(a) Calculate the number of electrons in a small, electrically neutral silver pin that has a mass of 13.0 g. Silver has 47 electrons per atom, and its molar mass is 107.87 g/mol. (b) Imagine adding electrons to the pin until the negative charge has the very large value 1.00 mC. How many electrons are added for every 109 electrons already present?
The protons in a nucleus are approximately 2×10−15 m apart. Consider the case where the protons are a distance d = 2.01×10−15 m apart. Calculate the magnitude of the electric force (in N) between two protons at this distance. N
Two charged particles, q1 and q2, are located on the x-axis, with q1 at the origin and q2 initially at x1 = 13.1 mm. In this configuration, q1 exerts a repulsive force of 2.62 μN on q2. Particle q2 is then moved to x2 = 19.0 mm. What is the force (magnitude and direction) that q2 exerts on q1 at this new location? (Give the magnitude in μN.) magnitude μN direction
Consider an electric field perpendicular to a work bench. When a small charged body of mass 4.02 g and charge −18.9 μC is carefully placed in the field, the body is in static equilibrium. What are the magnitude and direction of the electric field? (Give the magnitude in N/C.) magnitude N/C direction
Several species of bacteria, including Geobacter metallireducens, have been shown to "eat" electrons, bypassing the usual process of metabolizing sugar to obtain energy. During this process, the bacteria, which already have negatively charged cell membranes, acquire an even larger net negative charge, typically between 10.0 e and 85.0 e in magnitude. Individual Geobacter are typically 4.00 μm in diameter. What are the magnitude and the direction of the electric field of a bacterium with a net negative charge of magnitude 70.0 e at a distance of 1.80 mm from the microbe? (a) the magnitude (in N/C) N/C (b) the direction radially outward radially inward What are the magnitude and the direction of the electric force on a second bacterium of net negative charge 80.0 e distance of 1.80 mm from the first bacterium? (c) the magnitude (in N) N (d) the direction away from the first bacterium towards the first bacterium
The figure below shows the electric field lines for two charged particles separated by a small distance. (i) (a) Determine the ratio q1/q2. (b) What are the signs of q1 and q2 ? q1 q2
Two particles, an electron and a proton, are initially at rest in a uniform electric field of magnitude 484 N/C. If the particles are free to move, what are their speeds (in m/s ) after 43.2 ns? electron m/s proton m/s
An electron is traveling with initial kinetic energy K in a uniform electric field. The electron comes to rest momentarily after traveling a distance d. (a) What is the magnitude of the electric field? (Use any variable or symbol stated above along with the following as necessary: e for the charge of the electron.) E = (b) What is the direction of the electric field? in the direction of the electron's motion opposite to the direction of the electron's motion perpendicular to the direction of the electron's motion (c) What If? Fluoride ions (which have the same charge as an electron) are initially moving with the same speed as the electrons from part (a) through a different uniform electric field. The ions come to a stop in the same distance d. Let the mass of an ion be M and the mass of an electron be m. Find the ratio of the magnitude of electric field the ions travel through to the magnitude of the electric field found in part (a). (Use the following as necessary: d, k, m, M, and e for the charge of the electron.) Enew Epart (a) =
(a) Two protons in a molecule are 4.20×10−10 m apart. Find the electric force exerted by one proton on the other. magnitude N direction (b) State how the magnitude of this force compares with the magnitude of the gravitational force exerted by one proton on the other. Fe Fg = (c) What must be a particle's charge-to-mass ratio if the magnitude of the gravitational force between two of these particles is equal to the magnitude of electric force between them? C/kg
Two equal positively charged particles are at opposite corners of a trapezoid as shown in the figure below. (Use the following as necessary: Q, d, ke.) (a) Find a symbolic expression for the total electric field at the point P. E→P = (b) Find a symbolic expression for the total electric field at the point P′. E→P′ =
Three equal positive charges q are at the corners of an equilateral triangle of side a as shown in the figure below. Assume the three charges together create an electric field. (a) Sketch the field lines in the plane of the charges. Choose File No file chosen This answer has not been graded yet. (b) Find the location of one point (other than ∞ ) where the electric field is zero. at P at the center of the triangle at each vertex at the center of the base (c) What is the magnitude of the electric field at P due to the two charges at the base? (Use any variable or symbol stated above along with the following as necessary: ke.) E = (d) What is the direction of the electric field at P due to the two charges at the base? to the left to the right upward downward
