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physics
college physics 2nd

College Physics 2nd Edition OpenStax - Solutions

(a) Using the symmetry of the arrangement, show that the electric field at the center of the square in Figure 18.42 is zero if the charges on the four corners are exactly equal. (b) Show that this is also true for any combination of charges in which b = b pue Pb = об
Discuss pros and cons of a lightning rod being grounded versus simply being attached to a building.
(a) What is the direction of the total Coulomb force on q in Figure 18.42 if q is negative, qa = qc and both are negative, and qb= qd and both are positive? (b) What is the direction of the electric field at the center of the square in this situation? qa O qc O q 9b O qd
Considering Figure 18.42, suppose that qa = qd and qb= qc. First show that q is in static equilibrium. (You may neglect the gravitational force.) Then discuss whether the equilibrium is stable or unstable, noting that this may depend on the signs of the charges and the direction of displacement of
If qa = 0 in Figure 18.42, under what conditions will there be no net Coulomb force on q?Data from Figure 18.42
In regions of low humidity, one develops a special “grip” when opening car doors, or touching metal door knobs. This involves placing as much of the hand on the device as possible, not just the ends of one’s fingers. Discuss the induced charge and explain why this is done.
Tollbooth stations on roadways and bridges usually have a piece of wire stuck in the pavement before them that will touch a car as it approaches. Why is this done?
Suppose a person carries an excess charge. To maintain their charged status can they be standing on ground wearing just any pair of shoes? How would you discharge them? What are the consequences if they simply walk away?
Voltage is the common word for potential difference. Which term is more descriptive, voltage or potential difference?
If the voltage between two points is zero, can a test charge be moved between them with zero net work being done? Can this necessarily be done without exerting a force? Explain.
What is the relationship between voltage and energy? More precisely, what is the relationship between potential difference and electric potential energy?
Voltages are always measured between two points. Why?
How are units of volts and electron volts related? How do they differ?
Discuss how potential difference and electric field strength are related. Give an example.
What is the strength of the electric field in a region where the electric potential is constant?
Will a negative charge, initially at rest, move toward higher or lower potential? Explain why.
In what region of space is the potential due to a uniformly charged sphere the same as that of a point charge? In what region does it differ from that of a point charge?
Can the potential of a non-uniformly charged sphere be the same as that of a point charge? Explain.
What is an equipotential line? What is an equipotential surface?
Explain in your own words why equipotential lines and surfaces must be perpendicular to electric field lines.
Can different equipotential lines cross? Explain.
Does the capacitance of a device depend on the applied voltage? What about the charge stored in it?
Use the characteristics of the Coulomb force to explain why capacitance should be proportional to the plate area of a capacitor. Similarly, explain why capacitance should be inversely proportional to the separation between plates.
How does the polar character of water molecules help to explain water’s relatively large dielectric constant? (Figure 19.18) H 104.5° H O Schematic Inherent (polar) separation of charge e e ee ee aa Electron cloud
Give the reason why a dielectric material increases capacitance compared with what it would be with air between the plates of a capacitor. What is the independent reason that a dielectric material also allows a greater voltage to be applied to a capacitor? (The dielectric thus increases and permits
Sparks will occur between the plates of an airfilled capacitor at lower voltage when the air is humid than when dry. Explain why, considering the polar character of water molecules.
Water has a large dielectric constant, but it is rarely used in capacitors. Explain why.
Membranes in living cells, including those in humans, are characterized by a separation of charge across the membrane. Effectively, the membranes are thus charged capacitors with important functions related to the potential difference across the membrane. Is energy required to separate these
If you wish to store a large amount of energy in a capacitor bank, would you connect capacitors in series or parallel? Explain.
How does the energy contained in a charged capacitor change when a dielectric is inserted, assuming the capacitor is isolated and its charge is constant? Does this imply that work was done?
