AP Physics 1 Assignment

AP Physics 1 Assignment – Electricity

Reading Sections: 18.1 – 18.3; 19.1; 20.1 – 20.4; 21.1 – 21.5, Open Stax College Physics
Sections: 18: 1 – 10; 19: 1 – 11, Giancoli

Objectives/HW

	The student will be able to:	HW:
1	Relate electrical phenomena to the motion and position of the fundamental charge found on electrons and protons and recognize the Coulomb as the SI unit of charge and e as the elementary quantum of charge.	1 – 6
2	State and apply Coulomb’s Law to solve problems relating force, charge, and distance.	7 – 11
3	Define electric current and the Ampere and solve problems relating current to charge and time.	12 – 14
4	Solve problems involving electric power.	15 – 22
5	Define resistance the Ohm and solve problems using Ohm’s Law to relate voltage, current, and resistance.	23 – 32
6	Determine resistance for series or parallel combinations of resistors or as a function of resistivity, length, and cross-sectional area for a single resistor.	33 – 37
7	State and apply Kirchoff’s node and loop rules and solve related problems, including analysis of battery resistor circuits with series and/or parallel connections.	38 – 48

Homework Problems

1. If you comb your hair on a dry day, your hair may stand on end indicating that it has become electrically charged. Can the comb that you used remain electrically neutral? Explain.

2. As you walk across a rug electrons may be removed from your shoes and deposited in the rug. Does the rug become positively or negatively charged? What about your shoes?

3. Compare and contrast Coulomb’s Law and Newton’s Law of Universal Gravitation.
(a) In what ways are the two laws similar? (b) In what ways are the two laws different?

4. Suppose it is determined that a certain pith ball has a charge of –4.00 × 10^-17 C. Of which are there more in the pith ball, electrons or protons? Determine how many more.

5. How many coulombs of charge are on the electrons in a nickel coin? Follow this method to find the answer. (a) Find the number of atoms in a 5.0 gram coin made of nickel. A mole of nickel (6.02 ´ 10²³ atoms) has a mass of 58 grams. (b) Find the number of electrons in the coin. Each nickel atom has 28 electrons. (c) Find how many coulombs of charge are on the electrons. (d) Suppose this nickel then obtains a net charge of + 2.0 nC. Explain this net charge as a surplus or deficit of electrons and calculate how many. (e) What percent of atoms would have gained or lost a single electron in order for the nickel to get this net charge.

6. Results of an experiment with ionized atoms indicate that each ion had a charge of +5.10 × 10^-19 C. (a) Explain why there is clearly experimental error in this value. (b) Assuming the error is less than 20%, what was the actual charge on each ion? (c) Determine how many electrons were gained or lost by each atom to form the ions.

7. A pith ball with mass 0.15 grams and charge –3.0 nC is released from rest at a position 0.20 m directly above the center of a charged sphere of –2.5 μC. (a) Determine the electric force on the pith ball. (b) Find the initial acceleration of the pith ball. (c) How far upward will the pith ball move before its speed starts to decrease?

8. An experiment shows that the electric repulsion between two pith balls is 6.0 × 10^-5 N when separated by a distance of 3.0 cm. It is known that one of the pith balls has a surplus of electrons. (a) Determine charge on each pith ball assuming the amounts to be equal. (b) Determine the charge on each ball assuming one has twice as much. (c) Find the force of repulsion if the distance is increased to 4.0 cm.

9. A hydrogen atom consists of one proton, mass 1.67 × 10^-27 kg, orbited by one electron, mass
9.11 × 10^-31 kg. The average distance between them is 5.3 × 10^-11 m. The proton and electron have the same amount of charge but opposite signs (± e). (a) Determine the magnitude of the electric force attracting one to the other. (b) Determine the magnitude of the gravitational force attracting one to the other. (c) Which force is stronger and by what factor? (And therefore is most responsible for holding the electron in orbit about the proton)

10. Subatomic particles such as protons, electrons, positrons, muons, etc. will always have charge amount e, but mass is unique to the type of particle. (a) For any two such particles of masses m₁ and m₂ derive an expression for the ratio of electric force to gravitational force in terms of the masses and appropriate constants. (b) Determine this ratio for two protons.

11. Two pith balls, each with mass 0.50 grams, are attached to one another by a string that is
20.0 cm long. The string passes over a hook so that the two balls hang next to each other, just touching. A rubber rod is used to electrically charge the two pith balls, after which the two balls repel one another to a certain angle as shown. The pith balls reach an equilibrium state of rest when their centers are distance d = 5.00 cm apart. Determine the electric charge on each pith ball, assuming these values to be equal.

