An unknown resistor is connected between the terminals of

During the 4.0 min a 5.0 A current is set up in a wire, how many (a) coulombs and (b) electrons pass through any cross section across the wires width?

An isolated conducting sphere has a 10 cm radius. One wire carries a current of 1.000 002 0 A into it. Another wire carries a current of 1.000 000 0 A out of it. How long would it take for the sphere to increase in potential by 1000 V?

A charged belt, 50 cm wide, travels at 30 m/s between a source of charge and a sphere.The belt carries charge into the sphere at a rate corresponding to 100 mA. Compute the surface charge density on the belt.

The (United States) National Electric Code, which sets maximum safe currents for insulated copper wires of various diameters, is given (in part) in the table. Plot the safe current density as a function of diameter.Which wire gauge has the maximum safe current density? (Gauge is a way of identifying wire diameters, and 1 mil ! 10 #3 in.)

A beam contains 2.0 $ 108 doubly charged positive ions per cubic centimeter, all of which are moving north with a speed of 1.0 $ 105 m/s.What are the (a) magnitude and (b) direction of the current density (c) What additional quantity do you need to calculate the total current i in this ion beam?

A certain cylindrical wire carries current. We draw a circle of radius r around its central axis in Fig. 26- 24a to determine the current i within the circle. Figure 26- 24b shows current i as a function of r 2 . The vertical scale is set by is ! 4.0 mA, and the horizontal scale is set by ! 4.0 mm2 (a) Is the current density uniform? (b) If so, what is its magnitude?

A fuse in an electric circuit is a wire that is designed to melt, and thereby open the circuit, if the current exceeds a predetermined value. Suppose that the material to be used in a fuse melts when the current density rises to 440 A/cm2 . What diameter of cylindrical wire should be used to make a fuse that will limit the current to 0.50 A?

A small but measurable current of 1.2 $ 10 #10 A exists in a copper wire whose diameter is 2.5 mm.The number of charge carriers per unit volume is 8.49 $ 1028 m#3 . Assuming the current is uniform, calculate the (a) current density and (b) electron drift speed.

The magnitude J(r) of the current density in a certain cylindrical wire is given as a function of radial distance from the center of the wires cross section as J(r) ! Br, where r is in meters, J is in amperes per square meter, and B ! 2.00 $ 105 A/m3 .This function applies out to the wires radius of 2.00 mm. How much current is contained within the width of a thin ring concentric with the wire if the ring has a radial width of 10.0 mm and is at a radial distance of 1.20 mm?

The magnitude J of the current density in a certain lab wire with a circular cross section of radius R ! 2.00 mm is given by J ! (3.00 $ 108 )r 2 , with J in amperes per square meter and radial distance r in meters. What is the current through the outer section bounded by r ! 0.900R and r ! R?

What is the current in a wire of radius R ! 3.40 mm if the magnitude of the current density is given by (a) Ja ! J0r/R and (b) Jb ! J0(1 # r/R), in which r is the radial distance and J0 ! 5.50 $ 104 A/m2 ? (c) Which function maximizes the current density near the wires surface?

Near Earth, the density of protons in the solar wind (a stream of particles from the Sun) is 8.70 cm#3 , and their speed is 470 km/s. (a) Find the current density of these protons. (b) If Earths magnetic field did not deflect the protons, what total current would Earth receive?

How long does it take electrons to get from a car battery to the starting motor? Assume the current is 300 A and the electrons travel through a copper wire with cross-sectional area 0.21 cm2 and length 0.85 m. The number of charge carriers per unit volume is 8.49 $ 1028 m#3 .

A human being can be electrocuted if a current as small as 50 mA passes near the heart. An electrician working with sweaty hands makes good contact with the two conductors he is holding, one in each hand. If his resistance is 2000 0, what might the fatal voltage be?

A coil is formed by winding 250 turns of insulated 16-gauge copper wire (diameter 1.3 mm) in a single layer on a cylindrical form of radius 12 cm. What is the resistance of the coil? Neglect the thickness of the insulation. (Use Table 26-1.)

Copper and aluminum are being considered for a high-voltage transmission line that must carry a current of 60.0 A. The resistance per unit length is to be 0.150 0/km. The densities of copper and aluminum are 8960 and 2600 kg/m3 , respectively. Compute (a) the magnitude J of the current density and (b) the mass per unit length l for a copper cable and (c) J and (d) l for an aluminum cable

A wire of Nichrome (a nickelchromiumiron alloy commonly used in heating elements) is 1.0 m long and 1.0 mm2 in cross-sectional area. It carries a current of 4.0 A when a 2.0 V potential difference is applied between its ends. Calculate the conductivity s of Nichrome.

