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physics
electricity and magnetism

Questions and Answers of Electricity and Magnetism

The current in a loop circuit that has a resistance of R1 is 2.00 A. The current is reduced to 1.60 A when an additional resistor R2 = 3.00 Ω is added in series with R1. What is the value of R1?
(a) Find the equivalent resistance between points a and b in Figure P28.6.(b) A potential difference of 34.0 V is applied between points a and b. Calculate the current in each resistor.
A lightbulb marked “75 W [at] 120 V” is screwed into a socket at one end of a long extension cord, in which each of the two conductors has resistance 0.800 '. The other end of the extension cord
Four copper wires of equal length are connected in series. Their cross-sectional areas are 1.00 cm2, 2.00 cm2, 3.00 cm2, and 5.00 cm2. A potential difference of 120 V is applied across the
Consider the circuit shown in Figure P28.9. Find (a) The current in the 20.0-Ω resistor and (b) The potential difference between points a and b.
For the purpose of measuring the electric resistance of shoes through the body of the wearer to a metal ground plate, the American National Standards Institute (ANSI) specifies the circuit shown in
Three 100-Ω resistors are connected as shown in Figure P28.11. The maximum power that can safely be delivered to any one resistor is 25.0 W.(a) What is the maximum voltage that can be applied
Using only three resistors—2.00 Ω, 3.00 Ω, and 4.00 Ω— find 17 resistance values that may be obtained by various combinations of one or more resistors. Tabulate the combinations in
The current in a circuit is tripled by connecting a 500- Ω resistor in parallel with the resistance of the circuit. Determine the resistance of the circuit in the absence of the 500- Ω
A 6.00-V battery supplies current to the circuit shown in Figure P28.14. When the double-throw switch S is open, as shown in the figure, the current in the battery is 1.00 mA. When the switch is
Calculate the power delivered to each resistor in the circuit shown in Figure P28.15.
Two resistors connected in series have an equivalent resistance of 690 Ω. When they are connected in parallel, their equivalent resistance is 150 Ω. Find the resistance of each resistor.
An electric teakettle has a multiposition switch and two heating coils. When only one of the coils is switched on, the well-insulated kettle brings a full pot of water to a boil over the time
In Figures 28.4 and 28.6, let R1 = 11.0 Ω, R2 = 22.0 Ω, and let the battery have a terminal voltage of 33.0 V. (a) In the parallel circuit shown in Figure 28.6, to which resistor is more
Four resistors are connected to a battery as shown in Figure P28.19. The current in the battery is I, the battery emf is , and the resistor values are R1 = R, R2 = 2R, R3 = 4R, R4 = 3R.(a) Rank the
The ammeter shown in Figure P28.20 reads 2.00 A. Find I1, I2, and ∑
Determine the current in each branch of the circuit shown in Figure P28.21.
In Figure P28.21, show how to add just enough ammeters to measure every different current. Show how to add just enough voltmeters to measure the potential difference across each resistor and across
The circuit considered in Problem 21 and shown in Figure P28.21 is connected for 2.00 min.(a) Find the energy delivered by each battery.(b) Find the energy delivered to each resistor.(c) Identify the
Using Kirchhoff’s rules, (a) Find the current in each resistor in Figure P28.24. (b) Find the potential difference between point’s c and f. Which point is at the higher potential?
Taking R = 1.00 k Ω and ∑ 250 V in Figure P28.25, determine the direction and magnitude of the current in the horizontal wire between a and e.
In the circuit of Figure P28.26, determine the current in each resistor and the voltage across the 200-' resistor.
A dead battery is charged by connecting it to the live battery of another car with jumper cables (Fig. P28.27). Determine the current in the starter and in the dead battery.
For the network shown in Figure P28.28, show that the resistance Rab = (27/17) Ω.
For the circuit shown in Figure P28.29, calculate(a) The current in the 2.00-' resistor and(b) The potential difference between points a and b.
Calculate the power delivered to each resistor shown in Figure P28.30.
