Name: AP Homework Coulomb s Law. Date: Class Period:

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1 AP Homework 12.1 Coulomb s Law Name: Date: Class Period: (Q1) Two metal spheres are hanging from nylon threads. When you bring the spheres close to each other, they tend to attract. Based on this information alone, discuss all the possible ways that the spheres could be charged. Is it possible that after the spheres touch, they will cling together? Explain. (Q2) Your clothing tends to cling together after going through the dryer. Why? Would you expect more or less clinging if all your clothing were made of the same material (say, cotton) than if you dried different kinds of clothing together? Again, why? (You may want to experiment with your next load of laundry.) (Q3) An uncharged metal sphere hangs from a nylon thread. When a positively charged glass rod is brought close to the metal sphere, the sphere is drawn toward the rod. But if the sphere touches the rod, it suddenly flies away from the rod. Explain why the sphere is first attracted and then repelled. (1) Lightning occurs when there is a flow of electric charge (principally electrons) between the ground and a thundercloud. The maximum rate of charge flow in a lightning bolt is about 20,000 C/s; this lasts for 100 ms or less. How much charge flows between the ground and the cloud in this time? How many electrons flow during this time? (2.00 C, 1.25x10 19 ) (2) You have a pure (24-karat) gold ring with mass 17.7 g. Gold has an atomic mass of 197 g/mol and an atomic number of 79. (a) How many protons are in the ring, and what is their total positive charge? (b) If the ring carries no net charge, how many electrons are in it? (4.27x10 24, 6.83x10 5 C)

2 (3) Two small spheres spaced 20.0 cm apart have equal charge. How many excess electrons must be present on each sphere if the magnitude of the force of repulsion between them is 4.57x10-21 N? (890) (4) Two small plastic spheres are given positive electrical charges. When they are 15.0 cm apart, the repulsive force between them has magnitude N. What is the charge on each sphere (a) if the two charges are equal and (b) if one sphere has four times the charge of the other?. μc;. μc,. μc (5) Two very small 8.55-g spheres, 15.0 cm apart from center to center, are charged by adding equal numbers of electrons to each of them. Disregarding other forces, how many electrons would you have to add to each sphere so that they each accelerate at 25.0g when released? Which way will they accelerate? (1.43x10-13 ) (6) Three point charges are arranged on a line. Charge q 3 = nc and is at the origin. Charge q 2 = nc and is at x = cm. Charge q 1 is at x = cm. What is q 1 if the net force on q 3 is zero? (0.750 nc)

3 AP Homework 12.2 Voltage, Current, Resistance Name: Date: Class Period: (1) In one model of the hydrogen atom, an electron in its lowest state moves in a circular orbit around the nucleus (a single proton) at a distance of 5.29x10-11 m. Find the electric potential energy of a hydrogen atom. (2) A point charge q 1 is held stationary at the origin. A second charge q 2 is placed at point a, and the electric potential energy of the pair of charges is +5.4x10-8 J. When the second charge is moved to point b, the electric force on the charge does -1.9x10-8 J of work. What is the electric potential energy of the pair of charges when the second charge is at point b? Is point b closer to or farther away from the origin? (3) A small particle has charge -.00 μc and mass 2.00x10-4 kg. It moves from point A, where the electric potential is V A = +200 V, to point B, where the electric potential is V B = +800 V. The electric force is the only force acting on the particle. The particle has speed 5.00 m/s at point A. What is its speed at point B? Is it moving faster or slower at B than at A? Explain. Four parti les ith harges.0 μc,.0 μc,.0 μc, a d -.0 μc are pla ed at the or ers of a.0.0 square. Determine the voltage at the center of the square. (5) A silver wire 2.6 mm in diameter transfers a charge of 420 C in 80 min. What is the current in the wire?

4 (6) During lightning strikes from a cloud to the ground, currents as high as 25,000 A can occur and last for about 40 ms. How much charge is transferred from the cloud to the earth during such a strike? (7) In an old-fashio ed tu e tele isio, the ea urre t is 0.0 μa. Ho a ele tro s strike the s ree every second? (8) In household wiring, copper wire 2.05 mm in diameter is often used. Find the resistance of a 24.0-m length of this wire 9 A ire. 0 lo g ith dia eter of.0 has a resista e of Ω. What aterial is the ire ost likely made of? (10) What diameter must a copper wire have if its resistance is to be the same as that of an equal length of aluminum wire with diameter 3.26 mm?

