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physics
electricity and magnetism

Questions and Answers of Electricity and Magnetism

Copper has 85 X 1028 free electrons per cubic meter. A 71.0-cm length of 12-gauge copper wire that is 2.05 mm in diameter carries 4.85 A of current. (a) How much time does it take for an electron to
Consider the 18-gauge wire in Example 25.1. How many atoms are in 1.00 m3 of copper? With the density of free electrons given in the example, how many free electrons are there per copper atom?
The current in a wire varies with time according to the relationship I = 55 A - (0.65 A/S2)t2. (a) How many coulombs of charge pass a cross section of the wire in the time interval between t = 0 and
Current passes through a solution of sodium chloride. In 1.00 s, 2.68 X 1016 Na + ions arrive at the negative electrode and 392 X 1016 C1- ions arrive at the positive electrode. (a) What is the
Assume that in silver metal there is one free electron per silver atom. Compute the free electron density for silver, and compare it to the value given in Exercise 25.2.
(a) At room temperature what is the strength of the electric field in a 12-gauge copper wire (diameter 2.05 mm) that is needed to cause a 2.75-A current to flow? (b) What field would be needed if the
A 1.50-m cylindrical rod of diameter 0500 cm is connected to a power supply that maintains a constant potential difference of 15.0 V across its ends, while an ammeter measures the current through it.
A copper wire has a square cross section 2.3 mm on a side. The wire is 4.0 m long and carries a current of 3.6 A. The density of free electrons is 8.5 X 1028/m3. Find the magnitudes of (a) The
In an experiment conducted at room temperature, a current of 0.820 A flows through a wire 3.26 mm in diameter. Find the magnitude of the electric field in the wire if the wire is made of (a)
A wire 650 m long with diameter of 2.05 mm has a resistance of 0.0290 Ω. What material is the wire most likely made of?
A cylindrical tungsten filament 15.0 cm long with a diameter of 1.00 mm is to be used in a machine for which the temperature will range from room temperature (20°C) up to 120°C. It will carry a
A cylindrical tungsten filament 15.0 cm long with a diameter of 1.00 mm is to be used in a machine for which the temperature will range from room temperature (20°C) up to 120°C. It will carry a
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.
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?
You need to produce a set of cylindrical copper wires 350 m long that will have a resistance of 0.125 Ω each. What will be the mass of each of these wires?
A tightly coiled spring having 75 coils, each 3.50 cm in diameter, is made of insulated metal wire 3.25 mm in diameter. An ohmmeter connected across its opposite ends reads 1.74 Ω. What is the
An aluminum cube has sides of length of 1.80 m. What is the resistance between two opposite faces of the cube?
A battery-powered light bulb has a tungsten filament. When the switch connecting the bulb to the battery is first turned on and the temperature of the bulb is 20oC, the current in the bulb is 0.860
A rectangular solid of pure germanium measures 12 cm X 12 cm X 25 cm. assuming that each of its faces is an equipotential surface, what is the resistance between opposite faces that are (a) Farthest
You apply a potential difference of 4.50 V between the ends of a wire that is 250 m in length and 0.654 mm in radius. The resulting current through the wire is 17.6 A. What is the resistivity of the
A current-carrying gold wire has diameter 0.84 mm. The electric field in the wire is 0.49 V/m. What are? (a) The current carried by the wire; (b) The potential difference between two points in the
The potential difference between points in a wire 75.0 cm apart is 0.938 V when the current density is 4.40 X 107 A/m2. What are? (a) The magnitude of E in the wire and (b) The resistivity of the
(a) What is the resistance of a Nichrome wire at 0.0°C if its resistance is 100.00 0 at 11.5°C?(b) What is the resistance of a carbon rod at 25.8°C if its resistance is 0.0160 0 at 0.0°C?
