Extra Problems Phys 102

Chapter 17 1- The equation for a standing wave is given by: y = 4.00*10**(-3) sin(2.09 x) cos(60.0 t) (SI units). What is the distance between two consecutive antinodes? [1.50 m] 2- A string under a tension of 15 N, is set into vibration to produce a wave of speed 20 m/s, and a maximum transverse speed of 8 m/s. For this wave, the average power is: [24 W] 3- Standing waves are produced in a string at the two consecutive resonant frequencies 155 and 195 Hz. If the mass of the string is 5.00 g and its length is 0.80 m, then the tension applied to the string should be: [25.6 N] 4- A transverse wave in a 3.0 m long string is given by the harmonic wave equation:

y = 0.4*cos[pi*(x/4 + 6t)] (SI units) If the string is kept under a constant tension of 70 N, find the power transmitted to the wave. [83 W] 5- A sinusoidal wave traveling in the positive x direction has an amplitude of 10 cm, a wavelength of 20 cm, and a frequency of 5.0 Hz. A particle at x = 0 and t = 0 has a displacement of 10 cm. Write the equation of the displacement of the particles as a function of x and t. [y = (0.1 m)*sin[pi*(10x-10t-3/2)]] 6- A harmonic wave is described by y = 0.2*sin(25x-10t) (SI units). How far does a wave crest move in 20 sec? [8 m] 7- The equation of a wave traveling along a string, under a tension of 10 N, is given by: y = (6.0 cm) sin(0.02*pi*x+40.0*pi*t), where x is in centimeters and t is in seconds. Determine the mass per unit length of the string. [25 g/m] 8- A transverse sinusoidal wave traveling in the negative x direction has an amplitude of 10.0 cm, a wavelength of 20.0 cm, and a frequency of 8.00 Hz. Write the expression for y as a function of x(in meters) and t(in seconds)if y(0,0) = 10.0 cm.[y = (0.1 m) sin[31.4*x+50.3*t+(pi/2)]] 9- A sinusoidal wave is described as: y = (0.1 m) * sin[10*pi*(x/5 + t - 3/2)], where x is in meters and t is in seconds. What are the values of its frequency(f), and its velocity(v)? [f=5 Hz, v = 5 m/s moving in -x-direction.] 10- A 100-Hz oscillator is used to generate a sinusoidal wave, on a string, of wavelength 10 cm. When the tension in the string is doubled, the oscillator produces a wave with a frequency and wavelength of: [100 Hz and 14 cm] 11- The lowest resonant frequency, in a certain string clamped at both ends, is 50 Hz. When the string is clamped at its midpoint, the lowest resonant frequency is:[100 Hz]

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Chapter 18 1- A man strikes a long steel rod at one end. Another man, at the other end with his ear close to the rod, hears the sound of the of the blow twice (one through air and once through the rod), with a 0.1 seconds interval between. How long is the rod?[For the steel, the bulk modulus = 2.1*10**11 Pa, and the density = 7.0*10**3 kg/m**3. Speed of sound in air = 340 m/s.][36 m] 2- If two successive frequencies of a pipe, closed at one end and filled by air, are 500 Hz and 700 Hz, the length of the pipe is: [speed of sound in air = 340 m/s]. [0.85 m] 3- If the distance from a source of sound increases by 1 meter, the sound level is decreased by 2 dB. Assume the loudspeaker that is emitting this sound emits sound in all directions. The original distance from the sound source is:[3.86 m] 4- An ambulance siren emits a sound of frequency 1.60 kHz. A person running with a speed of 2.50 m/s hears a frequency of 1.70 kHz as the ambulance approaches him from the back. How fast is the ambulance moving? (speed of sound is 340 m/s).[22.4 m/s] 5- The maximum pressure amplitude that the human ear can tolerate in loud sounds is 28 Pa. What is the displacement amplitude for such a sound in air of density 1.21 kg/m**3 at a frequency of 5.0*10**3 Hz? [speed of sound in air = 343 m/s]. [2.15*10**(-6) m] 6- Two sound waves, from two different sources with the same frequency, 660 Hz, travel at a speed of 330 m/s. The sources are in phase. What is the phase difference of the waves at a point that is 5.0 m from one source and 4.0 m from the other? (The waves are traveling in the same direction.)[4 Pi radian] 7- A tube 1.5 m long is closed at one end. A stretched wire is placed near the open end. The wire is 0.33 m long and has a mass of 9.8 g. It is fixed at both ends and vibrates in its fundamental mode. By resonance, it sets the air column in the tube into oscillation at that column's fundamental frequency. Find the tension in the wire.[Speed of sound in air = 343 m/s]. [42 N] 8- A 1.5*10**(-6) W point source emits sound waves isotropically. What is the sound level 2.5 m from the source? [43 dB] 9- A police car is approaching a stationary observer at 34.0 m/s with its siren emitting a frequency of 450 Hz. What is the frequency heard by the observer? [Speed of sound in air = 343 m/s]. [500 Hz] 10- Two small identical speakers are connected (in phase) to the same source. The speakers are 3 m apart and at ear level. An observer stands at X, 4 m in front of one speaker as shown. The sound he hears will be least intense if the wavelength is: [2 m ]