Consider a series RC circuit (see Fig. 28.19) for which R = 1.00 MΩ, C = 5.00 )F, and Є= 30.0 V. Find (a) The time constant of the circuit and (b) The maximum charge on the capacitor
A 2.00-nF capacitor with an initial charge of 5.10 μC is discharged through a 1.30-kΩ resistor. (a) Calculate the current in the resistor 9.00 μs after the resistor is connected
A fully charged capacitor stores energy U0. How much energy remains when its charge has decreased to half its original value?
A capacitor in an RC circuit is charged to 60.0% of its maximum value in 0.900 s. What is the time constant of the circuit?
Show that the integral in Equation (1) of Example 28.14 has the value RC/2.
In the circuit of Figure P28.36, the switch S has been open for a long time. It is then suddenly closed. Determine the time constant(a) Before the switch is closed and(b) After the switch is
The circuit in Figure P28.37 has been connected for a long time.(a) What is the voltage across the capacitor?(b) If the battery is disconnected, how long does it take the capacitor to discharge to
In places such as a hospital operating room and a factory for electronic circuit boards, electric sparks must be avoided. A person standing on a grounded floor and touching nothing else can typically
A 4.00-M' resistor and a 3.00-)F capacitor are connected in series with a 12.0-V power supply. (a) What is the time constant for the circuit? (b) Express the current in the circuit and the charge
Dielectric materials used in the manufacture of capacitors are characterized by conductivities that are small but not zero. Therefore, a charged capacitor slowly loses its charge by “leaking”
Assume that a galvanometer has an internal resistance of 60.0 Ω and requires a current of 0.500 mA to produce full-scale deflection. What resistance must be connected in parallel with the
A typical galvanometer, which requires a current of 1.50 mA for full-scale deflection and has a resistance of 75.0 Ω, may be used to measure currents of much greater values. To enable an
The same galvanometer described in the previous problem may be used to measure voltages. In this case a large resistor is wired in series with the galvanometer, as suggested in Figure 28.29. The
Meter loading Work this problem to five-digit precision. Refer to Figure P28.44.(a) When a 180.00- Ω resistor is connected across a battery of emf 6.000 0 V and internal resistance 20.000 ',
Design a multirange ammeter capable of full-scale deflection for 25.0 mA, 50.0 mA, and 100 mA. Assume the meter movement is a galvanometer that has a resistance of 25.0 Ω and gives a full-scale
Design a multirange voltmeter capable of full-scale deflection for 20.0 V, 50.0 V, and 100 V. Assume the meter movement is a galvanometer that has a resistance of 60.0 Ω and gives a full-scale
A particular galvanometer serves as a 2.00-V full-scale voltmeter when a 2 500- Ω resistor is connected in series with it. It serves as a 0.500-A full-scale ammeter when a 0.220- Ω resistor
An 8.00-ft extension cord has two 18-gauge copper wires, each having a diameter of 1.024 mm. At what rate is energy delivered to the resistance in the cord when it is carrying a current of (a) 1.00
An electric heater is rated at 1 500 W, a toaster at 750 W, and an electric grill at 1 000 W. The three appliances are connected to a common 120-V household circuit. (a) How much current does each
Aluminum wiring has sometimes been used instead of copper for economy. According to the National Electrical Code, the maximum allowable current for 12-gauge copper wire with rubber insulation is 20
Turn on your desk lamp. Pick up the cord, with your thumb and index finger spanning the width of the cord. (a) Compute an order-of-magnitude estimate for the current in your hand. You may assume
Four 1.50-V AA batteries in series are used to power a transistor radio. If the batteries can move a charge of 240 C, how long will they last if the radio has a resistance of 200 Ω?
A battery has an emf of 9.20 V and an internal resistance of 1.20 Ω. (a) What resistance across the battery will extract from it a power of 12.8 W? (b) A power of 21.2 W?
Calculate the potential difference between points a and b in Figure P28.54 and identify which point is at the higher potential.
Assume you have a battery of emf and three identical lightbulbs, each having constant resistance R. What is the total power delivered by the battery if the bulbs are connected? (a) In series? (b)
A group of students on spring break manages to reach a deserted island in their wrecked sailboat. They splash ashore with fuel, a European gasoline-powered 240-V generator, a box of North American
A battery has an emf Є and internal resistance r. A variable load resistor R is connected across the terminals of the battery. (a) Determine the value of R such that the potential difference
A 10.0-μF capacitor is charged by a 10.0-V battery through a resistance R. The capacitor reaches a potential difference of 4.00 V in a time 3.00 s after charging begins. Calculate R.