A wire 4.00 m long and 6.00 mm in diameter has a resistance of 15.0 m0.A potential difference of 23.0 V is applied between the ends. (a) What is the current in the wire? (b) What is the magnitude of the current density? (c) Calculate the resistivity of the wire material. (d) Using Table 26-1, identify the material.

What is the resistivity of a wire of 1.0 mm diameter, 2.0 m length, and 50 m resistance?

A certain wire has a resistance R. What is the resistance of a second wire, made of the same material, that is half as long and has half the diameter?

A common flashlight bulb is rated at 0.30 A and 2.9 V (the values of the current and voltage under operating conditions). If the resistance of the tungsten bulb filament at room temperature (20/C) is 1.1 0, what is the temperature of the filament when the bulb is on?

Kiting during a storm. The legend that Benjamin Franklin flew a kite as a storm approached is only a legendhe was neither stupid nor suicidal. Suppose a kite string of radius 2.00 mm extends directly upward by 0.800 km and is coated with a 0.500 mm layer of water having resistivity 150 0 &m. If the potential difference between the two ends of the string is 160 MV, what is the current through the water layer? The danger is not this current but the chance that the string draws a lightning strike, which can have a current as large as 500 000 A (way beyond just being lethal)

When 115 V is applied across a wire that is 10 m long and has a 0.30 mm radius, the magnitude of the current density is 1.4 $ 108 A/m2 . Find the resistivity of the wire.

Figure 26-25a gives the magnitude E(x) of the electric fields that have been set up by a battery along a resistive rod of length 9.00 mm (Fig. 26-25b).The vertical scale is set by Es ! 4.00 $ 103 V/m. The rod consists of three sections of the same material but with different radii. (The schematic diagram of Fig. 26-25b does not indicate the different radii.) The radius of section 3 is 2.00 mm. What is the radius of (a) section 1 and (b) section 2? ILW 0 SSM x = 0 x = 9 mm V E (103 V/m) Es 0 3 x (mm) 96 1 2 3 (a) (b)

A wire with a resistance of 6.0 0 is drawn out through a die so that its new length is three times its original length. Find the resistance of the longer wire, assuming that the resistivity and density of the material are unchanged.

In Fig. 26-26a, a 9.00 V battery is connected to a resistive strip that consists of three sections with the same cross-sectional areas but different conductivities. Figure 26-26b gives the electric potential V(x) versus position x along the strip. The horizontal scale is set by xs 8.00 mm. Section 3 has conductivity 3.00 107 (0 &m)#1 .What is the conductivity of section (a) 1 and (b) 2?

Two conductors are made of the same material and have the same length. Conductor A is a solid wire of diameter 1.0 mm. Conductor B is a hollow tube of outside diameter 2.0 mm and inside diameter 1.0 mm. What is the resistance ratio RA/RB, measured between their ends

Figure 26-27 gives the electric potential V(x) along a copper wire carrying uniform current, from a point of higher potential Vs ! 12.0 mV at x ! 0 to a point of zero potential at xs ! 3.00 m. The wire has a radius of 2.00 mm. What is the current in the wire?

A potential difference of 3.00 nV is set up across a 2.00 cm length of copper wire that has a radius of 2.00 mm. How much charge drifts through a cross section in 3.00 ms?

If the gauge number of a wire is increased by 6, the diameter is halved; if a gauge number is increased by 1, the diameter decreases by the factor 21/6 (see the table in Problem 4). Knowing this, and knowing that 1000 ft of 10-gauge copper wire has a resistance of approximately 1.00 0, estimate the resistance of 25 ft of 22-gauge copper wire

An electrical cable consists of 125 strands of fine wire, each having 2.65 m0 resistance. The same potential difference is applied between the ends of all the strands and results in a total current of 0.750 A. (a) What is the current in each strand? (b) What is the applied potential difference? (c) What is the resistance of the cable?