What happens to the energy stored in a capacitor connected to a battery when a dielectric is inserted? Was work done in the process?
Can a wire carry a current and still be neutral—that is, have a total charge of zero? Explain.
If two different wires having identical cross-sectional areas carry the same current, will the drift velocity be higher or lower in the better conductor? Explain in terms of the equation by considering how the density of charge carriers relates to whether or not a material is a good conductor.
Car batteries are rated in ampere-hours (A · h). To what physical quantity do ampere-hours correspond (voltage, charge, . . .), and what relationship do ampere-hours have to energy content?
Why are two conducting paths from a voltage source to an electrical device needed to operate the device?
In cars, one battery terminal is connected to the metal body. How does this allow a single wire to supply current to electrical devices rather than two wires?
Why isn’t a bird sitting on a high-voltage power line electrocuted? Contrast this with the situation in which a large bird hits two wires simultaneously with its wings.
The IR drop across a resistor means that there is a change in potential or voltage across the resistor. Is there any change in current as it passes through a resistor? Explain.
How is the IR drop in a resistor similar to the pressure drop in a fluid flowing through a pipe?
In which of the three semiconducting materials listed in Table 20.1 do impurities supply free charges? Conductors Silver Copper Gold Aluminum Tungsten Iron Platinum Material Steel Lead Manganin (Cu, Mn, Ni alloy) Resistivity p (9 m) 1.59 × 10-8 1.72 × 10-8 2.44 x 10-8 2.65 x 10-8 5.6 x 10-8 9.71
Does the resistance of an object depend on the path current takes through it? Consider, for example, a rectangular bar—is its resistance the same along its length as across its width? (See Figure 20.33.) R- + V I' = ? + V | R' = ?
If aluminum and copper wires of the same length have the same resistance, which has the larger diameter? Why?
Explain why R = R0 (1 + αΔT) for the temperature variation of the resistance R of an object is not as accurate as ρ = ρ0(1 + αΔT), which gives the temperature variation of resistivity ρ.
Why do incandescent lightbulbs grow dim late in their lives, particularly just before their filaments break?
The power dissipated in a resistor is given by P = V2/R, which means power decreases if resistance increases. Yet this power is also given by P= I2 R, which means power increases if resistance increases. Explain why there is no contradiction here.
Give an example of a use of AC power other than in the household. Similarly, give an example of a use of DC power other than that supplied by batteries.
Why do voltage, current, and power go through zero 120 times per second for 60-Hz AC electricity?
You are riding in a train, gazing into the distance through its window. As close objects streak by, you notice that the nearby fluorescent lights make dashed streaks. Explain.
Using an ohmmeter, a student measures the resistance between various points on his body. They find that the resistance between two points on the same finger is about the same as the resistance between two points on opposite hands—both are several hundred thousand ohms. Furthermore, the resistance
What are the two major hazards of electricity?
Why isn’t a short circuit a shock hazard?
What determines the severity of a shock? Can you say that a certain voltage is hazardous without further information?
An electrified needle is used to burn off warts, with the circuit being completed by having the patient sit on a large butt plate. Why is this plate large?
Some surgery is performed with high-voltage electricity passing from a metal scalpel through the tissue being cut. Considering the nature of electric fields at the surface of conductors, why would you expect most of the current to flow from the sharp edge of the scalpel? Do you think highor
Some devices often used in bathrooms, such as hairdryers, often have safety messages saying “Do not use when the bathtub or basin is full of water.” Why is this so?
We are often advised to not flick electric switches with wet hands, dry your hand first. We are also advised to never throw water on an electric fire. Why is this so?
Before working on a power transmission line, experts will touch the line with the back of the hand as a final check that the voltage is zero. Why the back of the hand?
Why is the resistance of wet skin so much smaller than dry, and why do blood and other bodily fluids have low resistances?