You are still fascinated by the process of inkjet printing, as described in the opening storyline for this chapter. You convince your father to take you to his manufacturing facility to see the machines that print expiration dates on eggs. You strike up a conversation with the technician operating the machine. He tells you that the ink drops are created using a piezoelectric crystal, acoustic waves, and the Plateau-Rayleigh instability, which creates uniform drops of mass m = 1.25×10−8 g. While you don't understand the fancy words, you do recognize mass! The technician also tells you that the drops are charged to a controllable value of q and then projected vertically downward between parallel deflecting plates at a constant terminal speed of 17.5 m/s. The plates are ℓ = 2.15 cm long and have a uniform electric field of magnitude E = 6.75×104 N/C between them. Noting your interest in the process, the technician asks you, "If the position on the egg at which the drop is to be deposited requires that its deflection at the bottom end of the plates be 0.17 mm, what is the required charge on the drop (in C)?" You quickly get to work to find the answer. (Neglect the force of gravity.) C
You are working on a research project in which you must control the direction of travel of electrons using deflection plates. You have devised the apparatus shown in the figure below. (i) The plates are of length ℓ = 0.750 m and are separated by a distance d = 4.95 cm. Electrons are fired at vi = 5.50×106 m/s into a uniform electric field from the left edge of the lower, positive plate, aimed directly at the right edge of the upper, negative plate. Therefore, if there is no electric field between the plates, the electrons will follow the broken line in the figure. With an electric field existing between the plates, the electrons will follow a curved path, bending downward. (a) Determine the range of angles (in degrees) over which the electron can leave the apparatus. (Assume θ is measured counterclockwise from the +x-axis. Enter your answers as a comma-separated list from smallest to largest. Do not enter units in your answer. ) (θmin, θmax) = ( )。 (b) Determine the electric field (in N/C ) required to give the maximum possible deviation angle. (Enter the magnitude.) N/C
You are working in a manufacturing plant. In one particular machine, electric charges are suspended above a uniformly charged disk of radius R. The disks become corroded rapidly and must be replaced daily. Your supervisor comes to you one day and tells you that he wants to replace the disks with much cheaper washers of radius R with a concentric hole of radius R 4. He asks you to determine by what factor the charge on the disk must be increased so that a uniform charge on the washer would provide the same electric field at a distance x = R on the central axis as did the disk. qwasher qdisk =
A rod 12.0 cm long is uniformly charged and has a total charge of −24.0 μC. Determine the magnitude and direction of the electric field along the axis of the rod at a point 38.0 cm from its center. magnitude N/C direction
A 46.0-cm-diameter circular loop is rotated in a uniform electric field until the position of maximum electric flux is found. The flux in this position is measured to be 5.72×105 N⋅m2 /C. What is the magnitude of the electric field? MN/C
A vertical electric field of magnitude 2.55×104 N/C exists above the Earth's surface on a day when a thunderstorm is brewing. A car with a rectangular size of 6.00 m by 3.00 m is traveling along a dry gravel roadway sloping downward at 20.6∘. Determine the electric flux through the bottom of the car. kN⋅m2 /C
The following charges are located inside a submarine: 6.40 μC, −9.00 μC, 27.0 μC, and −82 μC. (a) Calculate the net electric flux through the hull of the submarine. N⋅m2 /C (b) Is the number of electric field lines leaving the submarine greater than, equal to, or less than the number entering it? greater than equal to less than
An uncharged nonconductive hollow sphere of radius 12.0 cm surrounds a 13.0 μC charge located at the origin of a cartesian coordinate system. A drill with a radius of 1.00 mm is aligned along the z axis, and a hole is drilled in the sphere. Calculate the electric flux through the hole. N⋅m2/C
(a) A small Styrofoam bead with a mass of 14.2 g and a charge of −0.754 μC is suspended in equilibrium above the center of a large, horizontal sheet of plastic that has a uniform charge density on its surface. Find the charge per unit area on the plastic sheet (in μC/m2). μC/m2 (b) What If? What are the magnitude and direction of the acceleration of the piece of Styrofoam if its charge is doubled? (Enter the magnitude in m/s2.) magnitude m/s2 direction