Earths lower atmosphere contains negative and positive ions that are produced by radioactive elements in the soil and cosmic rays from space. In a certain region, the atmospheric lectric field strength is 120 V/m and the field is directed vertically down.This field causes singly charged positive ions, at a density of 620 cm#3, to drift downward and singly charged negative ions, at a density of 550 cm# to drift upward (Fig. 26-28). The measured conductivity of the air in that region is 2.70 $ 10 #14 (0 &m)#1 Calculate (a) the magnitude of the current density and (b) the ion drift speed, assumed to be the same for positive and negative ions

A block in the shape of a rectangular solid has a crosssectional area of 3.50 cm2 across its width, a front-to-rear length of 15.8 cm, and a resistance of 935 0. The blocks material contains 5.33 $ 1022 conduction electrons/m3 . A potential difference of 35.8 V is maintained between its front and rear faces. (a) What is the current in the block? (b) If the current density is uniform, what is its magnitude? What are (c) the drift velocity of the conduction electrons and (d) the magnitude of the electric field in the block?

Figure 26-29 shows wire section 1 of diameter D1 4.00R and wire section 2 of diameter D2 ! 2.00R, connected by a tapered section. The wire is copper and carries a current. Assume that the current is uniformly distributed across any cross-sectional area through the wires width. The electric potential change V along the length L ! 2.00 m shown in section 2 is 10.0 mV. The number of charge carriers per unit volume is 8.49 $ 1028 m#3 . What is the drift speed of the conduction electrons in section 1?

In Fig. 26-30, current is set up through a truncated right circular cone of resistivity 731 , left radius a 2.00 mm, right radius b ! 2.30 mm, and length L ! 1.94 cm. Assume that the current density is uniform across any cross section taken perpendicular to the length.What is the resistance of the cone?

Swimming during a storm. Figure 26-31 shows a swimmer at distance D 35.0 m from a lightning strike to the water, with current I 78 kA. The water has resistivity 30 0 &m, the width of the swimmer along a radial line from the strike is 0.70 m, and his resistance across that width is 4.00 k0. Assume that the current spreads through the water over a hemisphere centered on the strike point.What is the current through the swimmer?

Show that, according to the free-electron model of electrical conduction in metals and classical physics, the resistivity of metals should be proportional to where T is the temperature in kelvins. (See Eq. 19-31.)

In Fig. 26-32a, a 20 0 resistor is connected to a battery. Figure 26-32b shows the increase of thermal energy Eth in the resistor as a function of time t. The vertical scale is set by Eth,s ! 2.50 mJ, and the horizontal scale is set by ts ! 4.0 s. What is the electric potential across the battery?

A certain brand of hot-dog cooker works by applying a potential difference of 120 V across opposite ends of a hot dog and allowing it to cook by means of the thermal energy produced. The current is 10.0 A, and the energy required to cook one hot dog is 60.0 kJ. If the rate at which energy is supplied is unchanged, how long will it take to cook three hot dogs simultaneously?

Thermal energy is produced in a resistor at a rate of 100 W when the current is 3.00 A.What is the resistance?

A 120 V potential difference is applied to a space heater whose resistance is 14 when hot. (a) At what rate is electrical energy transferred to thermal energy? (b) What is the cost for 5.0 h at US$0.05/kW&h?

In Fig. 26-33, a battery of potential difference V ! 12 V is connected to a resistive strip of resistance R ! 6.0 0. When an electron moves through the strip from one end to the other, (a) in which direction in the figure does the electron move, (b) how much work is done on the electron by the electric field in the strip, and (c) how much energy is transferred to the thermal energy of the strip by the electron?

An unknown resistor is connected between the terminals of a 3.00 V battery. Energy is dissipated in the resistor at the rate of 0.540 W. The same resistor is then connected between the terminals of a 1.50 V battery. At what rate is energy now dissipated?

A student kept his 9.0 V, 7.0 W radio turned on at full volume from 9:00 P.M. until 2:00 A.M. How much charge went through it?

A 1250 W radiant heater is constructed to operate at 115 V. (a) What is the current in the heater when the unit is operating? (b) What is the resistance of the heating coil? (c) How much thermal energy is produced in 1.0 h?

A copper wire of cross-sectional area 2.00 $ 10 #6 m2 and length 4.00 m has a current of 2.00 A uniformly distributed across that area. (a) What is the magnitude of the electric field along the wire? (b) How much electrical energy is transferred to thermal energy in 30 min?

A heating element is made by maintaining a potential difference of 75.0 V across the length of a Nichrome wire that has a 2.60 $ 10 #6 m2 cross section. Nichrome has a resistivity of 5.00 $ 10 #7 0 &m. (a) If the element dissipates 5000 W, what is its length? (b) If 100 V is used to obtain the same dissipation rate, what should the length be?