Note that in Figure 20.25, both the concentration gradient and the Coulomb force tend to move Na+ ions into the cell. What prevents this? Coulomb force Diffusion Diffusion Na+ Outside CI Coulomb force + + + (K+) Membrane Coulomb force Inside Diffusion
In view of the small currents that cause shock hazards and the larger currents that circuit breakers and fuses interrupt, how do they play a role in preventing shock hazards?
Define depolarization, repolarization, and the action potential.
A switch has a variable resistance that is nearly zero when closed and extremely large when open, and it is placed in series with the device it controls. Explain the effect the switch in Figure 21.41 has on current when open and when closed. E R
Explain the properties of myelinated nerves in terms of the insulating properties of myelin.
What is the voltage across the open switch in Figure 21.41? E R
There is a voltage across an open switch, such as in Figure 21.41. Why, then, is the power dissipated by the open switch small? E R
Why is the power dissipated by a closed switch, such as in Figure 21.41, small? E R
A student in a physics lab mistakenly wired a light bulb, battery, and switch as shown in Figure 21.42. Explain why the bulb is on when the switch is open, and off when the switch is closed. (Do not try this—it is hard on the battery!) E R
Knowing that the severity of a shock depends on the magnitude of the current through your body, would you prefer to be in series or parallel with a resistance, such as the heating element of a toaster, if shocked by it? Explain.
Would your headlights dim when you start your car’s engine if the wires in your automobile were superconductors? (Do not neglect the battery’s internal resistance.) Explain.
Some strings of holiday lights are wired in series to save wiring costs. An old version utilized bulbs that break the electrical connection, like an open switch, when they burn out. If one such bulb burns out, what happens to the others? If such a string operates on 120 V and has 40 identical
If two household lightbulbs rated 60 W and 100 W are connected in series to household power, which will be brighter? Explain.
Suppose you are doing a physics lab that asks you to put a resistor into a circuit, but all the resistors supplied have a larger resistance than the requested value. How would you connect the available resistances to attempt to get the smaller value asked for?
Before World War II, some radios got power through a “resistance cord” that had a significant resistance. Such a resistance cord reduces the voltage to a desired level for the radio’s tubes and the like, and it saves the expense of a transformer. Explain why resistance cords become warm and
Some light bulbs have three power settings (not including zero), obtained from multiple filaments that are individually switched and wired in parallel. What is the minimum number of filaments needed for three power settings?
Explain which battery is doing the charging and which is being charged in Figure 21.43. Έ, = 12.0 V η = 1.0 Ω · Έg = 18.0 V r2 = 0.5 Ω
Is every emf a potential difference? Is every potential difference an emf? Explain.
Given a battery, an assortment of resistors, and a variety of voltage and current measuring devices, describe how you would determine the internal resistance of the battery.
Two different 12-V automobile batteries on a store shelf are rated at 600 and 850 “cold cranking amps.” Which has the smallest internal resistance?
What are the advantages and disadvantages of connecting batteries in series? In parallel?
