ‘falls’ from a potential of 1000 Volts to a potential of 980 Volts. How much potential energy did it lose? 6. A charge of +3.5 C ‘falls’ from a potential of 20 Volts to a potential of 0 Volts. How much potential energy did it lose? 7. A charge of +3.5 C ‘falls’ from a potential of-80 Volts to a potential of-l00 Volts. How much potential energy did it lose? 8. A conventional car battery stores on the order of 5.0 MJ of potential energy and creates a potential difference of 12 Volts. How much total charge must the battery move through the circuit to convert this energy from chemical energy to electrical energy? As long as no outside work is done then any lost potential energy is converted into kinetic energy. Thus potential energy in the equation above can be replaced by kinetic energy. (technically APE = -AKE but we’re just worried about the amount) 9. How much kinetic energy does the charge in problem 5 end up with? If it has a mass of 10 kg, and starts from rest how fast is it moving when it gets to a potential of 980 V? 10. What potential difference would be needed to get a mass of 2.0 kg with a charge of +8.0 mC up to a speed of 50 mIs? 11. Would work be needed to move charge of -2.5 mC from 40 Volts to ground (ground is considered to be zero volts)? If so, how much work is done and if not how much potential energy would be lost? 12. A proton falls through a potential difference of 6 volts. How much kinetic energy did it gain? (charge of a proton = +1.6 x i0’ C) 13. Convert your answer from the last problem from joules (jou did remember the unit right?) into electron volts (abbreviated eV). 1 eV = 1.6 x 10 J Challenge. Mr. H brings his Alpha Ray gun to school. It fires Alpha particles which have a charge of +2e and a mass of 6.4 x I 027 kg. These particles are fired at about th 1110 of the speed of light. What voltage does the Ray gun need to produce these rays? How many AAA batteries will it require at 1.5 volts each?

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Physics Unit: Current Electricity Worksheet 2: Electrical Current

Useful information: 1 elementary charge = e 1.6 x 1019 C http ://www.physicsclassroom.comlClass/circuits/u912c.cfm Review: 1. What amount of work must be done to move 500 mC of positive charge from an electric potential of 0 volts to one of 12 volts? 2. What potential difference would be needed to give a helium nucleus with a charge of +3.2 x i0’ C a kinetic energy of I x i0’ J if it started from rest? 3. A -0.15 C charge is released at a point at which the electric potential is 100 V. a. Would that charge naturally move toward a point of 0 V or 200 V? b. What kinetic energy would it have when it got to the point mentioned in the last problem? c. If the charge has a mass of 5 kg, what velocity will it have when it gets to the new position? 4. A normal long-life triple A battery will supply an average potential difference of 1.225 V during its lifetime (it is generally 1.5 volts at first but its internal resistance increases as it is used decreasing its effective voltage). Such a battery stores about 5000 joules of energy. What amount of total charge will flow out of (and back into) the battery over its lifetime? 5. A long-life D cell battery has the same average potential difference but will move a total of 61,200 coulombs of charge over its lifetime! What total energy does it store? Quick side note on electric fields and electric potential: We know that positive charges naturally move to lower potential. We also know that electric fields point in the direction that a positive charged will get pushed. Obviously, that means that electric fields point to lower potential. In fact, besides N/C (newtons per coulomb), another possible unit for electric fields are Vim (volts per meter). Thus the stronger the electric field, the greater the kinetic energy gained by a charge in a given distance. Electric current If a potential difference is created across a conductive path (like a copper wire), electrons will drift toward the higher potential (towards the positive) and away from lower potential (away from the negative). Mathematically, electrical current represents the net quantity of electrical charge flowing into a cross section of the wire per amount of time. Current is expressed in units of coulombs per second (C/s) also known as Amperes (A). So 1 A = 1 C/s. Q is charge in coulombs and t is time in seconds. Current = I = —

Q

—

t

Continued on next page

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22222222222222222222222222222222222222222222222222222222 6. What current flows from a battery if 30 millicoulombs of charge move into a section of a wire in 6 seconds? 7. A current of 1.30 A flows in a wire. How many electrons flow past any point in the wire in one second? (charge of an electron at the top of the first page) 8. Nervous impulses are communicated through the flow of ions (charged atoms) across cell membranes. If 1200 Na ions (each with a charge of +1 elementary charges) flow across a cell membrane in 3.5 is what is the current in amperes? 9. A 60-Watt bulb draws a current of about 0.5 amps. How much electric charge must move into (and later out of) the bulb in 30 minutes? 10. Current represents the net flow of charge through a cross sectional area of conductor per amount of time. What does drift speed mean? What is a typical drift speed? Conventional Current Direction: Ben Franklin believed that the carriers of electric current were positive charges rather than electrons as we now understand. He believed that these positive charges were repelled by the positive terminal of the battery and were attracted by the negative terminal. This system became so ingrained by the time electrons were discovered that we still us it today. We use the term conventional current to represent this flow of positive charge through a circuit as shown in the diagram below. Conventional current, I