P

2 8

2. 00

1. 00

V (m3)

Chapter 19 1- In a constant-volume gas thermometer, the pressure is 0.019 atm at 100 degrees Celsius. Find the temperature when the pressure is 0.027 atm.[257 degrees Celsius] 2- A 100 g of water at 100 degrees Celsius is added to a 20-g aluminum cup containing 50 g of water at 20 degrees Celsius. What is the equilibrium temperature of the system? The specific heat of aluminum is 900 J/(kg*K) and the specific heat of water is 4186 J/(kg*K).[72 degrees Celsius] 3- A solid aluminum rod, of length 1.60 m and cross-sectional area of 3.14*10**(-4) m**2, has one end in boiling water and the other end in ice. How much ice melts in one minute? [The thermal conductivity of aluminum is 205 Watts/(m*K) and the heat of fusion of water is 3.35*10**5 J/kg.](neglect any heat loss, by the system, to the surrounding)[7.2*10**(-4) kg] 4- An iron ball has a diameter of 6.0 cm and is 0.01 mm too large to pass through a hole in a brass ring when both are at a temperature of 30 degrees Celsius. To what temperature should the brass ring be heated so that the ball just passes through the hole? [The coefficient of volume expansion of iron = 3.6*10**(-5) K**-1 and of brass = 5.7*10**(-5) K**-1][39 degrees Celsius] 5- The coefficient of linear expansion of gold is 14.20*10**(-6)/K. If the density of gold is 19.30 g/cm**3 at 20 degrees Celsius, the density of gold at 90 degrees Celsius will be:[19.24 g/cm**3] 6- By what factor does the rate of radiant emission of heat, from a heating element, increases when the temperature of a heating element increases from 27 degrees Celsius to 327 degrees Celsius?[16] 7- A thermometer, of mass 0.06 kg and specific heat 836 J/(kg K), reads 15 degrees Celsius. It is then completely immersed in 0.15 kg of water of specific heat 4180 J/(kg K). The final temperature reading of the thermometer in the water is 45 degrees Celsius. Assuming no heat losses from the system to the surrounding, the initial temperature of the water was:[47.4 degrees Celsius] 8- A closed cubical box (60 cm on edge and 5 cm on thickness) contains ice at zero degrees Celsius. When the outside temperature is 20 degrees Celsius, it is found that 250 grams of ice melt each hour. What is the value of the thermal conductivity of the walls of the box?[0.03 Watts/(m*K)] 9- A certain metal rod has a length of 10.00 m at 100.00 degree-C and a length of 10.04 m at 773 K. Find its length at zero degree-C.[9.99 m] 10- In a P-V diagram, a system of an ideal gas goes through the process shown in figure. How much heat is absorbed after the system goes 100 times through the cycle? [300 J] 11- Consider a copper slab of thickness L and area of 5.0 m**2. If the conduction rate through the copper slab is 1.2*10**6 J/s and the temperature on the left of the slab is 102 degree-C while on the right of the slab it is -12.0 degree-C, what must be the thickness of the slab? [Take the coefficient of thermal conductivity of copper as 400 W/(m K)]. [19 cm]



