Two capacitors, C1 = 18.0 μF and C2 = 36.0 μF, are connected in series, and a 12.0-V battery is connected across them. (a) Find the equivalent capacitance, and the energy contained in this equivalent capacitor. (b) Find the energy stored in each individual capacitor. Show that the sum of these two energies is the same as the energy found in part (a). Will this equality always be true, or does it depend on the number of capacitors and their capacitances? (c) If the same capacitors were connected in parallel, what potential difference would be required across them so that the combination stores the same energy as in part (a)? Which capacitor stores more energy in this situation, C1 or C2?
> Gold is the most ductile of all metals. For example, one gram of gold can be drawn into a wire 2.40 km long. The density of gold is 19.3 x 103 kg/m3, and its resistivity is 2.44 x 10-8 Ω · m. What is the resistance of such a wire at 20.0°C?
> A length of aluminum wire has a resistance of 30.0 Ω at 20.0°C. When the wire is warmed in an oven and reaches thermal equilibrium, the resistance of the wire increases to 46.2 Ω. (a) Neglecting thermal expansion, find the temperature of the oven. (b) Qu
> Digital thermometers often make use of thermistors, a type of resistor with resistance that varies with temperature more than standard resistors. Find the temperature coefficient of resistivity for a linear thermistor with resistances of 75.0 Ω at 0.00°C
> If a certain silver wire has a resistance of 6.00 Ω at 20.0°C, what resistance will it have at 34.0°C?
> Starting from Ohm’s law, show that E = Jρ, where E is the magnitude of the electric field (assumed constant) and J = I/A is called the current density. The result is in fact true in general.
> The human body can exhibit a wide range of resistances to current depending on the path of the current, contact area, and sweatiness of the skin. Suppose the resistance across the chest from the left hand to the right hand is 1.0 x 106 Ω. (a) How much vo
> The resistivity of copper is 1.70 x 10-8 Ω · m. (a) Find the resistance of a copper wire with a radius of 1.29 mm and a length of 1.00 m. (b) Calculate the volume of copper in the wire. (c) Suppose that volume of copper is formed into a new wire with a l
> A rectangular block of copper has sides of length 10. cm, 20. cm, and 40. cm. If the block is connected to a 6.0 - V source across two of its opposite faces, what are (a) The maximum current and (b) The minimum current the block can carry?
> A copper wire has a circular cross section with a radius of 1.25 mm. (a) If the wire carries a current of 3.70 A, find the drift speed of electrons in the wire. (Take the density of mobile charge carriers in copper to be n = 1.10 x 1029 electrons/m3.) (b
> 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 36.0 A. Assume a temperature of 20°C and, using Table 17.1, identify the metal out of which the wire is m
> A large room in a house holds 975 kg of dry air at 30.0°C. A woman opens a window briefly and a cool breeze brings in an additional 50.0 kg of dry air at 18.0°C. At what temperature will the two air masses come into thermal equilibrium, assuming they for
> The current supplied by a battery in a portable device is typically 0.15 A. Find the number of electrons passing through the device in one hour.
> A potential difference of 12 V is found to produce a current of 0.40 A in a 3.2 - m length of wire with a uniform radius of 0.40 cm. What is (a) The resistance of the wire? (b) The resistivity of the wire?
> A wire of diameter 0.800 mm and length 25.0 m has a measured resistance of 1.60 Ω. What is the resistivity of the wire?
> Nichrome wire of cross - sectional radius 0.791 mm is to be used in winding a heating coil. If the coil must carry a current of 9.25 A when a voltage of 1.20 x 102 V is applied across its ends, find (a) The required resistance of the coil and (b) The len
> Suppose you wish to fabricate a uniform wire out of 1.00 g of copper. If the wire is to have a resistance R = 0.500 Ω, and if all the copper is to be used, what will be (a) The length and (b) The diameter of the wire?
> A person notices a mild shock if the current along a path through the thumb and index finger exceeds 80. μA. Compare the maximum possible voltage without shock across the thumb and index finger with a dry - skin resistance of 4.0 x 105 Ω and a wet - skin
> Germanium is a semiconducting metal with a resistivity of 0.460 Ω · m. (a) Determine the current per unit area through a 5.00 - V germanium junction with a length of 2.00 mm. (b) Find the current through the junction if its cross - sectional area is 2.00
> A voltmeter connected across the terminals of a tungsten - filament light bulb measures 115 V when an ammeter in line with the bulb registers a current of 0.522 A. (a) Find the resistance of the light bulb. (b) Find the resistivity of tungsten at the bul
> An electric heater carries a current of 13.5 A when operating at a voltage of 1.20 x 102 V. What is the resistance of the heater?