A carbon resistor is to be used as a thermometer. On a winter day when the temperature is 4.0°C, the resistance of the carbon resistor is 217.3 Ω. What is the temperature on a spring day when
A strand of wire has resistance 5.60µΩ. Find the net resistance of 120 such strands if they are. (a) Placed side by side to form a cable of the same length as a single strand, and (b)
A hollow aluminum cylinder is 2.50 m long and has an inner radius of 3.20 cm and an outer radius of 4.60 cm. Treat each surface (inner, outer, and the two end faces) as an equipotential surface. At
A copper transmission cable 100 km long and 10.0 cm in diameter carries a current of 125 A. (a) What is the potential drop across the cable? (b) How much electrical energy is dissipated as thermal
Consider the circuit shown in Fig. 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?
An idealized voltmeter is connected across the terminals of a battery while the current is varied. Figure 25.34 shows a graph of the voltmeter reading Vas a function of the current I through the
An idealized ammeter is connected to a battery as shown in Fig. Find (a) The reading of the ammeter, (b) The current through the 4.00-Ω. Resistor, (c) The terminal voltage of the battery.
An ideal voltmeter V is connected to a 2.0-Ω resistor and a battery with emf 5.0 V and internal resistance 0.5 0. as shown in Fig.(a) What is the current in the 2.0- Ω resistor?(b) What
The circuit shown in Fig. contains two batteries, each with an emf and an internal resistance, and two resistors. Find(a) The current in the circuit (magnitude and direction);(b) The terminal voltage
When switch S in Fig 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
In the circuit of Fig, the 5.0-Ω resistor is removed and replaced by a resistor of unknown resistance R. When this is done, an ideal voltmeter connected across the points b and c reads 1.9 V.
In the circuit shown in Fig, the 16.0-V battery is removed and reinserted with the opposite polarity, so that its negative terminal is now next to point a. Find (a) The current in the circuit
The following measurements were made on a Thyrite resistor:(a) Graph V ab as a function of I.(b) Does Thyrite obey Ohm's law? How can you tell?(c) Graph the resistance R = Vab/I as a function of I.
The following measurements of current and potential difference were made on a resistor constructed of Nichrome wire:(a) Graph Vab as a function of I.(b) Does Nichrome obey Ohm's law? How can you
A resistor with a 15.0-V potential difference across its ends develops thermal energy at a rate of 327 W. (a) What is its resistance? (b) What is the current in the resistor?
Light Bulbs 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
If a “75-W” bulb (see Problem 25.43) is connected across a 220-V potential difference (as is used in Europe), how much power does it dissipate?
European Light Bulb in Europe the standard voltage in homes is 220 V instead of the 120 V used in the United States. Therefore a “100-W” European bulb would be intended for use with a 220-V
A battery-powered global positioning system (GPS) receiver operating on 9.0 V draws a current of 0.13 A. How much electrical energy does it consume during 1.5 h?
Consider a resistor with length L, uniform cross-sectional area A, and uniform resistivity p that is carrying a current with uniform current density J. Use Eq. (25.18) to find the electrical power
Consider the circuit of Fig. (a) What is the total rate at which electrical energy is dissipated in the 5.00-Ω and 9.00- Ω resistors? (b) What is the power output of the 16.0-V battery?
The capacity of a storage battery, such as those used in automobile electrical systems, is rated in ampere-hours (A· h). A 50- A h battery can supply a current of 50 A for 1.0 h, or 25 A for 2.0 h,
The capacity of a storage battery, such as those used in automobile electrical systems, is rated in ampere-hours (A• h). A 50- A h battery can supply a current of 50 A for 1.0 h, or 25 A for 2.0 h,
A 25.0-Ω bulb is connected across the terminals of a 12.0-V battery having 3.50 Ω of internal resistance. What percentage of the power of the battery is dissipated across the internal
n idealized voltmeter is connected across the terminals of a 15.0-V battery, and a 75.0-Ω appliance is also connected across its terminals. If the voltmeter reads 11.3 V: (a) How much power is
In the circuit in Fig, find(a) The rate of conversion of internal. (Chemical) energy to electrical energy within the battery;(b) The rate of dissipation of electrical energy in the battery;(c) The
A typical small flashlight contains two batteries, each having an emf of 1.5 V, connected in series with a bulb having resistance 17 Ω. (a) If the internal resistance of the batteries is
A “540-W” electric heater is designed to operate from 120-V lines. (a) What is its resistance? (b) What current does it draw? (c) If the line voltage drops to 110 V, what power does the heater
Pure silicon contains approximately 1.0 X 1016 free electrons per cubic meter. (a) Referring to Table 25.1, calculate the mean free time., for silicon at room temperature. (b) Your answer in part (a)
An electrical conductor designed to carry large currents has a circular cross section 2.50 mm in diameter and is 14.0 m long. The resistance between its ends is 0.104 n. (a) What is the resistivity
A plastic tube 25.0 m long and 4.00 cm in diameter is dipped into a silver solution, depositing a layer of silver 0.100 mm thick uniformly over the outer surface of the tube. If this coated tube is
On your first day at work as an electrical technician, you are asked to determine the resistance per meter of a long piece of wire. The company you work for is poorly equipped. You find a battery, a
A 2.0-mm length of wire is made by welding the end of a 120-cm-long silver wire to the end of an 80-cm-long copper wire. Each piece of wire is 0.60 mm in diameter. The wire is at room temperature, so
A 3.00-m length of copper wire at 20oC has a 1.20-m-long section with diameter 1.60 mm and a 1.80-m-long section with diameter 0.80 mm. There is a current of 2.5 m A in the 1.60-mm diameter section.