5 AP Homework 12.3 Ohm s Law & Power Name: Date: Class Period: (1) A 14-gauge copper wire of diameter mm carries a current of 12.5 ma. (a) What is the potential difference across a 2.00-m length of the wire? (b) What would the potential difference in part (a) be if the wire were silver instead of copper, but all else were the same? (2) You apply a potential difference of 4.50 V between the ends of a wire that is 2.50 m in length and mm in radius. The resulting current through the wire is 17.6 A. What is the resistivity of the wire? (3) The current in a resistor is 0.5 A when it is connected to a potential difference of 110 V. What is the current in this same resistor if (a) the voltage is 90.0 V? (b) the voltage is 130 V? (4) Consider the circuit shown. The terminal voltage of the 24.0-V battery is 21.2 V. What are (a) the internal resistance r of the battery and (b) the resistance R of the circuit resistor? (5) An idealized ammeter is connected improperly to a battery as shown. Why is this connection improper, and what problem will it cause? Find (a) the reading of the ammeter, (b) the current through the 4.00-Ω resistor, (c) the terminal voltage of the battery.

6 (6) An ideal voltmeter V is connected improperly to a 2.0-Ω resistor a d a attery ith emf 5.0 V and internal resistance 0.5-Ω as shown. Why is this connection improper and what problem will it cause? (a) What is the current in the 2.0-Ω resistor? What is the terminal voltage of the battery? (c) What is the reading on the voltmeter? (7) When switch S is open, the voltmeter V of the battery reads 3.08 V. When the switch is closed, the voltmeter reading drops to 2.97 V, and the ammeter A reads 1.65 A. Find the emf, the internal resistance of the battery, and the circuit resistance R. (8) The power rating of a light bulb (such as a 100-W bulb) is the power it dissipates when connected across a 120-V potential difference. What is the resistance of (a) a 100-W bulb and (b) a 60-W bulb? (c) How much current does each bulb draw in normal use? (9) In Europe the standard voltage in homes is 220 V instead of the 120 V used in the United States. Therefore a -W Europea ul ould e i te ded for use ith a -V pote tial differe e. a If you ri g a - W Europea ul ho e to the United States, what should be its U.S. power rating? (b) How much current will the 100-W European bulb draw in normal use in the United States? (10) A heart defibrillator is used to enable the heart to start beating if it has stopped. This is done by passing a large current of 12 A through the body at 25 V for a very short time, usually about 3.0 ms. (a) What power does the defibrillator deliver to the body, and (b) how much energy is transferred? (11 A 5. Ω ul is o e ted a ross the ter i als of a. -V attery ha i g.5 Ω of i ternal resistance. What percentage of the power of the battery is dissipated across the internal resistance and hence is not available to the bulb?

7 AP Homework 12.4 Series, Parallel, Loops, & Junctions Name: Date: Class Period: (1) A 32-Ω resistor and a 20-Ω resistor are o e ted i parallel, a d the o i atio is o e ted a ross a 240-V voltage source. (a) What is the resistance of the parallel combination? (b) What is the total current through the parallel combination? (c) What is the current through each resistor? (2) A resistor with R 1 =. Ω is o e ted to a attery that has egligi le i ter al resista e a d ele tri al energy is dissipated by R 1 at a rate of 36.0W. If a second resistor with R 2 =. Ω is connected in series with R 1, what is the total rate at which electrical energy is dissipated by the two resistors? (3) Three resistors having resista es of. Ω,. Ω, a d.8 Ω are o e ted i parallel to a 28.0-V battery that has negligible internal resistance. Find the equivalent resistance of the combination; (b) the current in each resistor; (c) the total current through the battery; (d) the voltage across each resistor; (e) the power dissipated in each resistor. (f) Which resistor dissipates the most power: the one with the greatest resistance or the least? (4) Now the three resistors of problem (3) are connected in series to the same battery. Answer the same questions for this situation. (5) Compute the equivalent resistance in each of the networks shown, and find the current in each resistor. The battery has negligible internal resistance.

8 (6) T o light ul s ha e resista es of Ω a d 8 Ω. If the t o light ul s are o e ted i series a ross a 120-V line, find (a) the current through each bulb; (b) the power dissipated in each bulb; (c) the total power dissipated in both bulbs. The two light bulbs are now connected in parallel across the 120-V line. Find (d) the current through each bulb; (e) the power dissipated in each bulb; (f) the total power dissipated in both bulbs. (g) In each situation, which of the two bulbs glows the brightest? (h) In which situation is there a greater total light output from both bulbs combined? (7) Determine the current in and voltage across the 2.0 Ω resistor. (8) Determine the current, voltage drop, and power across each resistor in this circuit. (9) Assume that al the resistors in problem (8) are light bulbs. If R 2 were removed from the circuit, what would happen to the brightness of the R 1 bulb? (10) Calculate the current in, potential difference, and power across each resistor.