> If a current of 80.0 mA exists in a metal wire, (a) How many electrons flow past a given cross section of the wire in 10.0 min? (b) In what direction do the electrons travel with respect to the current?
> A medium-sized banana provides about 105 Calories of energy. (a) Convert 105 Cal to joules. (b) Suppose that amount of energy is transformed into kinetic energy of a 1.00-kg object initially at rest. Calculate the final speed of the object. (c) If that s
> An ionized oxygen molecule (O2+) at point A has charge +e and moves at 2.00 x 103 m/s in the positive x - direction. A constant electric force in the negative x - direction slows the molecule to a stop at point B, a distance of 0.750 mm past A on the x -
> (a) Find the potential difference ΔVe required to stop an electron (called a “stopping potential”) moving with an initial speed of 2.85 x 107 m/s. (b) Would a proton traveling at the same speed require a greater or lesser magnitude potential difference?
> An electron is fired at a speed v0 = 5.6 x 106 m/s and at an angle θ0 = -45° between two parallel conducting plates that are D = 2.0 mm apart, as in Figure P16.72. If the voltage difference between the plates is ΔV = 1
> Metal sphere A of radius 12.0 cm carries 6.00 μC of charge, and metal sphere B of radius 18.0 cm carries -4.00 μC of charge. If the two spheres are attached by a very long conducting thread, what is the final distribution of charge on the two spheres?
> Two positive charges each of charge q are fixed on the y - axis, one at y = d and the other at y = -d as in Figure P16.70. A third positive charge 2q located on the x - axis at x = 2d is released from rest. Find symbolic expressions for (a) The total ele
> Oppositely charged parallel plates are separated by 5.33 mm. A potential difference of 600. V exists between the plates. (a) What is the magnitude of the electric field between the plates? (b) What is the magnitude of the force on an electron between the
> Capacitors C1 = 6.0 μF and C2 = 2.0 μF are charged as a parallel combination across a 250 - V battery. The capacitors are disconnected from the battery and from each other. They are then connected positive plate to negative plate and negative plate to po
> When a certain air - filled parallel - plate capacitor is connected across a battery, it acquires a charge of 150. μC on each plate. While the battery connection is maintained, a dielectric slab is inserted into, and fills, the region between the plates.
> The immediate cause of many deaths is ventricular fibrillation, an uncoordinated quivering of the heart, as opposed to proper beating. An electric shock to the chest can cause momentary paralysis of the heart muscle, after which the heart will sometimes
> A spherical capacitor consists of a spherical conducting shell of radius b and charge -Q concentric with a smaller conducting sphere of radius a and charge Q. (a) Find the capacitance of this device. (b) Show that as the radius b of the outer sphere appr
> An aluminum cup contains 225 g of water and a 40-g copper stirrer, all at 27°C. A 400-g sample of silver at an initial temperature of 87°C is placed in the water. The stirrer is used to stir the mixture until it reaches its final equilibrium temperature
> Find the equivalent capacitance of the group of capacitors shown in Figure P16.65. Figure P16.65:
> Two charges of 1.0 μC and -2.0 μC are 0.50 m apart at two vertices of an equilateral triangle as in Figure P16.64. (a) What is the electric potential due to the 1.0-μC charge at the third vertex, point P? (b) Wha
> A parallel-plate capacitor is constructed using a dielectric material whose dielectric constant is 3.00 and whose dielectric strength is 2.00 x 108 V/m. The desired capacitance is 0.250 μF, and the capacitor must withstand a maximum potential difference
> Two capacitors give an equivalent capacitance of Cp when connected in parallel and an equivalent capacitance of Cs when connected in series. What is the capacitance of each capacitor?
> A parallel-plate capacitor with a plate separation d has a capacitance C0 in the absence of a dielectric. A slab of dielectric material of dielectric constant k and thickness d/3 is then inserted between the plates as in Figure P16.61a. Show that the cap
> For the system of four capacitors shown in Figure P16.41, find (a) The total energy stored in the system and (b) The energy stored by each capacitor. (c) Compare the sum of the answers in part (b) with your result to part (a) and explain your observation
> Three parallel-plate capacitors are constructed, each having the same plate area A and with C1 having plate spacing d1, C2 having plate spacing d2, and C3 having plate spacing d3. Show that the total capacitance C of the three capacitors connected in ser
> When a potential difference of 150. V is applied to the plates of an air-filled parallel-plate capacitor, the plates carry a surface charge density of 3.00 x 10-10 C/cm2. What is the spacing between the plates?