Chapter 20 1- One mole of an ideal gas is taken through the cyclic process ABCA as shown in Fig. (2). What is the net heat transfer during the cycle? [-1.0*10*3 J] 2- A diatomic ideal gas, at a pressure of 1.0 atm, expands isobarically from a volume of 2.0 Liters to a volume of 5.0 Liters. Calculate the change in internal energy of the gas during the process. [7.6*10**2 J] 3- Two identical containers, one has 2.0 moles of type 1 molecules, of mass m1, at 20 degrees Celsius. The other has 2.0 moles of type 2 molecules, of mass m2 = 2*m1, at 20 degrees Celsius. The ratio between the average translational kinetic energy of type 2 to that of type 1 is: [1] 4- 300 grams of water at 25 degree-C are added to 100 grams of ice 20 at zero degree-C. The final temperature of the mixture is: [zero degree-C] 5- One mole of oxygen molecule (M = 32 g/mol) occupies a cubic vessel of side length 10 cm at a temperature of 27 degree-C. Calculate the pressure of the gas on the walls. [2.49*10**6 Pa] 6- The equation of state of a certain gas is given as P*V**2 = K, where P is the pressure, V is the volume and K is a constant. Find the work done by the gas if its volume increases from Vi = 2.0 m**3 to a final volume Vf = 4.0 m**3. [K/4] 7- A diatomic ideal gas undergoes a constant pressure process in which its internal energy increases by 540 J. Find the heat added to the gas and the work done by the gas.[Q = 756 J, W = 216 J] 8- 5 moles of hydrogen gas occupy a balloon that is inflated to a volume of 0.3 m**3 and at 1.0 atmospheric pressure. What is the root-mean square velocity of the molecules inside the balloon? [The mass of hydrogen atom is 1.66*10**(-27) kg]. [4.3*10**3 m/s] 9- Helium gas is heated at constant pressure from 32 degrees Fahrenheit to 212 degrees Fahrenheit. If the gas does 20.0 Joules of work during the process, what is the number of moles? [0.024 moles] 10- Two moles of helium (monatomic) gas are heated from 100 degrees Celsius to 250 degrees Celsius. How much heat is transferred to the gas if the process is isobaric? [6.23 kJ] 11- An ideal diatomic gas, initially at a pressure Pi = 1.0 atm and volume Vi, is allowed to expand isothermally until its volume doubles. The gas is then compressed adiabatically until it reaches its original volume. The final pressure of the gas will be: [1.3 atm]



Chapter 21 1- An ideal engine, whose low-temperature reservoir is at 27 degrees Celsius, has an efficiency of 20%. By how much should the temperature of the high-temperature reservoir be increased to increase the efficiency to 50%? [225 K.] 2- An ideal monatomic gas is confined to a cylinder by a piston. The piston is slowly pushed in so that the gas temperature remains at 27 degree C. During the compression, 750 J of work is done on the gas. The change in the entropy of the gas is:[- 2.5 J/K.] 3- Five moles of an ideal monatomic gas are taken though the cycle shown in the Figure. Calculate the efficiency of the cycle. [0.17] 4- Five moles of an ideal gas undergo a reversible isothermal compression from volume V to volume V/2 at temperature 30 degrees C. What is the change in the entropy of the gas? [-29 J/K.] 5- An automobile engine operates with an overall efficiency of 20%. How many gallons of gasoline is wasted for each 10 gallons burned? [8] 6- One mole of a monatomic ideal gas is taken from an initial state (i) to a final state (f) as shown in figure. The curved line is an isotherm. Calculate the increase in entropy of the gas for this process. [36.5 J/K.] 7- One mole of a diatomic ideal gas is taken through the cycle shown in Figure. Process b-c is adiabatic, Pa = 0.3 atm, Pb = 3.0 atm, Vb = 1.0*10**(-3) m**3, and Vc = 4.0*Vb. What is the efficiency of the cycle? [53%.] 8- You mix two samples of water, A and B. Sample A is 100 g at 20 degree-C and sample B is also 100 g but at 80 degree-C. Calculate the change in the entropy of sample B.[- 8.9 cal/K] 9- What mass of water at 0 degrees-C can a freezer make into ice cubes in one hour, if the coefficient of performance of the refrigerator is 3.0 and the power input is 0.2 Kilowatt? [6.5 kg] 10- An ideal heat engine has a power output of 200 W. The engine operates between two reservoirs at 300 K and 600 K. How much energy is absorbed per hour? [1.44*10**6 J]

500 K

adiabatic

V(liter)

P(atm)