(a) A small plastic bead with a charge of −60.0 nC is at the center of an insulating rubber spherical shell with an inner radius of 20.0 cm and an outer radius of 27.0 cm. The rubber material of the spherical shell is charged, with a uniform volume charge density of −1.30 μC/m3. A proton moves in a circular orbit just outside the spherical shell. What is the speed of the proton (in m/s )? m/s (b) What If? Suppose the spherical shell carries a positive charge density instead. What is the maximum value the charge density (in μC/m3 ) the spherical shell can have below which a proton can orbit the spherical shell? μC/m3
Problem 2: Consider the forces shown in the figure. Free-body diagram Part (a) Find the magnitude of the force F1 shown in the figure in Newtons. Numeric : A numeric value is expected and not an expression. F1 = Part (b) Find the magnitude of the force F2 shown in the figure in Newtons. Numeric : A numeric value is expected and not an expression. F2 =
Three forces are applied to an object, as shown in the figure. Force F1→ has a magnitude of 20.0 newtons (20.0 N) and is directed 30.0∘ to the left of the +y axis. Force F2→ has a magnitude of 15.8 N and points along the +x axis. What must be the (a) magnitude and (b) direction (specified by the angle θ in the drawing) of the third force F3→ such that the vector sum of the three forces is 0 N? (a) Number Units (b) Number Units
Problem 4. A particle of mass m is attached to two nearby walls by springs, each of which has spring constant k, as in the figure below. When the particle is situated at the midpoint between the two walls, both springs are un-stretched. The mass is now pulled to the right by an amount A, and then at time t = 0 is released from rest (i. e., with no initial velocity). Ignore gravity, and ignore any motion in the transverse (i. e., y ) direction. (20 points total) (a) By applying Newton's laws of motion, find the differential equation that governs the subsequent motion of the particle. (10 points) (b) What is x(t) for this particle? What is the frequency of oscillation of this particle, ω, as a function of k and m? (5 points) (c) What is the period of oscillation, T? (5 points)
In the Dreamworks animated movie "Spirit", one of the most culminating scenes is when Spirit, the horse, and his horse buddies with a total force F pull a train with mass m = 1,000 kg up a steep slope at an angle β = 30∘ for a distance of d to create a path to lay the railway tracks. The train starts at rest and the horse increases it speed at a constant acceleration until it reaches a velocity of vf = 2 m/s within 4 seconds. There is friction along the surface of the slope with coefficient μ = 0.1. The gravitational constant is defined as g = 10 m/sec2. How many horses do you need to achieve this if each horse can provide 1061 N ? Solve the problem using Newton-Euler (make sure to set up your FBD = KD equations). Solve the problem using Work-Energy Theorem. If the answers are the same, why would you use one method or another? Briefly talk about this with your team to help you identify strategies of the benefits and costs of each.
(Force and Motion - I) Consider the system shown in figure with mA = 9.5 kg and mB = 11.5 kg. The angles θA = 59∘ and θB = 32∘. i Draw the free body diagrams for block A and block B. ii In the absence of friction, what force F would be required to pull the masses at a constant velocity up? iii The force F now is removed. What is the magnitude and direction of acceleration of the two blocks? iv In the absence of F, what is the tension in the string? Answer: ii) 140 N iii) a→ = −6.7 m/s2 i^ iv) 17 N
For the following problem draw the forces acting on each of the boxes and setup the force tables for each of them. Then write the force equations for each of the following boxes. Use g = 9.8 m/s2 a) Find the acceleration of each box b) Find the tension acting on each box c) Determine how far the 5 kg block will slide in 1 s.
Set up the free-body diagram and the equations for Newton's 2 nd law for each object along each axis. Assume friction is present between all surfaces and the coefficient of friction is different between the different surfaces. (Note you should have 2 free body diagrams)
When system in the figure is released from rest, m2 moves down m1 moves to the right, and the disk of mass M and radius R rotates around its center, while the rope does not slip over the rim of the disk. a) Draw free body diagrams and write the equations of motion for m1, m2, and the disk. b) Find the acceleration of m1 and m2, and the angular acceleration of the disk. (I = (MR2)/2 for the disk.)