12. Just as a switch is turned on, a 10.0 amp fuse in an overloaded circuit melts and breaks in 0.15 s. Determine the minimum amount of charge that must have passed through the fuse in this time interval in order to cause it to “blow”.

13. How many electrons flow past a point in a wire each second if the wire has a current of 1.00 Amperes?

14. A certain rechargeable battery is rated at 400 mA×h. This is indicative of the total amount of electric charge it can deliver before it “dies”. (a) Determine this amount of charge. (b) If the battery is recharged in a time period of 5.0 h what is the required charging current?

15. The current through a toaster connected to a 120 V source is 8.0 A. What power is dissipated by the toaster?

16. A lamp draws 0.50 A from a 120 V generator. (a) How much power does the generator deliver to the lamp? (b) How much electric energy does the lamp convert to light and heat in a period of 5.0 minutes?

17. A 12 V automobile battery is connected to a 4.0 kW electric starter motor. (a) What current is needed? (b) In how much time would 100 C of charge pass through the motor?

18. A particular car battery has a “cranking amps” rating of 525 A. This means that it is capable of delivering this much current for 30 seconds without the voltage of the battery dropping below 7.2 volts. Given these values, what amount of electrical energy can be extracted from the battery in 30 seconds?

19. A 4.0 kW clothes dryer is connected to a 220 V circuit. How much current does the dryer require?

20. Freddy’s cell phone has a battery that is 3.8 V and it is rated 2.0 amp-hours. (a) Determine the total energy storage capacity in joules. (b) If Freddy typically drains the battery from 100% charged to zero in 24 hours, what is the average current and power?

21. A 60 W light bulb is connected to a voltage of 120 V and left on for 3.5 hours. The light bulb is 12% efficient. (a) How much electric charge passes through the bulb in this time period? (b) How much light energy is given off by the bulb in this time period? (c) How much heat energy is given off by the bulb in this time period?

22. A transistor radio operates by means of a 9.0 V battery that supplies it with a 50 mA current. The cost of the battery is $0.90 and it will run the radio for 300 hours before going dead.
(a) What is the cost per kW-hr to operate the radio using the battery? (1 kW-hr is equal to 3.6 MJ) (b) The same radio, by means of a converter, is plugged into a household circuit by a homeowner who pays $0.080 per kW-hr. What does it now cost to operate the radio for 300 hours?

23. A resistance of 60 Ω has a current of 0.40 A through it when it is connected to the terminals of a certain battery. (a) What is the voltage of the battery? (b) If the same resistor is connect to a different battery of voltage 12.0 V what will be the current through it?

24. A 75 V battery is connected to a 15 Ω resistor. (a) What is the current through the resistor? (b) What is the power output of the battery?

25. A 100 Watt light bulb operates on 120 Volts. Determine the resistance of the bulb.

26. Derive an expression giving the current I through a resistor in terms of its resistance R and the power P of its heat dissipation.

27. The damage caused by electric shock depends on the current flowing through the body – 1 mA can be felt; 5 mA is painful. Above 15 mA, a person loses muscle control, and 70 mA can be fatal. A person with dry skin has a resistance from one arm to the other of about 100 kΩ. When skin is wet, the resistance drops to about 5 kΩ. (a) What is the minimum voltage placed across the arms that would produce a current that could be felt by a person with dry skin? (b) What current and what effect would the same voltage have if the person had wet skin? (c) What would be the minimum voltage that would produce a current that could be felt when the skin is wet?

28. A certain lamp draws 66 mA when connected to a 6.0 V battery and 75 mA when connected to a 9.0 V battery. (a) Show numerically whether or not this is an ohmic device (i.e. show whether or not the resistance is constant). (b) From 6.0 V to 9.0 V is a 50% increase in voltage. Determine the percent increase in power output of the lamp.

29. Suppose an experiment is done to verify Ohm’s Law and determine the unknown resistance of a particular device. (a) Draw a schematic circuit diagram illustrating connections of a battery, the device, a voltmeter, and an ammeter that could be used to perform the experiment. (b) If there is only one battery available, but many different resistors, how can the voltage across the device be varied? Explain and illustrate in the circuit diagram. (c) Explain how a graph of voltage versus current can be used to achieve the goals of the experiment.

30. A 220 Ω resistor is rated 5.0 W. This is the maximum allowable power for the resistor.
(a) Determine the maximum allowable current that can flow through this resistor.
(b) Determine the maximum allowable voltage to which this resistor should be connected.