200 K 350 K

3Vo

V

Isothermal

a

3Po

P

Po i

f

Vo

Pb

P (atm)

V(10-3 m3)

Adiabatic

Pa

Va

a

b

c

Vc



Chapters 22 & 23 1- A charge of + 3.2*10**(-6) C is placed at the origin. A second charge (q2) is placed at x = 3.0 m. If a charge of 1.0*10**(-6) C experiences no force if placed at x = 4.0 m, then q2 is: [- 0.2*10**(-6) C.] 2- A proton is shot out along the +x-axis from the origin with a speed of 1.0*10**6 m/s. In this region a uniform electric field of 2500 N/C exits in the negative x-direction. Find the distance traveled by the proton before it momentarily comes to rest. [2.1 m.] 3- An electric dipole consists of charges +2e and -2e separated by 0.78*10**(-9) m. It is in an electric field of strength 3.0*10**6 N/C. Calculate the magnitude of the torque on the dipole when the dipole is perpendicular to the field. [e is the magnitude of the charge on the electron.] [ 7.5*10**(-22) N.m.] 4- Two fixed particles, of charges q1 = + 1.0*10**(-6) C and q2 = - 9.0 x 10-6 C, are 10 cm apart. How far from each should a third charge be located so that no net electrostatic force acts on it? [5 cm from q1 and 15 cm from q2.] 5- An electric dipole consists of two opposite charges, each of magnitude 5.0*10**(-19) C, separated by a distance of 1.00*10**(-9) m. The dipole is placed in an electric field of strength 2.45*10**5 N/C. Calculate the magnitude of the torque exerted on the dipole when the dipole moment is perpendicular to the electric field. [1.2*10**(-22) N*m .] 6- Consider two identical conductor spheres, A and B. Initially, sphere A has a charge of -80 Q and Sphere B has a charge of +20 Q. If the spheres touched and then are separated by a distance of 0.3 m, what is the resultant force between them? [Take Q = 5.7*10-8 C] [0.3 N.] 7- For the arrangement of charges shown in figure, the electric field at the point P is: [1.3*k*q/(d**2) in the negative y-direction.] 8- In figure, a 0.3 g metallic ball hangs from an insulating string in a vertical electric field of 4000 N/C directed upward as shown. If the tension in the string is 0.005 N, then the charge on the ball is: [-0.52 micro-C] 9- A particle of mass 5.0 g and charge 40 mC moves in a region of space where the electric field is uniform and given by E = -5.5 i (N/C). If the velocity of the particle at t = 0 is given by v = 50 j (m/s), find the speed of the particle at t = 2 s. [i, and j are the unit vectors in the directions of x, and y respectively]. [101 m/s.]

(m,q)

E

+q -2q +q

(-d,0) (d,0)

(0,d) x p

y

X



Chapter 24 1- Calculate the electric flux (phi) through the curved surface of a cone of base radius R and height h. The electric field E is uniform and perpendicular to the base of the cone, and the field lines enter through the base. The cone has no charge enclosed in it. [π R2 E.] 2- A point charge of -50e lies at the center of a hollow spherical metal shell that has a net charge of -100e. Calculate the charge on the )a) shell's inner surface, and (b) on its outer surface. [e is the magnitude of the charge on the electron.[(a) 50e b) -150e]. 3- A point charge of 2.0 micro-C is placed at the center of a cube 50 cm on edge. What is the flux through the bottom surface? [3.8*10**4 N*m**2/C.] 4- An isolated conductor of arbitrary shape has a net charge of -15*10**(-6) C. Inside the conductor is a cavity within which is a point charge q= -5.0*10**(-6) C. What is the charge on the cavity-wall, q(in), and what is the charge on the outer surface of the conductor, q(out)? [q(in) = 5.0*10**(-6) C; q(out) = -20*10**(-6) C.] 5- For the two infinite dielectric sheets, see figure find the magnitude of the electric field at a point P. Consider that each sheet has a positive surface charge density of 102 C/m2. [ 1.1*10**13 N/C.] 6- A point charge of +4.0 micro-C lies at the center of a hollow spherical conducting shell that has a net charge of -13.0 micro-C. If the inner radius of the shell is 2.0 cm and the outer radius is 3.0 cm, then the ratio between the charge density on the inner surface to the charge density on the outer surface is: [1 : 1.] 7- A cube, as in figure, has an edge length of 3.00 m in a region of a uniform electric field given by the equation: E = (- 5.00 j + 6.00 k) N/C, where i, j, and k are the unit vectors in the directions of x, y, and z respectively. Find the electric flux through the top face (shaded). [- 45 N*m**2/C.] 8- A point charge, q1 = -2.0*10**(-6) C, is placed inside a cube of side 5.0 cm, and another point charge q2 = 3.0*10**(-6) C is placed outside the cube. Find the net electric flux through the surfaces of the cube. [-2.3*10**5 N m**2/C] 9- Figure shows portions of two large, parallel, nonconducting sheets, A and B. The surface charge densities are: sigma1 = -4.5 micro-C/m2 and sigma2 = -6.5 micro-C/m**2. Find the electric field at any point between the two sheets. [1.1*105 N/C towards B. 10- A hollow metallic sphere, of radius 2.0 cm, is filled with a non-conducting material which carries a charge of 5.0 pico-C distributed uniformly throughout its volume. What is the magnitude of the electric field 1.5 cm from the center of the sphere?[84 N/C.]