The freight cars A and B have a mass of 20 Mg and 15 Mg, respectively. Determine the velocity of A after collision if the cars collide and rebound, such that B moves to the right with a speed of 2 m>s. If A and B are in contact for 0.5 s, find the average impulsive force which acts between them.
Problem 2 - Motion in One Dimension A particle of mass m moves along the x-axis. The magnitude of the net force acting on the particle at the time t is F(t) = F0(1 − t2 T2). The force is directed along the x-axis. F0 and T are constants. As it can be seen from the formula above, F(t) vanishes when t = T. The velocity and the position of the particle at the time t = 0 are v(0) = 0 and x(0) = 0. a) Calculate the velocity of the particle at the time t = T. (10 points) b) Calculate the position of the particle along the x axis at the time t = T. ( 5 points)
Problem 3 - Newton's 2 nd Law A block of m1 = 3.30 kg is placed on a frictionless inclined plane which makes an angle θ = 31∘ with the horizontal line. The block of mass m1 is connected to a second block of mass m2 = 1.93 kg by means of a cord of negligible mass and a frictionless pulley. a) Draw the free body diagram for each block. (5 points) b) Calculate the acceleration of the masses. (5 points) c) Calculate the tension of the cord. (5 points)
Calculate the torque (magnitude and direction) about point O due to the force F→ in each of the cases sketched in the figure below. In each case, the force F→ and the rod both lie in the plane of the page, the rod has length 4.00 m, and the force has magnitude F = 10.0 N. (a) (b) (c) (d) (e) (f)
Part A In the figure (Figure 1), if mA = 1.20 kg, mB = 1.50 kg and θ = 35.0∘, what will be the magnitude of the acceleration of the system? Handwritten Solutions (Submitted into Canvas): Write down your Givens and what you are asked to Find for each Part. Clearly define your coordinate system (+/- directions) and origin, draw free body diagrams, apply Newton's Law, define Action-Reaction Pairs, and show how you obtained your equations and final answers. Show all steps and write down all equations used (not just numbers). Show how you obtained your final answer(s) including diagrams, equations, algebra and geometry, appropriate units, and significant figures. Put a box around your final answer(s).
Three objects are connected on a table as shown in Figure below. The coefficient of kinetic friction between the block of mass m2 and the table is 0.350 . The objects have masses of m1 = 4.00 kg, m2 = 1.00 kg, and m3 = 2.00 kg as shown, and the pulleys are frictionless. Determine the acceleration of each object, including its direction.
Three objects are connected by light strings as shown in Figure below. The string connecting the 4.00−kg object and the 5.00−kg object passes over a light frictionless pulley. Determine (a) the acceleration of each object and (b) the tension in the two strings.
Two packing crates of masses 10.0 kg and 5.00 kg are connected by a light string that passes over a frictionless pulley as in Figure below. The 5.00−kg crate lies on a smooth incline of angle 40.0∘. a) Find the acceleration of the 5.00−kg crate b) Find the tension in the string c) If the coefficient of static friction between the 5.00−kg crate and the 40.0∘ incline is 0.300 . Find tension in the string and acceleration of the crate.
The recommended daily allowance for an average adult that does not want to gain or lose weight is roughly 2000 kcal. Suppose all of that energy was converted into internal energy, with no losses. What would the final temperature of the person be in Celsius if they started at 37∘C and had an equivalent mass of water of 113 pounds? ( 1 kg weighs 2.2 pounds on Earth). 1 kcal = 4186 joules Round to 2 sig figs.