31. Two resistors, R₁ = 100 Ω and R₂ = 300 Ω, can be connected various ways in an electrical circuit. (a) Calculate the voltage across each resistor if the current through each one is the same 15.0 mA. (b) Calculate the current through each resistor if the voltage across each one is the same 6.00 V. (c) Which resistor connected which way dissipates the greatest heat? Calculate its power.

32. A certain wire in a household circuit has a resistance of 0.15 Ω and is designed to carry up to 15 A of current. (a) At its maximum current, what power is dissipated by the wire’s resistance? (b) How much heat does the wire give off in 10.0 minutes at its maximum capacity? (c) What is the electric potential difference from one end of the wire to the other when operated at its maximum capacity? (This is how much the voltage “drops” from its original value due to resistance of the wire.)

33. Resistance of a wire or resistor can be modeled by R = ρL/A, where L = length, A = cross-sectional area, and ρ = resistivity, an inherent property of the material used. Copper has resistivity ρ = 1.68 × 10^-8 Ω m. Calculate the resistance of three copper wires: (a) 20.0 m long, diameter 2.050 mm; (b) 30.0 m long, diameter 2.050 mm; (c) 30.0 m long, diameter 1.025 mm. (d) Determine the resistivity of the carbon/ceramic material in a 47 k Ω resistor of length 0.80 cm, radius 1.0 mm. Note: use A = πr² for area for each calculation.

34. Why does the equivalent resistance decrease as more resistors are added to a parallel circuit?

35. Give at least two reasons why household wiring is done in parallel instead of in series.

36. (a) Why should an ammeter have a very low resistance? (b) Why should a voltmeter have a very high resistance?

37. For each part of this question, write the form of circuit that applies: series or parallel.
(a) The current is the same for each element in the circuit. (b) The voltage is the same for each element in the circuit. (c) The total resistance is equal to the sum of the individual resistances. (d) Adding a resistor decreases the total resistance.

38. A 20.0 Ω lamp and a 5.00 Ω lamp are connected in series and placed across a potential difference of 50.0 V. (a) Determine the equivalent resistance of the two lamps.
(b) Determine the current delivered by the power source. (c) Determine the voltage across each lamp. (d) Determine the power output of each lamp.

39. Five identical lamps are connected in series to a 6.0 V battery. What is the voltage drop across each lamp?

40. The load across a 12 V battery consists of a series combination of three resistors of 15 Ω, 21 Ω, and 24 Ω. Determine the current in the circuit.

41. A current of 0.10 A flows in a series circuit consisting of a battery and two resistors: 15 Ω and 45 Ω. Determine the electric potential of the battery.

42. Two wires are used to connect a 47.0 Ω resistor to a 9.00 V battery. Typically the resistance of wires is ignored. However, in this problem consider that each wire has resistance 0.20 Ω and the circuit may be seen as a series connection of three resistances. (a) Find the current through the resistor. (b) Determine the “drop off” in voltage due to the resistance of the wires. (c) What percent error in the current results from ignoring the resistance of the wires?

43. A 40.0 V power source, a resistor of 16.0 W, and a resistor of 20.0 W are all connected in a parallel circuit. (a) Determine the equivalent resistance of the two resistors. (b) Determine the current supplied by the power source. (c) Determine the power dissipated by each resistor.

44. Current of 20.0 mA flows through a 1.5 V cell when connected to two particular parallel resistors. One of the resistors carries 15.0 mA. Determine the resistance of each resistor.

45. An electric potential of 5.0 V is required to run certain computer chips. A 6.0 V battery may be used to do this but it must be connect to two resistors in series. Supposing one has a resistance of 330 Ω what should the other be? (The computer chip requires very little current and will be driven by the voltage across only one of the two resistors.)

46. Consider the circuit shown below. (a) Determine the current reading of the ammeter.
(b) Determine the voltage reading of the voltmeter. (c) Determine the power dissipated by the 500 Ω resistor.

47. Consider the circuit shown below. (a) Determine the current reading of the ammeter.
(b) Determine the voltage reading of the voltmeter. (c) Determine the power dissipated by the 45.0 Ω resistor.

48. In the circuit shown below the resistors have resistance R₁ = R₂ = R₃ = R and the switch can be at position 1, position 2, or it can be in between making no contact. (a) Determine the maximum current that can occur in resistor R₃ and the position of the switch that will cause this. (b) Determine the maximum current that can occur in resistor R₁ and the position of the switch that will cause this. (c) Determine the maximum power output of the cell and the position of the switch that will cause this.