x

y

z

1.0 m P

+++++++

+++++++

0.5 m

A

σ1

B

σ2



Chapter 25 1- An infinite nonconducting sheet has a surface charge density 0.10*10**(-6) C/m**2 on one side. How far apart are equipotential surfaces whose potentials differ by 90 V? [1.6 cm.] 2- Two equal charges, each of 0.12 C, are separated by a distance of 1.8 m. What is the work done, by an external agent, to bring a charge of 0.15 C from infinity to the midpoint between the two charges? [3.6*10**8 J.] 3- Consider a metallic sphere carrying a charge of 4.0*10**(-8) C and having a potential of 400 V. Find the diameter of the sphere.. [1.8 m.] 4- What is the external work required to bring four 2.0*10**(-9) C point charges from infinity and to place them at the corner of a square of side 0.14 m? [1.4*10**(-6) Joule.] 5- In figure, Q1 = 2.0*10**(-6) C and Q2 = - 2.0*10**(-6) C. What is the external work needed to move a charge Q = - 4.0*10**(-6) C at constant speed from point A at the center of the square to point B at the corner? [Zero.] 6- The electric potential at points in the xy–plane is given by: V = (x**3 - 2*x*y) Volts, where x and y are in meters. The magnitude of the electric field at the point with the coordinates x = 1 m and y = 2 m is: [Sqrt(5) V/m.] 7- In figure, what is the net potential at point P due to the four point charges if V = 0 at infinity ? [take d = 2 cm, q = 1.0 micro-C]. [9.0*10**5 V.] 8- Two balls with charges 5.0 micro-C and 10 micro-C are at a distance of 1.0 m from each other. In order to reduce the distance between them to 0.5 m the amount of work to be performed is: [0.45 J.] 9- Find the electrostatic potential at x = 0 for the following distribution of charges:-2q at x= 10 cm and -2q at x= -10 cm. [Take q = 1.0*10**(-9) C, and the electrostatic potential at infinity = 0 ] [ -360 V.] 10- Three point charges are initially infinitely far apart. Two of the point charges are identical and have charge Q. If zero net work is required to assemble the three charges at the corners of an equilateral triangle of side d, then the value of the third charge is [ - Q/2.] 11- Consider two concentric conducting shells of radii (a) and (b), b > a. The smaller (inner) shell has a positive charge (q) and the larger (outer) shell has a charge (Q). If the potential of the inner shell is zero, what is the value of Q? [ Q = -b*q/a.]