> A model of a red blood cell portrays the cell as a spherical capacitor, a positively charged liquid sphere of surface area A separated from the surrounding negatively charged fluid by a membrane of thickness t. Tiny electrodes introduced into the interio
> Lead pellets, each of mass 1.00 g, are heated to 200.°C. How many pellets must be added to 0.500 kg of water that is initially at 20.0°C to make the equilibrium temperature 25.0°C? Neglect any energy transfer to or from the container.
> A parallel-plate capacitor has plates of area A = 7.00 x 10-2 m2 separated by distance d = 2.00 x 10-4 m. (a) Calculate the capacitance if the space between the plates is filled with air. What is the capacitance if the space is filled half with air and h
> Determine (a) The capacitance and (b) The maximum voltage that can be applied to a Teflon-filled parallel-plate capacitor having a plate area of 175 cm2 and an insulation thickness of 0.0400 mm.
> (a) How much charge can be placed on a capacitor with air between the plates before it breaks down if the area of each plate is 5.00 cm2? (b) Find the maximum charge if polystyrene is used between the plates instead of air. Assume the dielectric strength
> The voltage across an air-filled parallel-plate capacitor is measured to be 85.0 V. When a dielectric is inserted and completely fills the space between the plates as in Figure P16.53, the voltage drops to 25.0 V. (a) What is the dielectric constant of t
> Each plate of a 5.00 μF capacitor stores 60.0 μC of charge. (a) Find the potential difference across the plates. (b) How much energy is stored in the capacitor?
> A parallel-plate capacitor has capacitance 3.00 μF. (a) How much energy is stored in the capacitor if it is connected to a 6.00-V battery? (b) If the battery is disconnected and the distance between the charged plates doubled, what is the energy stored?
> A constant electric field accelerates a proton from rest through a distance of 2.00 m to a speed of 1.50 x 105 m/s. (a) Find the change in the proton’s kinetic energy. (b) Find the change in the system’s electric potential energy. (c) Calculate the magni
> A 12.0-V battery is connected to a 4.50-μF capacitor. How much energy is stored in the capacitor?
> Four capacitors are connected as shown in Figure P16.48. (a) Find the equivalent capacitance between points a and b. (b) Calculate the charge on each capacitor, taking ΔVab = 15.0 V. Figure P16.48:
> What mass of water at 25.0°C must be allowed to come to thermal equilibrium with a 1.85-kg cube of aluminum initially at 1.50 x 102°C to lower the temperature of the aluminum to 65.0°C? Assume any water turned to steam subsequently recondenses.
> A 1.00-μF capacitor is charged by being connected across a 10.0-V battery. It is then disconnected from the battery and connected across an un-charged 2.00-μF capacitor. Determine the resulting charge on each capacitor.
> (a) Find the equivalent capacitance between points a and b for the group of capacitors connected as shown in Figure P16.46 if C1 = 5.00 μF, C2 = 10.00 μF, and C3 = 2.00 μF. (b) If the potential between points a a
> A 25.0-μF capacitor and a 40.0-μF capacitor are charged by being connected across separate 50.0-V batteries. (a) Determine the resulting charge on each capacitor. (b) The capacitors are then disconnected from their batteries and connected to each other,
> Three capacitors are connected to a battery as shown in Figure P16.44. Their capacitances are C1 = 3C, C2 = C, and C3 = 5C. (a) What is the equivalent capacitance of this set of capacitors? (b) State the ranking of the capacitors according to the charge
> Find the charge on each of the capacitors in Figure P16.43. Figure P16.43:
> Consider the combination of capacitors in Figure P16.42. (a) Find the equivalent single capacitance of the two capacitors in series and redraw the diagram (called diagram 1) with this equivalent capacitance. (b) In diagram 1, find the equivalent capacita
> For the system of capacitors shown in Figure P16.41, find (a) The equivalent capacitance of the system, (b) The charge on each capacitor, and (c) The potential difference across each capacitor. Figure P16.41:
> Two capacitors give an equivalent capacitance of 9.00 pF when connected in parallel and an equivalent capacitance of 2.00 pF when connected in series. What is the capacitance of each capacitor?