To melt an 50 gram ice cube that is at 0 degrees Celsius you have to supply heat. If the latent heat of fusion of ice is 330 J/gram then how much energy is require to just melt the cube but not raise its temperature? 16500 Joules 660 Joules 6.6 Joules 330 Joules
A solenoid that is 70.8 cm long has a cross-sectional area of 19.1 cm2. There are 1370 turns of wire carrying a current of 8.54 A. (a) Calculate the energy density of the magnetic field inside the solenoid. (b) Find the total energy in joules stored in the magnetic field there (neglect end effects). (a) Number Units (b) Number Units
A particle with a charge of q = 10.0 μC travels from the origin to the point (x, y) = (20.0 cm, 50.0 cm) in the presence of a uniform electric field E→ = 220 i^ V/m. Determine the following. (a) the change in the electric potential energy (in J) of the particle-field system (b) the electric potential difference (in V) through which the particle moves V
While you are studying for an upcoming physics exam, a lightning storm is brewing outside your window. Suddenly, you see a tree across the street struck by lightning. There is a loud sound and you see smoke rising from various parts of the tree. You stop studying for your exam and do online research on lightning, trees, and sap. You find that a typical lightning bolt represents a potential difference of 1.00×108 V between the cloud and the ground and that it can transfer a typical charge of 50.0 C between the cloud and the ground. Some models show that when a tree is hit by lightning, perhaps 2.00% of the energy in the lightning bolt can be delivered to the sap, causing it to boil. Model the sap as water initially at 30.0∘C. If all of the sap in the tree is vaporized to gaseous sap at 100∘C, determine how much sap (in kg ) there is in the tree. (Use any necessary values found in this table or this table.) kg
An insulating rod having linear charge density λ = 10.0 μC/m and linear mass density μ = 0.100 kg/m is released from rest in a uniform electric field E = 30 V/m directed perpendicular to the rod. (a) Determine the speed of the rod after it has traveled 1.50 m. m/s (b) How does your answer to part (a) change if the electric field is not perpendicular to the rod? It increases. It decreases. It stays the same. Explain. This answer has not been graded yet.
Two charged point-like objects are located on the x-axis. The point-like object with charge q1 = 6.00 μC is located at x1 = 1.25 cm and the point-like object with charge q2 = −2.40 μC is located at x2 = −1.80 cm (a) Determine the total electric potential (in V ) at the origin. V (b) Determine the total electric potential (in V ) at the point with coordinates (0, 1.50 cm). V
After learning about the electric field due to a ring of charge, you decide to apply this knowledge to a bead launcher to be used to fire beads vertically into the air. You build a metal ring of radius R = 0.240 m and lay it flat on the ground. At the center of the ring, you mount a vertical nonconducting wire that will serve as a guide for the bead as it is launched upward. You place a 2.50 g bead on the upper end of the wire and slide the bead to the bottom end, where it is just above the center point of the ring. You place a charge of +4.00 μC on the bead, and +4.00 μC on the metal ring. You then release the bead so that it is repelled from the ring and launched upward. Determine to what height (in m) the bead rises before coming to rest and beginning to fall back downward. (Hint: To begin, assume that this height is much larger than the radius of the ring, and then check your result against this assumption. Round your answer to at least one decimal place.) m
The potential at a point P a distance a above one end of a uniformly charged rod of length ℓ lying along the x axis is given by the following equation. V = keQℓ ln(ℓ + a2 + ℓ2 a) Use this result to derive an expression for the y component of the electric field at P. (Use the following as necessary: ke′, ℓ, y, and Q.) Ey =
A charge Q is distributed uniformly around the perimeter of a ring of radius R. Determine the electric potential difference between the point at the center of the ring and a point on its axis at a distance 19 R from the center. (Use any variable or symbol stated above along with the following as necessary: ke.) ΔV = V(0) − V(19 R) =
A spherical conductor with a 0.233 m radius is initially uncharged. How many electrons should be removed from the sphere in order for it to have an electrical potential of 5.90 kV at the surface? electrons
(a) How much charge is on each plate of a 2.00−μF capacitor when it is connected to a 13.0−V battery? μC (b) If this same capacitor is connected to a 2.00−V battery, what charge is stored? μC