y

x Q2

10 cm

10 cm

A

B Q1

Q

x

3q

3q

-2q

-2q

d

d

d

d

P



Chapter 26 1- Consider the circuit shown in the figure. If C1 = 1 micro F, C2 = 6 micro F and C3 = 3 micro F, what is the charge on C3? [3 micro C] 2- A 2.5 micro F capacitor, C1, is charged to a potential difference V1 = 10 V, using a 10 V battery. The battery is then removed and the capacitor is connected to an uncharged capacitor, C2, with capacitance of 10 micro F. What is the potential difference across C1 and C2, respectively? [2 V, 2 V] 3- A parallel-plate capacitor has a plate area of 0.2 m2 and a plate separation of 0.1 mm. If the charge on each plate has a magnitude of 4.0*10-6 C the electric field between the plates is approximately: [2.3*106 V/m.] 4- A 2 micro-F and a 1 micro-F capacitor are connected in series and a potential difference is applied across the combination. What is the ratio of the potential difference across each of them? [ The 2 micro-F capacitor has half the potential difference of the 1 micro-F capacitor] 5- Capacitors A and B are identical. Capacitor A is charged so it stores 4 J of energy and capacitor B is uncharged. The capacitors are then connected in parallel. The total stored energy in the capacitors is now: [2 Joules]. 6- Find the equivalent capacitance of three capacitors connected in series. Assume the three capacitors are: C1 = 2.00 micro-F, C2 = 4.00 micro-F and C3 = 8.00 micro-F. [1.14 micro-F]. 7- An air filled parallel-plate capacitor has a capacitance of 1.00*10-12 F. The plate separation is then doubled and a wax dielectric is inserted, completely filling the space between the plates. As a result the, capacitance becomes 2.00*10-12 F. The dielectric constant of the wax is: [4.00] 8- In figure (2), find the charge stored by the capacitor C3 if the potential difference across the battery is 10.0 V. Use the values C1 = C2 = 2.0 micro-F and C3 = 4.00 micro-F. [20 micro-C] 9- Two concentric spherical shells of radii 10 cm and 5.0 cm are charged to a potential difference of 20 V. How much energy is stored in this spherical capacitor? [2.2*10-9 J] 10- A parallel-plate air-filled capacitor, of area 25 cm**2 and plate separation of 1.0 mm, is charged to a potential difference of 600 V. Find the energy density between the plates. [1.6 J/m3] 11- A parallel-plate capacitor has an area A and a separation d. Find its capacitance if it is filled with two dielectrics as shown in figure 3. [Co is the capacitance of the air-filled parallel-plate capacitor. K1 = 3 and K2 = 1.5 are the dielectric constants] [2*Co]

C1

C2 C3 10 V

C1

V

C3

C2



Chapter 27 1- At 20 degree C, a 100-W light bulb has a resistance of 12 ohms. To increase the resistance of the light bulb to 48 ohms, the temperature of the filament should be:[Assume the temperature coefficient of resistivity of the filament is constant and = 0.006 (degree C)-

1] [520 degree C] 2- If 4.7*1016 electrons pass a particular point in a wire every minute, what is the current in the wire? [1.3*10-4 A] 3- An electric device, which heats water by immersing a resistance wire in the water, generates 153 J of heat per second when an electric potential difference of 12 V is placed across its ends. What is the resistance of the heater wire? [0.94 Ohms] 4- A 20% increase in the resistance of a copper wire was noticed when its temperature was raised above room temperature. Find the final temperature of the wire if the temperature coefficient of resistivity for copper is 4.0*10** (-3) /K. [Assume the room temperature = 290 K] [340 K] 5- A potential difference of 9.0 V is applied across the length of a cylindrical conductor with radius 2.0 mm. Calculate the current density if the conductor has a resistance of 90 ohms. [8.0*10**3 A/m**2] 6- A current of 5.0 A exists in a 10 ohms resistor for 5.0 min. How many electrons pass through any cross section of the resistor in this time? [9.4*10**21] 7- A nichrome wire is 1 m long and 1 × 10–6 m2 in cross-sectional area. When connected to a potential difference of 2 V, a current of 4 A exists in the wire. The resistivity of this nichrome is: [5 × 10–7 Ω ⋅ m ] 8- An unknown resistor dissipates 0.5 W when connected to a 3 V potential difference. When connected to a 1 V potential difference, this resistor will dissipate: [0.056 W] 9- The mechanical equivalent of heat is 1 cal = 4.18 J. The specific heat of water is 1 cal/g·K. An electric immersion water heater, rated at 400 W, should heat a liter of water from 10°C to 30°C in about: [3.5 min ] 10- An electric device, which heats water by immersing a resistance wire in the water, generates 153 J of heat per second when an electric potential difference of 12 V is placed across its ends. What is the resistance of the heater wire? [0.94 Ohms]

11- A current of 0.3 A is passed through a lamp for 2 minutes using a 6 V power supply. The energy dissipated by this lamp during the 2 minutes is: [216 J ]