Critical Current Density in Superconductors One problem with some of the newer high-temperature super conductors is getting a large enough current density for practical use without causing the
A material of resistivity p is formed into a solid, truncated cone of height h and radii r1 and r2 at either end (Fig).(a) Calculate the resistance of the cone between the two flat end faces.(b) Show
The region between two concentric conducting spheres with radii a and b is filled witha conducting material with resistivity p.(a) Show that the resistance between the spheres is given by(b) Derive
Leakage in a Dielectric Two parallel plates of a capacitor have equal and opposite charges Q. The dielectric has a dielectric constant K and a resistivity p. Show 1hat the “leakage” current J
In the circuit shown in Fig, R is a variable resistor whose value can range from 0 to ∞, and a and b are the terminals of a battery having an emf E = 15.0 V and an internal resistance of 4.00
The temperature coefficient of resistance a in Eq. (25.12) equals the temperature coefficient of resistivity a in Eq. (25.6) only if 1he coefficient of Thermal expansion is small. A cylindrical
(a) What is the potential difference Vad in the circuit of Fig?(b) What is the terminal voltage of the 4.00-V battery?(c) A battery with emf 10.30z V and internal resistance 0.50 0 is inserted in the
The potential difference across the terminals of a battery is 8.4 V when there is a current of 1.50 A in the battery from the negative to the positive terminal. When the current is 3.50 A in the
A person with body resistance between his hands of 10 kΩ accidentally grasps the terminals of a 14-kV power supply. (a) If the internal resistance of the power supply is 2000 Ω, what is
(a) What is the resistance between the hands if the skin resistance is negligible? (b) What potential difference between the hands is needed for a lethal shock current of 100 mA? (Note that your
A typical cost for electric power is 12.0¢ per kilowatt-hour. (a) Some people leave their porch light on all the time. What is the yearly cost to keep a 75-W bulb burning day and night? (b) Suppose
A 12.6-V car battery with negligible internal resistance is connected to a series combination of a 3.2-Ω resistor that obeys Ohm's law and a thermistor that does not obey Ohm's law but instead
A cylindrical copper cable 1.50 km long is connected across a 220.0-V potential difference. (a) What should be its diameter so that it produces beat at a rate of 50.0 W? (b) What is the electric
A Nonideal Ammeter Unlike the idealized ammeter described in Section 25.4, any real ammeter has a nonzero resistance.