An isolated charged conducting sphere has a radius R = 15.0 cm. At a distance of r = 18.0 cm from the center of the sphere the electric field due to the sphere has a magnitude of E = 4.90×104 N/C. (a) What is its surface charge density (in μC/m2)? μC/m2 (b) What is its capacitance (in pF)? pF (c) What If? A larger sphere of radius 29.0 cm is now added so as to be concentric with the first sphere. What is the capacitance (in pF) of the two-sphere system? pF
An engineer has three different capacitors of unknown capacitance. She labels them C1, C2, and C3. First, she connects C1 to a battery, and the charge on C1 is q1 = 33.0 μC. Then, she disconnects and discharges C1, and connects it in series with C2. When she connects this series combination of C2 and C1 across the battery, the charge on C1 is q2 = 22.1 μC. The engineer disconnects the circuit and discharges both capacitors. Next, she connects C3, C1, and the battery in series, which results in a charge on C1 of q3 = 26.9 μC. If, after being disconnected and discharged, she connects C1, C2, and C3 in series with the battery, what is the charge on C1 (in μC)? μC
A group of identical capacitors is connected first in series and then in parallel. The combined capacitance in parallel is 196 times larger than for the series connection. How many capacitors are in the group? capacitors
A student connects an 18.0 V battery to a capacitor of unknown capacitance. The result is that 51.6 μC of charge is stored on the capacitor. How much energy (in J) is stored in the capacitor? J
Each capacitor in the combination shown in the figure below (C = 17.0 μF) has a breakdown voltage of 16.0 V. What is the breakdown voltage of the combination? V
An infinite line of positive charge lies along the y axis, with charge density λ = 1.30 μC/m. A dipole is placed with its center along the x axis at x = 21.0 cm. The dipole consists of two charges ±10.0 μC separated by 2.00 cm. The axis of the dipole makes an angle of 30.0∘ with the x axis, and the positive charge is farther from the line of charge than the negative charge. Find the net force exerted on the dipole. F→ =
The general form of Gauss's law describes how a charge creates an electric field in a material, as well as in vacuum. ∫E→⋅dA→ = qin ε where ε = κε0 is the permittivity of the material. (a) A sheet with charge Q uniformly distributed over its area A is surrounded by a dielectric. Show that the sheet creates a uniform electric field with magnitude E = Q/2Aε. This answer has not been graded yet. (b) Two large sheets of area A, carrying opposite charges of equal magnitude Q, are a small distance d apart. Show that they create a uniform electric field in the space between them with magnitude E = Q/Aε. This answer has not been graded yet. (c) Assume that the negative plate is at zero potential. Show that the positive plate is at a potential Qd/Aε. This answer has not been graded yet. (d) Show that the capacitance of the pair of plates is given by C = Aε/d = κAε0/d.
Particles with a charge of +5e are incident on a target. If the beam of particles carries a current of 117 μA, how many particles strike the target in a period of 29.0 s ? particles
The electron beam emerging from a certain high-energy electron accelerator has a circular cross section of radius 1.05 mm. (a) The beam current is 7.65 μA. Find the current density in the beam assuming it is uniform throughout. A/m2 (b) The speed of the electrons is so close to the speed of light that their speed can be taken as 300 Mm/s with negligible error. Find the electron density in the beam. m−3 (c) Over what time interval does Avogadro's number of electrons emerge from the accelerator? s
An aluminum wire has a length of 1.50 m and a cross sectional area of 0.360 mm2. If the resistivity of aluminum is 2.82×10−8 Ω⋅m and a potential difference of 0.700 V is maintained across its length, determine the current in the wire (in A). A
If the magnitude of the drift velocity of free electrons in a copper wire is 6.94×10−4 m/s, what is the electric field in the conductor? V/m
An advanced lab student is studying the effect of temperature on the resistance of a current carrying wire. She applies a voltage to a tungsten wire at a temperature of 52.0∘C and notes that it produces a current of 1.20 A. If she then applies the same voltage to the same wire at −88.0∘C, what current should she expect (in A)? The temperature coefficient of resistivity for tungsten is 4.50×10−3(∘C)−1. (Assume that the reference temperature is 20∘C.) A
An iron wire has a resistance of 6.50 Ω at 26.0∘C. Determine its resistance (in Ω) at 426∘C. The temperature coefficient of resistivity for iron wire is 5.00×10−3 (∘C)−1. (Assume that the temperature coefficient of resistivity was measured using the reference temperature 20∘C.) Ω