Chapter 28 1- In the figure, all the resistors have a value of 2 Ohms. The battery is ideal with an emf = 15 V. What is the potential difference across the resistor R3? [3.0 Volts]

2- The current in the 5.0-ohm resistor in the circuit shown in the figure is: [5.0 A] 3- In the figure, what is the potential difference Va-Vb? [26 V] 4- At t=0, a 2.0*10-6 Farad capacitor is connected in series to a 20-V battery and a 2.0*106 Ohm resistor. How long does it take for the potential difference across the capacitor to be 12 V? [3.7 s] 5- In the figure, a battery of emf of 12-Volt and internal resistance of r = 3.0 Ohm is connected to a bulb of resistance R. If the bulb will light at a steady current of 0.1 A, what should the value of R be? [117 Ohm] 6- In the figure, if R = 10 Ohm find the current in R. [- 0.2 A] 7- What is the power dissipated in the 4.0-Ohm resistor in the figure. [9.0 W] 8- Find the potential difference (VB-VA) between points B and A of the circuit shown in figure. [-10 volts] 9- Find the value of R1 in the circuit of the figure. [6.0 ohms] 10- A 6-V battery supplies a total of 48 W to two identical light bulbs connected in parallel. The resistance (in ohm)of each bulb is: [1.5] 11- A capacitor, initially uncharged in a single-loop RC circuit, is charged to 85% of its final potential difference in 2.4 s. What is its time constant in seconds? [1.3]

R

12 V

r

10 V

R=10 Ω

I2

15 V

b

I1 I3

a

30 Ω

20 Ω

20 V

7 Ώ

12 Ώ 4 Ώ

15 Ω

5 Ω B

15 Ω 20 V

A

1 5 Ω R2

R1 2.0 A

50 V

b

3.0 A

a

R3=10 Ω 20 V

I



Chapter 29 1- A proton that has velocity v = ( 3.0*10**6 i - 2.0*10**6 j ) m/s moves in a magnetic field B = (0.50 i) T. Find the force on the proton. [1.6*10**(-13) k N] 2- An electric field of 1.5*10**3 V/m and a magnetic field of 0.50 T act on a moving electron to produce no net force. Calculate the minimum speed of the moving electron.[3.0*10**3 m/s] 3- What uniform magnetic field, applied perpendicular to a beam of electrons moving at 1.4*10**6 m/s is required to make the electrons travel in a circular orbit of radius 0.40 m ? [2.0*10**(-5) T] 4- The magnitude of the magnetic field at 88.0 cm from the axis of an infinitely long wire is 7.30*10**(-6) T. What is the current in the wire? [32.1 A] 5- In the figure, a loop of wire carrying a current, I, of 3.0 A is in the shape of a right triangle with two equal sides, each 2.0 m long. A 2.0 T uniform magnetic field is in the plane of the triangle and is parallel to the hypotenuse. The resultant torque on the loop is:12 N*m. 6- A straight horizontal length of copper wire is located in a place where the magnetic field of the earth B = 0.5*10**(-4)T (see the figure). What minimum current in the wire is needed to balance the gravitational force on the wire? [The linear density of the wire is 60.0 gram/m] [1.2*10**4 A into the page] 7- At one instant an electron is moving with a velocity: v = (5*10**5 i + 3*10**5 j) m/s in a magnetic field of B = (0.8 i) T. At that instant the magnetic force on the electron is: [3.8*10**(-14) k N] 8- An electron that has velocity v = 3.2*10**7 i m/s traveling parallel to a uniform magnetic field of strength 2.60*10**(-3) Tesla. The force on the electron is: [zero] 9- An electron moving at right angle to a uniform magnetic field completes a circular orbit in 10**(-8) s. What is the magnitude of the magnetic field. [3.6*10**(-3) T] 10- At a point in a uniform magnetic field the acceleration of an electron is 5.0*10**14 m/s**2 and its speed is 7.0*10**6 m/s. If the magnitude of the magnetic field is 1.0 mT, what is the angle between the electron’s velocity and the magnetic field? [24 degrees] 11- A proton moves with constant velocity, v = (8.0*10**5 m/s) i, through crossed electric and magnetic fields. If the magnetic field is B = (2.5 mT) j, what is the electric field? [(-2.0 kV/m) k]