A 10.0-μF capacitor is charged by a 10.0-V battery through a resistance R. The capacitor reaches a potential difference of 4.00 V in a time 3.00 s after charging begins. Find R.
When two unknown resistors are connected in series with a battery, the battery delivers 225 W and carries a total current of 5.00 A. For the same total current, 50.0 W is delivered when the resistors
When two unknown resistors are connected in series with a battery, the battery delivers total power P s and carries a total current of I. For the same total current, a total power Pp is delivered
A power supply has an open-circuit voltage of 40.0 V and an internal resistance of 2.00 Ω. It is used to charge two storage batteries connected in series, each having an emf of 6.00 V and
Two resistors R1 and R2 are in parallel with each other. Together they carry total current I. (a) Determine the current in each resistor. (b) Prove that this division of the total current I
The value of a resistor R is to be determined using the ammeter€“voltmeter setup shown in Figure P28.63. The ammeter has a resistance of 0.500 Ω, and the voltmeter has a resistance of
The values of the components in a simple series RC circuit containing a switch (Fig. 28.19) are C = 1.00 μF, R = 2.00 x 106 Ω, and Є= 10.0 V. At the instant 10.0 s after the switch is
The switch in Figure P28.66a closes when ∆Vc > 2∆V/3 and opens when ∆Vc
Three 60.0-W, 120-V lightbulbs are connected across a 120-V power source, as shown in Figure P28.67. Find(a) The total power delivered to the three bulbs and(b) The voltage across each. Assume that
A battery is used to charge a capacitor through a resistor, as shown in Figure 28.19. Show that half the energy supplied by the battery appears as internal energy in the resistor and that half is
Switch S has been closed for a long time, and the electric circuit shown in Figure P28.68 carries a constant current. Take C1 = 3.00 μF, C2 = 6.00 μF, R1 = 4.00 kΩ, and R2 = 7.00
Four resistors are connected in parallel across a 9.20-V battery. They carry currents of 150 mA, 45.0 mA, 14.00 mA, and 4.00 mA. (a) If the resistor with the largest resistance is replaced with one
Figure P28.70 shows a circuit model for the transmission of an electrical signal, such as cable TV, to a large number of subscribers. Each subscriber connects a load resistance RL between the
In Figure P28.71, suppose the switch has been closed for a time sufficiently long for the capacitor to become fully charged. Find(a) The steady-state current in each resistor and(b) The charge Q on
A regular tetrahedron is a pyramid with a triangular base. Six 10.0-Ω resistors are placed along its six edges, with junctions at its four vertices. A 12.0-V battery is connected to any two of
The circuit shown in Figure P28.73 is set up in the laboratory to measure an unknown capacitance C with the use of a voltmeter of resistance R = 10.0 MΩ and a battery whose emf is 6.19 V. The
The student engineer of a campus radio station wishes to verify the effectiveness of the lightning rod on the antenna mast (Fig. P28.74). The unknown resistance Rx is between points C and E. Point E
This problem6 illustrates how a digital voltmeter affects the voltage across a capacitor in an RC circuit. A digital voltmeter of internal resistance r is used to measure the voltage across a
The circuit in Figure P28.75 contains two resistors, R1 = 2.00 k' and R2 = 3.00 k Ω, and two capacitors, C1 = 2.00 μF and C2 = 3.00 μF, connected to a battery with emf Є = 120 V. No
How much work is done (by a battery, generator, or some other source of potential difference) in moving Avogadro’s number of electrons from an initial point where the electric potential is 9.00 V
An ion accelerated through a potential difference of 115 V experiences an increase in kinetic energy of 7.37 x 10-17 J. Calculate the charge on the ion.
(a) Calculate the speed of a proton that is accelerated from rest through a potential difference of 120 V. (b) Calculate the speed of an electron that is accelerated through the same potential
What potential difference is needed to stop an electron having an initial speed of 4.20 x 105 m/s?