A turbine of a coal burning installation delivers 1, 500 hp of mechanical energy to a generator. The generator then converts 80.0% of the mechanical energy into electrical energy. If the terminal potential difference of the generator is 1790 V, what current does it deliver (in A)? A
A GPS draws a current of 23 mA at 120 V. How much power (in W) does the device require? W
An aluminum wire having a cross-sectional area equal to 2.70×10−6 m2 carries a current of 7.00 A. The density of aluminum is 2.70 g/cm3. Assume each aluminum atom supplies one conduction electron per atom. Find the drift speed of the electrons in the wire. mm/s
A teapot with a surface area of 715 cm2 is to be plated with silver. It is attached to the negative electrode of an electrolytic cell containing silver nitrate (Ag+NO3−). The cell is powered by a 12.0−V battery and has a resistance of 1.30 Ω. If the density of silver is 1.05×104 kg/m3, over what time interval does a 0.133−mm layer of silver build up on the teapot? h
A 270-km-long high-voltage transmission line 2.00 cm in diameter carries a steady current of 1,060 A. If the conductor is copper with a free charge density of 8.50×1028 electrons per cubic meter, how many years does it take one electron to travel the full length of the cable? (Use 3.156×107 for the number of seconds in a year.) yr
(a) A lightbulb has a resistance of 225 Ω when operating with a potential difference of 160 V across it. What is the current in the lightbulb (in mA)? mA (b) What If? What would be the current in the lightbulb (in mA ) if it were used in Barbados, where the potential difference across it would be 115 V? mA
Two wires have the same resistance and radius. If the wires are made of silver and iron with resistivities respectively of 1.59×10−8 Ω⋅m and 10.0×10−8 Ω⋅m, determine the ratio of their lengths. LAg LFe =
A wire 50.0 m long and 2.00 mm in diameter is connected to a source with a potential difference of 9.11 V, and the current is found to be 33.7 A. Assume a temperature of 20.0∘C and, using this table, identify the metal out of which the wire is made. copper gold iron aluminum tungsten platinum lead silver
An electric heater carries a current of 11.5 A when operating at a voltage of 120 V. What is the resistance of the heater? Ω
A current density of 8.00×10−13 A/m2 exists in the atmosphere at a location where the electric field is 116 V/m. Calculate the electrical conductivity of the Earth's atmosphere in this region. (Ω⋅m)−1
You are an expert witness, having been hired by an attorney who is defending a wire manufacturing company in a lawsuit. The company is being sued by a firm that manufactures electronic measurement devices. The wire company provides copper wires with precision lengths and radii to be used in thermal measurement devices manufactured by the device firm. The device firm lost a major contract due to inaccuracy of their thermal measurement device. This firm is claiming that the precision of the wires provided by the wire company was not sufficient. You have inspected the wires in the laboratory and have found the lengths to be precise and the radii to be uniform, well within the specifications provided by the device firm. You report this information during the trial, and the legal team for the device firm looks frustrated. The lawyer confers with his client, jumps up, and says, "The wire company did not allow for thermal expansion of the wire! From 20∘C to 85.0∘C, thermal expansion could make a difference of several percent in the resistance of the wire!" A recess in the trial is called until the next day while you perform some calculations to determine the percentage by which thermal expansion would change the resistance of a wire so that you can report your result. (Assume the coefficient of linear expansion is 17.0×10−6(∘C)−1.) %
As the temperature of a metal rod varies, so does the resistance and the dimensions of the rod. If a copper rod has a resistance of 3.64 Ω at 20.0∘C, determine the resistance of the rod (in Ω ) at 120∘C by accounting for the changes in both the resistivity and the dimensions of the rod. The coefficient of linear expansion for copper is 1.67×10−5 (∘C)−1 and the temperature coefficient of resistivity is 4.04×10−3(∘C)−1. Ω
What is the fractional change in the resistance of an iron filament when its temperature changes from 28.0∘C to 51.0∘C ? R−R0 R0 =
An electric coffee maker has a heating element that operates at 120 V and with a current of 2.00 A. Assuming the water absorbs all the energy delivered to the heating element, calculate the time interval (in s) during which the temperature of 0.419 kg of water rises from room temperature (23.0∘C) to the boiling point. (The specific heat of water is 4, 186 J/(kg⋅∘C).)