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Chapter 30 1- The Figure shows four long straight wires passing through the plane of the paper. They are fixed at the corners of a square of diagonal 2.0 cm. Each wire carries a current of 2 A. Three of them are out of the paper and one is into the paper. The magnitude of the magnetic field at the center "C" of the square has magnitude: [8.0*10**(-5) T] 2- The segment of wire is formed into the shape as shown in the figure and carries a current I = 6 A. When R = 6.28 cm, what is the magnetic field at the point P? [3.0*10**(-5) T into the page] 3- The figure shows two concentric circular loops of radii a and b and both carry a current I. Find the resultant magnetic field at the center of the two loops if a = 10 cm, b = 20 cm and I = 20 A. [63 micro-T, out of the page] 4- Three parallel wires lie in the xy-plane. The separation between adjacent wires is 0.1 m, and each wire carries a 10-A current in the same direction. Find the magnitude of the net force per unit length on one of the outer wires. [3.0*10**(-4) N] 5- A circular loop of radius 0.1 m has a resistance of 6 Ohms. If it is attached to a 12 V battery, how large a magnetic field is produced at the center of the loop? [1.3*10**(-5) T] 6- Solenoid 2 has twice the radius and six times the number of turns per unit length as solenoid 1. If they have the same current, then the ratio of the magnetic field in the interior of 2 to that in the interior of 1 is: [6] 7- Two parallel wires, carrying equal currents of 10 A, attract each other with a force F. If both currents are doubled, and the distance between them reduced by 50%, the new force will be: [8*F] 8- Two long parallel wires, D and B, are separated by 2.0 cm. The current in D is THREE times the current in B. If the magnitude of the force on 2.0 m length of one of the wires is equal to 60 micro-N, find the current in B. [1.0 A] 9- The radius R of a long current-carrying wire is 2.3 cm. If the magnetic field at r1 = 2.0 cm is equal to THREE times the magnetic field at r2, r2 > R, calculate the distance r2. [7.9 cm] 10- A hollow cylindrical conductor of inner radius 3.0 mm and outer radius 5.0 mm carries a current of 80 A parallel to its axis. The current is uniformly distributed over the cross section of the conductor. Find the magnitude of the magnetic field at a point that is 2.0 mm from the axis of the conductor. [zero]

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Chapter 31 1- A single turn plane loop of wire of cross sectional area 40 cm**2 is perpendicular to a magnetic field that increases uniformly in magnitude from 0.5 T to 5.5 T in 2.0 seconds.What is the resistance of the wire if the induced current has a value of 1.0*10**(-3) A? [10 Ohms] 2- A 2.0 Tesla uniform magnetic field makes an angle of 60 degrees with the xy-plane. The magnetic flux through an area of 3 m**2 portion of the xy-plane is : 5.2 Wb. 3- A rectangular loop of wire is placed midway between two long straight parallel conductors as shown in figure. The conductors carry currents i1 and i2 as indicated. If i1 is increasing and i2 is constant, then the induced current in the loop is [counterclockwise]

4- The square coil shown in the figure is 20 cm on a side and has 15 turns of wire on it. It is moving to the right at 2 m/s. Find the induced emf in it at the instant shown, and the direction of the induced current in the coil. (The magnetic field is 0.2 T and its direction is out of the page). [1.2 V, clockwise] 5- A long straight wire is in the plane of a rectangular conducting loop as shown in the figure. The straight wire carries an increasing current “i” in the direction shown. The current in the rectangular is: [counter clockwise] 6- The circuit shown in figure 9 is in a uniform magnetic field that is into the page and is decreasing in magnitude at a rate of 150 T/s. The current in the circuit is: [0.22 A] 7- The figure shows a bar moving to the right on two conducting rails. To make an induced current in the direction indicated, a constant magnetic field in region “A” should be in what direction? [Into the page] 8- A 400-turn coil of total resistance 6.0 ohm has a cross sectional area of 30 cm**2. How rapidly should a magnetic field parallel to the coil axis change in order to induce a current of 0.3 A in the coil? [1.5 T/s] 9- A circular wire loop of area 0.5 m**2 is perpendicular to a magnetic field of 0.8 T. If the coil is removed completely from the field in 0.1 s, the average emf induced in the loop has a magnitude [4.0 V]

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Extra Problems Phys 102

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Transcript of Extra Problems Phys 102