Electron urrent 4 c

11. We know that electrical current is caused by the flow of (protons, neutrons or electrons) from the (positive or negative) terminal of a battery to the (positive or negative) terminal of the battery. (choose the best term in each set ofparentheses) 12. By convention, we say that current is the flow of terminal of the battery.

charge from the

13. How long will the D battery in problem 5 last if it supplies a current of 0.5 Amps? Challenge Problem: Batteries are often rated with other quantities besides voltage since that is similar for most (rechargeable batteries generally supply a little less voltage). Two frequent units are milliamp-hours (mAh) and Watt-hours (Wh). What do each of the units measure? Hint: Convert each into standard base units and make cancellations.

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Physics Unit: Current Electricity Worksheet 3: Circuits and Ohm’s Law Review 1. A battery is rated at 6.0 Volts and is used for 24 seconds. During that time 0.054 C of charge flows into (and out of) the battery. a. What is the current through the battery? b. How much of the.baneriestored energy is used? +

frvj

5

2. How much work must be done to move a +3.4 mC charge from a potential of 1.7 V to a potential of 4.6 V? 3. An object of mass 4.3 kg and charge -58 mC is released from rest and accelerates through a potential difference of 20 V. a. If the initial potential is 5 V, what is the final potential? b. How fast is the charge moving at the end of the 20 Volt difference? Requirement of an electric circuit: All electric circuits have two basic requirements a. There must be an energy supply capable of doing work on charge to move it from a low energy location to a high energy location and thus establish an electric potential difference across the two ends of the external circuit. We sometimes summarize this requirement as a source of potential difference like a battery. b. There must be a closed conducting loop in the external circuit which stretches from the high potential, positive terminal to the low potential, negative terminal. —

Conventional current, I

We might summarize these requirements by looking at the diagram to the left. Positive charges are lifted to a high potential within the battery and exit the battery with a large amount of potential energy. That potential energy is converted into kinetic energy or work within some device. The positive charge is returned to the negative terminal of the battery at low energy. Chemical reactions in the battery then move positive charge back to the positive side of the battery at high energy. 4. If an electric circuit could be compared to a water circuit at a water park, then the battery would be analogous to the positive terminal of the battery would be analogous to the current would be analogous to the charge would be analogous to the electric potential difference would be analogous to the Choices: B. gallons of water flowing down slide per minute A. water pressure D. bottom of the slide C. water F. top of the slide E. water pump

_________(high,

_________

_______

_________

_________ _______

______(long,

_______ ________

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5. The diagram at the right shows a light bulb connected to a 12-V car battery. The

+

- terminals are shown.

and

a. As a + charge moves through the battery from D to A, it (gains, loses) potential energy and (gains, loses) electric potential. The point of highest energy within a battery is the (+, -) terminal. b. As a + charge moves through the external circuit from A to D, it (gains, loses) potential energy and (gains, loses) electric potential. The point of highest energy within the external circuit is (+, -) terminal. closest to the

c A

_D

Ohm’s Law: Georg Simon Ohm found that the current, I, through a wire was generally proportional to the potential difference, V, applied to the two ends. Thus, if the voltage was doubled, the current would double as well. Because of this the value of V/I would remain constant for a particular wire. The result of V/I is known as the resistance of the wire so that V/I = R although the law is generally written as

V

=

IR

or, as i sometimes prefer

V

‘ =

R

Resistance is essentially a measure of the degree to which the atoms of the wire restrict the flow of electrons. Conductors have a very low resistance. The unit for resistance is called the ohm and is abbreviated as L Thus a wire with a resistance of 20 with a potential difference of 100 volts across it would support a current of 5 A. The resistance of a wire depends on a. the material of which it is made (specifically its resistivity), b. the length of the wire (longer wires cause more resistance, and c. the cross sectional area. A larger area allows electrons to pass more freely. 6. What voltage would be required to force a current of 250 mA through a wire of resistance 400 2? 7. By what factor would the current through a wire change if the potential difference across the wire doubled and the resistance was cut in half? 8. What is the resistance of a toaster if 120 V produces a current of 4.2 A. 9. A hair dryer draws 7.5 A when plugged into a 120-V line. (a) What is its resistance? (b) how much charge passes through it in 15 minutes? 10. To get the most current with the same voltage, a wire should be short), have a low) resistivity and should have a (large, small) diameter. Challenge: A 9.0-V battery is connected to a bulb whose resistance is 1.6 . How many electrons leave the battery per minute?