Can all of the currents going into the junction in Figure 21.44 be positive? Explain. 12 1₁ 13
Semitractor trucks use four large 12-V batteries. The starter system requires 24 V, while normal operation of the truck’s other electrical components utilizes 12 V. How could the four batteries be connected to produce 24 V? To produce 12 V? Why is 24 V better than 12 V for starting the truck’s
Apply the junction rule to junction b in Figure 21.45. Is any new information gained by applying the junction rule at e? (In the figure, each emf is represented by script E.) a R₁ ww 200 0.50 18 V P₂ www 15 2 P₂ 在 0 1₂ 6 2 g 3.0V 0.25 02 R₂ w 82 24VI 百 12V 0.5 (2 "₁ m d 0.75 22
Apply the loop rule to loop afedcba in Figure 21.45. a R₁ ww 200 0.50 18 V P₂ www 15 2 P₂ 在 0 1₂ 6 2 g 3.0V 0.25 02 R₂ w 82 24VI 百 12V 0.5 (2 "₁ m d 0.75 22
Apply the loop rule to loops abgefa and cbgedc in Figure 21.45. AT 20 2 0.50 R₁ 18 V A₂ www 15 2 P₂ E₂ 1₂ b 1₂ 692 g 3.0 V 0.250 R₂ ww 852 El 24 V E, √3 "₁ m 0.75 22 12 V 0.52 d
Why should you not connect an ammeter directly across a voltage source as shown in Figure 21.46? (Note that script E in the figure stands for emf.) E Do not do this! A
Specify the points to which you could connect a voltmeter to measure the following potential differences in Figure 21.47:(a) The potential difference of the voltage source; (b) The potential difference across R1; (c) Across R2; (d) Across R3; (e) Across R2 and R3. Note that there may be more
Suppose you are using a multimeter (one designed to measure a range of voltages, currents, and resistances) to measure current in a circuit and you inadvertently leave it in a voltmeter mode. What effect will the meter have on the circuit? What would happen if you were measuring voltage but
To measure currents in Figure 21.47, you would replace a wire between two points with an ammeter. Specify the points between which you would place an ammeter to measure the following:(a) The total current; (b) The current flowing through R1; (c) Through R2;(d) Through R3. Note that there may be
Why can a null measurement be more accurate than one using standard voltmeters and ammeters? What factors limit the accuracy of null measurements?
If a potentiometer is used to measure cell emfs on the order of a few volts, why is it most accurate for the standard emfs, to be the same order of magnitude and the resistances to be in the range of a few ohms?
Regarding the units involved in the relationship τ = RC, verify that the units of resistance times capacitance are time, that is, Ω . F= s.
When making an ECG measurement, it is important to measure voltage variations over small time intervals. The time is limited by the RC constant of the circuit-it is not possible to measure time variations shorter than RC. How would you manipulate R and C in the circuit to allow the necessary
The RC time constant in heart defibrillation is crucial to limiting the time the current flows. If the capacitance in the defibrillation unit is fixed, how would you manipulate resistance in the circuit to adjust the RC constant τ? Would an adjustment of the applied voltage also be needed to
Draw two graphs of charge versus time on a capacitor. Draw one for charging an initially uncharged capacitor in series with a resistor, as in the circuit in Figure 21.37, starting from t = 0. Draw the other for discharging a capacitor through a resistor, as in the circuit in Figure 21.38, starting
When charging a capacitor, as discussed in conjunction with Figure 21.37, how long does it take for the voltage on the capacitor to reach emf? Is this a problem?Data given in Figure 21.37 R ww Switch (a) Von capacitor E 0.632E 0 0 T = RC 2T (b) 3T 47
When discharging a capacitor, as discussed in conjunction with Figure 21.38, how long does it take for the voltage on the capacitor to reach zero? Is this a problem?Data given in Figure 21.38 R I Switch (a) V = V₁ e/RC (discharging). C +q Von capacitor V 0.368V 0 0 T = RC 2T (b) 3r 4r
Referring to Figure 21.37, draw a graph of potential difference across the resistor versus time, showing at least two intervals of . Also draw a graph of current versus time for this situation.Data given in Figure 21.37 R ww Switch (a) Von capacitor E 0.632E 0 0 T = RC 2T (b) 3T 47
A long, inexpensive extension cord is connected from inside the house to a refrigerator outside. The refrigerator doesn’t run as it should. What might be the problem?
In Figure 21.40, does the graph indicate the time constant is shorter for discharging than for charging? Would you expect ionized gas to have low resistance? How would you adjust to get a longer time between flashes? Would adjusting R affect the discharge time?Data given in Figure 21.40
An electronic apparatus may have large capacitors at high voltage in the power supply section, presenting a shock hazard even when the apparatus is switched off. A “bleeder resistor” is therefore placed across such a capacitor, as shown schematically in Figure 21.48, to bleed the charge from it

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