A 1.50-m cylinder of radius 1.10 cm is made of a complicated mixture of materials. Its resistivity depends on the distance x from the left end and obeys the formula p(x) = a + bx2, where a and b are
According to the U.S. National Electrical Code, copper wire used for interior wiring of houses, hotels, office buildings, and industrial plants is permitted to carry no more than a specified maximum
A toaster using a Nichrome heating element operates on 120 V. When it is switched on at 20oC, the heating element carries an initial current of 1.35 A. A few seconds later the current reaches the
In the circuit of Fig, find(a) The current through the 8.0-Ω resistor and(b) The total rate of dissipation of electrical energy in the 8.0-Ω resistor and in the internal resistance of the
A lightning bolt strikes one end of a steel lightning rod, producing a 15,000-A current burst that lasts for 65 µs. The rod is 20 m long and 1.8 cm in diameter and its other end is connected to the
A 12.0-V battery has an internal resistance of 0.24 Ω and a capacity of 50.0 A. h (see Exercise 25.49). The battery is charged by passing a 10-A current through it for 5.0 h. (a) What is the
Repeat Problem 25.81 with charge and discharge currents of 30 A. The charging and discharging times will now be 1.7 h rather than 5.0 h. What differences in performance do you see?
The Tolman-Stewart experiment in 1916 demonstrated that the free charges in a metal have negative charge and provided a quantitative measurement of their charge-w-mass ratio, |q|/m. The experiment
The current-voltage relationship of a semi conductor diode is given by(b) The value of V must be obtained by using a numerical method. One approach is to try a value of V, see how the left- and
The resistivity of a semi conductor can be modified by adding different amounts of impurities. A rod of semi conducting material of length L and cross-sectional area A lies along the x-axis between x
A source with emf e and internal resistance r is connected to an external circuit. (a) Show that the power output of the source is maximum when the current in the circuit is one-half the short
The temperature coefficient of resistivity a is given byWhere p is the resistivity at the temperature T. Equation (25.6) then follows if a is assumed constant and much smaller than (T €“
A uniform wire of resistance R is cut into three equal lengths. One of these is formed into a circle and connected between the other two (Fig). What is the resistance between the opposite ends a and
A machine part has a resistor X protruding from an opening in the side. This resistor is connected to three other resistors, as shown in Fig. An ohmmeter connected across a and b reads 2.00 Ω.
(a) Prove that when two resistors are connected in parallel, the equivalent resistance of the combination is always smaller than that of the smaller resistor. (b) Generalize your result from part (a)
A 32-Ω resistor and a 20-Ω resistor are connected in parallel, and the combination is connected across a 240-V dc line. (a) What is the resistance of the parallel combination? (b) What
A triangular array of resistors is shown in Fig. What current will this array draw from a 35.0-V battery having negligible internal resistance if we connect it across?(a) ab;(b) bc;(c) ac?(d) If the
For the circuit shown in Fig. both meters are idealized, the battery has no appreciable internal resistance, and the ammeter reads 1.25 A(a) What does the voltmeter read?(b) What is the emf E of the
For the circuit shown in Fig find the reading of the idealized ammeter if the battery has an internal resistance of 3.26 Ω.
Three resistors having resistances of 1.60Ω, 2.40 Ω, and 4.80 Ω are connected in parallel to a 28.0-V battery that has negligible internal resistance. Find (a) The equivalent
Now the three resistors of Exercise 26.8 are connected in series to the same battery. Answer the same questions for this situation.
Power Rating of a Resistor. The power rating of a resistor is the maximum power the resistor can safely dissipate without too great a rise in temperature and hence damage to the resistor. (a) If
Compute the equivalent resistance of the network in Fig, and find the current in each resistor. The battery has negligible internal resistance.
Compute the equivalent resistance of the network in Fig, and find the current in each resistor. The battery has negligible internal resistance.
In the circuit of Fig, each resistor represents a light bulb. Let R1 = R2 = R3 = R4 = 4.50Ω and E = 9.00V. (a) Find the current in each bulb. (b) Find the power dissipated in each bulb.
Consider the circuit shown in Fig. The current through the 6.00-Ω resistor is 4.00 A, in the direction shown. What are the currents through the 25.0-Ω and 20.0-Ω resistors?
In the circuit shown in Fig, the voltage across the 2.00-Ω resistor is 12.0 V. What are the emf of the battery and the current through the 6.00- Ω resistor?
A Three-way Light Bulb A three way light bulb has three brightness settings (low, medium, and high) but only two filaments. (a) A particular three-way light bulb connected across a 120-V line can
Light Bulbs in Series and in Parallel Two light bulbs have resistances of 400 Ω and 800 Ω. If the two light bulbs are connected in series across a 120-V line, find (a) The current through

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