Exploding shoes. The rain-soaked shoes of a person may explode if ground current from nearby lightning vaporizes the water. The sudden conversion of water to water vapor causes a dramatic expansion that can rip apart shoes. Water has density 1000 kg/m3 and requires 2256 kJ/kg to be vaporized. If horizontal current lasts 2.00 ms and encounters water with resistivity 150 0 &m, length 12.0 cm, and vertical cross-sectional area 15 $ 10#5 m2 , what average current is required to vaporize the water?

A 100 W lightbulb is plugged into a standard 120 V outlet. (a) How much does it cost per 31-day month to leave the light turned on continuously? Assume electrical energy costs US$0.06/kW&h. (b) What is the resistance of the bulb? (c) What is the current in the bulb?

The current through the battery and resistors 1 and 2 in Fig. 26-34a is 2.00 A. Energy is transferred from the current to thermal energy Eth in both resistors. Curves 1 and 2 in Fig. 26-34b give that thermal energy Eth for resistors 1 and 2, respectively, as a function of time t. The vertical scale is set by Eth,s 40.0 mJ, and the horizontal scale is set by ts 5.00 s. What is the power of the battery?

Wire C and wire D are made from different materials and have length LC ! LD ! 1.0 m. The resistivity and diameter of wire C are 2.0 $ 10 #6 0 &m and 1.00 mm, and those of wire D are 1.0 $ 10 #6 0 &m and 0.50 mm. The wires are joined as shown in Fig. 26-35, and a current of 2.0 A is set up in them. What is the electric potential difference between (a) points 1 and 2 and (b) points 2 and 3? What is the rate at which energy is dissipated between (c) points 1 and 2 and (d) points 2 and 3?

The current-density magnitude in a certain circular wire is J (2.75 1010 A/m4 )r 2 , where r is the radial distance out to the wires radius of 3.00 mm. The potential applied to the wire (end to end) is 60.0 V. How much energy is converted to thermal energy in 1.00 h?

A 120 V potential difference is applied to a space heater that dissipates 500 W during operation. (a) What is its resistance during operation? (b) At what rate do electrons flow through any cross section of the heater element?

Figure 26-36a shows a rod of resistive material. The resistance per unit length of the rod increases in the positive direction of the x axis. At any position x along the rod, the resistance dR of a narrow (differential) section of width dx is given by dR ! 5.00x dx, where dR is in ohms and x is in meters. Figure 26-36b shows such a narrow section. You are to slice off a length of the rod between x 0 and some position x L and then connect that length to a battery with potential difference V 5.0 V (Fig. 26- 36c). You want the current in the length to transfer energy to thermal energy at the rate of 200 W. At what position x ! L should you cut the rod?

A Nichrome heater dissipates 500 W when the applied potential difference is 110 V and the wire temperature is 800 C. What would be the dissipation rate if the wire temperature were held at 200 C by immersing the wire in a bath of cooling oil? The applied potential difference remains the same, and a for Nichrome at 800 C is 4.0 $ 10 #4 K#1 .

A potential difference of 1.20 V will be applied to a 33.0 m length of 18-gauge copper wire (diameter ! 0.0400 in.). Calculate (a) the current, (b) the magnitude of the current density, (c) the magnitude of the electric field within the wire, and (d) the rate at which thermal energy will appear in the wire

An 18.0 W device has 9.00 V across it. How much charge goes through the device in 4.00 h?

An aluminum rod with a square cross section is 1.3 m long and 5.2 mm on edge. (a) What is the resistance between its ends? (b) What must be the diameter of a cylindrical copper rod of length 1.3 m if its resistance is to be the same as that of the aluminum rod?

A cylindrical metal rod is 1.60 m long and 5.50 mm in diameter. The resistance between its two ends (at 20C) is 1.09 $ 10 #3 0. (a) What is the material? (b) A round disk, 2.00 cm in diameter and 1.00 mm thick, is formed of the same material. What is the resistance between the round faces, assuming that each face is an equipotential surface?