> Cathode ray tubes (CRTs) used in old-style televisions have been replaced by modern LCD and LED screens. Part of the CRT included a set of accelerating plates separated by a distance of about 1.50 cm. If the potential difference across the plates was 25.
> Find (a) The equivalent capacitance of the capacitors in Figure P16.39, (b) The charge on each capacitor, and (c) The potential difference across each capacitor. Figure P16.39:
> In the summer of 1958 in St. Petersburg, Florida, a new sidewalk was poured near the childhood home of one of the authors. No expansion joints were supplied, and by mid- July, the sidewalk had been completely destroyed by thermal expansion and had to be
> Two capacitors, C1 = 5.00 μF and C2 = 12.0 μF, are connected in parallel, and the resulting combination is connected to a 9.00-V battery. Find (a) The equivalent capacitance of the combination, (b) The potential difference across each capacitor, and (c)
> Given a 2.50-μF capacitor, a 6.25-μF capacitor, and a 6.00-V battery, find the charge on each capacitor if you connect them (a) In series across the battery and (b) In parallel across the battery.
> A small object with a mass of 350. μg carries a charge of 30.0 nC and is suspended by a thread between the vertical plates of a parallel-plate capacitor. The plates are separated by 4.00 cm. If the thread makes an angle of 15.08 with the vertical, what i
> A parallel-plate capacitor with area 0.200 m2 and plate separation of 3.00 mm is connected to a 6.00-V battery. (a) What is the capacitance? (b) How much charge is stored on the plates? (c) What is the electric field between the plates? (d) Find the magn
> A 1-megabit computer memory chip contains many 60.0 x 10-15-F capacitors. Each capacitor has a plate area of 21.0 x 10-12 m2. Determine the plate separation of such a capacitor. (Assume a parallel-plate configuration.) The diameter of an atom is on the o
> An air-filled capacitor consists of two parallel plates, each with an area of 7.60 cm2 and separated by a distance of 1.80 mm. If a 20.0-V potential difference is applied to these plates, calculate (a) The electric field between the plates, (b) The capac
> Air breaks down and conducts charge as a spark if the electric field magnitude exceeds 3.00 x 106 V/m. (a) Determine the maximum charge Qmax that can be stored on an air-filled parallel-plate capacitor with a plate area of 2.00 x 10-4 m2. (b) A 75.0 μF a
> An air-filled parallel-plate capacitor has plates of area 2.30 cm2 separated by 1.50 mm. The capacitor is connected to a 12.0-V battery. (a) Find the value of its capacitance. (b) What is the charge on the capacitor? (c) What is the magnitude of the unif
> (a) When a 9.00-V battery is connected to the plates of a capacitor, it stores a charge of 27.0 μC. What is the value of the capacitance? (b) If the same capacitor is connected to a 12.0-V battery, what charge is stored?
> A potential difference of 90.0 mV exists between the inner and outer surfaces of a cell membrane. The inner surface is negative relative to the outer surface. How much work is required to eject a positive sodium ion (Na+) from the interior of the cell?
> A swimming pool filled with water has dimensions of 5.00 m x 10.0 m x 1.78 m. (a) Find the mass of water in the pool. (b) Find the thermal energy required to heat the pool water from 15.5°C to 26.5°C. (c) Calculate the cost of heating the pool from 15.5°
> Consider the Earth and a cloud layer 8.0 x 102 m above the planet to be the plates of a parallel-plate capacitor. (a) If the cloud layer has an area of 1.0 km2 = 1.0 x 106 m2, what is the capacitance? (b) If an electric field strength greater than 3.0 x
> In the classical model of a hydrogen atom, an electron orbits a proton with a kinetic energy of +13.6 eV and an electric potential energy of -27.2 eV. (a) Use the kinetic energy to calculate the classical orbital speed. (b) Use the electric potential ene
> An alpha particle, which has charge 3.20 x 10-19 C, is moved from point A, where the electric potential is 3.60 x 103 J/C, to point B, where the electric potential is 5.80 x 103 J/C. Calculate the work done by the electric field on the alpha particle in
> An electric field does 1.50 x 103 eV of work on a carbon nucleus of charge 9.61 x 10-19 C. Find the change in the nucleus’ (a) Electric potential and (b) Electric potential energy in joules.
> Calculate the speed of (a) An electron and (b) A proton with a kinetic energy of 1.00 electron volt (eV). (c) Calculate the average translational kinetic energy in eV of a 3.00 x 102-K ideal gas particle.