A uniform electric field of magnitude 250 V/m is directed in the positive x direction. A) 12.0-+C charge moves from the origin to the point (x, y) = (20.0 cm, 50.0 cm). (a) What is the change in
The difference in potential between the accelerating plates in the electron gun of a TV picture tube is about 25 000 V. If the distance between these plates is 1.50 cm, what is the magnitude of the
An electron moving parallel to the x axis has an initial speed of 3.70 % 106 m/s at the origin. Its speed is reduced to 1.40 x 105 m/s at the point x = 2.00 cm. Calculate the potential difference
Suppose an electron is released from rest in a uniform electric field whose magnitude is 5.90 x 103 V/m. (a) Through what potential difference will it have passed after moving 1.00 cm? (b) How
A uniform electric field of magnitude 325 V/m is directed in the negative y direction in Figure P25.9. The coordinates of point A are (-0.200, -0.300) m, and those of point B are (0.400, 0.500) m.
Starting with the definition of work, prove that at every point on an equipotential surface the surface must be perpendicular to the electric field there.
A block having mass m and charge + Q is connected to a spring having constant k. The block lies on a frictionless horizontal track, and the system is immersed in a uniform electric field of magnitude
On planet Tehar, the free-fall acceleration is the same as that on Earth but there is also a strong downward electric field that is uniform close to the planet’s surface. A 2.00-kg ball having a
An insulating rod having linear charge density 1 = 40.0 μC/m and linear mass density μ = 0.100 kg/m is released from rest in a uniform electric field E = 100 V/m directed perpendicular to the
A particle having charge q = +2.00 μC and mass m = 0.010 0 kg is connected to a string that is L = 1.50 m long and is tied to the pivot point P in Figure P25.14. The particle, string and pivot
(a) Find the potential at a distance of 1.00 cm from a proton. (b) What is the potential difference between two points that are 1.00 cm and 2.00 cm from a proton? (c) What If? Repeat parts (a) and
Given two 2.00-+C charges, as shown in Figure P25.16, and a positive test charge q = 1.28 x 10-18 C at the origin,(a) What is the net force exerted by the two 2.00-+C charges on the test charge q?(b)
At a certain distance from a point charge, the magnitude of the electric field is 500 V/m and the electric potential is -3.00 kV. (a) What is the distance to the charge? (b) What is the magnitude
A charge + q is at the origin. A charge -2q is at x = 2.00 m on the x axis. For what finite value(s) of x is (a) The electric field zero? (b) The electric potential zero?
The three charges in Figure P25.19 are at the vertices of an isosceles triangle. Calculate the electric potential at the midpoint of the base, taking q = 7.00 μC.
Two point charges, Q1 = + 5.00 nC and Q2 = -3.00 nC, are separated by 35.0 cm. (a) What is the potential energy of the pair? What is the significance of the algebraic sign of your answer? (b)
Compare this problem with Problem 57 in Chapter 23. Four identical point charges (q = + 10.0 +C) are located on the corners of a rectangle as shown in Figure P23.57. The dimensions of the rectangle
Compare this problem with Problem 20 in Chapter 23. Two point charges each of magnitude 2.00 +C are located on the x axis. One is at x = 1.00 m, and the other is at x = -1.00 m. (a) Determine the
Show that the amount of work required to assemble four identical point charges of magnitude Q at the corners of a square of side s is 5.41keQ2/s.
Compare this problem with Problem 23 in Chapter 23. Five equal negative point charges -q are placed symmetrically around a circle of radius R. Calculate the electric potential at the center of the
Compare this problem with Problem 41 in Chapter 23. Three equal positive charges q are at the corners of an equilateral triangle of side a as shown in Figure P23.41. (a) At what point, if any, in
Two insulating spheres have radii 0.300 cm and 0.500 cm, masses 0.100 kg and 0.700 kg, and uniformly distributed charges of !2.00 +C and 3.00 +C. They are released from rest when their centers are
Two insulating spheres have radii r1 and r2, masses m1 and m2, and uniformly distributed charges -q1 and q2. They are released from rest when their centers are separated by a distance d. (a) How

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