> Four point charges each having charge Q are located at the corners of a square having sides of length a. Find symbolic expressions for (a) The total electric potential at the center of the square due to the four charges and (b) The work required to bring
> In Rutherford’s famous scattering experiments that led to the planetary model of the atom, alpha particles (having charges of +2e and masses of 6.64 x 10-27 kg) were fired toward a gold nucleus with charge +79e. An alpha particle, initi
> The metal sphere of a small Van de Graaff generator illustrated in Figure 15.23 has a radius of 18 cm. When the electric field at the surface of the sphere reaches 3.0 x 106 V/m, the air breaks down, and the generator discharges. What is the maximum pote
> A tiny sphere of mass 8.00 μg and charge -2.80 nC is initially at a distance of 1.60 μm from a fixed charge of +8.50 nC. If the 8.00 - mg sphere is released from rest, find (a) Its kinetic energy when it is 0.500 μm from the fixed charge and (b) Its spee
> A proton and an alpha particle (charge = 2e, mass = 6.64 x 10-27 kg) are initially at rest, separated by 4.00 x 10-15 m. (a) If they are both released simultaneously, explain why you can’t find their velocities at infinity using only conservation of ener
> A 1.5-kg copper block is given an initial speed of 3.0 m/s on a rough horizontal surface. Because of friction, the block finally comes to rest. (a) If the block absorbs 85% of its initial kinetic energy as internal energy, calculate its increase in tempe
> A proton is released from rest in a uniform electric field of magnitude 385 N/C. Find (a) The electric force on the proton, (b) The acceleration of the proton, and (c) The distance it travels in 2.00 μs.
> A proton is located at the origin, and a second proton is located on the x - axis at x = 6.00 fm (1 fm = 10-15 m). (a) Calculate the electric potential energy associated with this configuration. (b) An alpha particle (charge = 2e, mass = 6.64 x 10-27 kg)
> A positive point charge q = +2.50 nC is located at x = 1.20 m and a negative charge of -2q = -5.00 nC is located at the origin as in Figure P16.18. (a) Sketch the electric potential versus x for points along the x - axis in the range -1.50 m (b) Find a s
> The three charges in Figure P16.17 are at the vertices of an isosceles triangle. Let q = 7.00 nC and calculate the electric potential at the midpoint of the base. Figure P16.17:
> Three identical point charges each of charge q are located at the vertices of an equilateral triangle as in Figure P16.16. The distance from the center of the triangle to each vertex is a. (a) Show that the electric field at the center of the triangle is
> Two point charges Q1 = +5.00 nC and Q2 = -3.00 nC are separated by 35.0 cm. (a) What is the electric potential at a point midway between the charges? (b) What is the potential energy of the pair of charges? What is the significance of the algebraic sign
> Three charges are situated at corners of a rectangle as in Figure P16.13. How much work must an external agent do to move the 8.00-μC charge to infinity? Figure P16.13:
> (a) Find the electric potential, taking zero at infinity, at the upper right corner (the corner without a charge) of the rectangle in Figure P16.13. (b) Repeat if the 2.00-μC charge is replaced with a charge of -2.00 μC. Figu
> The two charges in Figure P16.12 are separated by d = 2.00 cm. Find the electric potential at (a) point A and (b) point B, which is halfway between the charges. Figure P16.12:
> An electron is at the origin. (a) Calculate the electric potential VA at point A, x = 0.250 cm. (b) Calculate the electric potential VB at point B, x = 0.750 cm. What is the potential difference VB - VA? (c) Would a negatively charged particle placed at
> A 0.200-kg aluminum cup contains 800. g of water in thermal equilibrium with the cup at 80.°C. The combination of cup and water is cooled uniformly so that the temperature decreases by 1.5°C per minute. At what rate is energy being removed? Express your
> On planet Tehar, the free-fall acceleration is the same as that on the 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 charge of 5.00 μC is thrown upward at a speed of 20.1
> A uniform electric field of magnitude 375 N/C pointing in the positive x - direction acts on an electron, which is initially at rest. After the electron has moved 3.20 cm, what is (a) The work done by the field on the electron, (b) The change in potentia
> Two small identical conducting spheres are placed with their centers 0.30 m apart. One is given a charge of 12 x 10-9 C, the other a charge of -18 x 10-9 C. (a) Find the electrostatic force exerted on one sphere by the other. (b) The spheres are connecte