The chocolate crumb mystery. This story begins with Problem 60 in Chapter 23 and continues through Chapters 24 and 25.The chocolate crumb powder moved to the silo through a pipe of radius R with uniform speed v and uniform charge density r. (a) Find an expression for the current i (the rate at which charge on the powder moved) through a perpendicular cross section of the pipe. (b) Evaluate i for the conditions at the factory: pipe radius R ! 5.0 cm, speed v ! 2.0 m/s, and charge density r ! 1.1 $ 10 #3 C/m3 . If the powder were to flow through a change V in electric potential, its energy could be transferred to a spark at the rate P ! iV. (c) Could there be such a transfer within the pipe due to the radial potential difference discussed in Problem 70 of Chapter 24? As the powder flowed from the pipe into the silo, the electric potential of the powder changed.The magnitude of that change was at least equal to the radial potential difference within the pipe (as evaluated in Problem 70 of Chapter 24). (d) Assuming that value for the potential difference and using the current found in (b) above, find the rate at which energy could have been transferred from the powder to a spark as the powder exited the pipe. (e) If a spark did occur at the exit and lasted for 0.20 s (a reasonable expectation), how much energy would have been transferred to the spark? Recall 8 8 8 SSM ! ! ! from Problem 60 in Chapter 23 that a minimum energy transfer of 150 mJ is needed to cause an explosion. (f) Where did the powder explosion most likely occur: in the powder cloud at the unloading bin (Problem 60 of Chapter 25), within the pipe, or at the exit of the pipe into the silo?

A steady beam of alpha particles (q 2e) traveling with constant kinetic energy 20 MeV carries a current of 0.25 mA. (a) If the beam is directed perpendicular to a flat surface, how many alpha particles strike the surface in 3.0 s? (b) At any instant, how many alpha particles are there in a given 20 cm length of the beam? (c) Through what potential difference is it necessary to accelerate each alpha particle from rest to bring it to an energy of 20 MeV?

A resistor with a potential difference of 200 V across it transfers electrical energy to thermal energy at the rate of 3000 W.What is the resistance of the resistor?

A 2.0 kW heater element from a dryer has a length of 80 cm. If a 10 cm section is removed, what power is used by the now shortened element at 120 V?

A cylindrical resistor of radius 5.0 mm and length 2.0 cm is made of material that has a resistivity of 3.5 $ 10 #5 0 &m.What are (a) the magnitude of the current density and (b) the potential difference when the energy dissipation rate in the resistor is 1.0 W

A potential difference V is applied to a wire of cross-sectional area A, length L, and resistivity r. You want to change the applied potential difference and stretch the wire so that the energy dissipation rate is multiplied by 30.0 and the current is multiplied by 4.00. Assuming the wires density does not change, what are (a) the ratio of the new length to L and (b) the ratio of the new cross-sectional area to A?

The headlights of a moving car require about 10 A from the 12 V alternator, which is driven by the engine. Assume the alternator is 80% efficient (its output electrical power is 80% of its input mechanical power), and calculate the horsepower the engine must supply to run the lights.

A 500 W heating unit is designed to operate with an applied potential difference of 115 V. (a) By what percentage will its heat output drop if the applied potential difference drops to 110 V? Assume no change in resistance. (b) If you took the variation of resistance with temperature into account, would the actual drop in heat output be larger or smaller than that calculated in (a)?

The copper windings of a motor have a resistance of 50 0 at 20C when the motor is idle. After the motor has run for several hours, the resistance rises to 58 0. What is the temperature of the windings now? Ignore changes in the dimensions of the windings. (Use Table 26-1.)

How much electrical energy is transferred to thermal energy in 2.00 h by an electrical resistance of 400 0 when the potential applied across it is 90.0 V?

A caterpillar of length 4.0 cm crawls in the direction of electron drift along a 5.2-mm-diameter bare copper wire that carries a uniform current of 12 A. (a) What is the potential difference between the two ends of the caterpillar? (b) Is its tail positive or negative relative to its head? (c) How much time does the caterpillar take to crawl 1.0 cm if it crawls at the drift speed of the electrons in the wire? (The number of charge carriers per unit volume is 8.49 $ 1028 m#3 .)

(a) At what temperature would the resistance of a copper conductor be double its resistance at 20.0 C? (Use 20.0 C as the reference point in Eq. 26-17; compare your answer with 8 8 SSM SSM ! % Figure 26-36 Problem 54. (a) x (m) 0 1.0 (b) (c) dx V Fig. 26-10.) (b) Does this same doubling temperature hold for all copper conductors, regardless of shape or size?

A steel trolley-car rail has a cross-sectional area of 56.0 cm2 . What is the resistance of 10.0 km of rail? The resistivity of the steel is 3.00 $ 10 #7 0 &m.

A coil of current-carrying Nichrome wire is immersed in a liquid. (Nichrome is a nickelchromiumiron alloy commonly used in heating elements.) When the potential difference across the coil is 12 V and the current through the coil is 5.2 A, the liquid evaporates at the steady rate of 21 mg/s. Calculate the heat of vaporization of the liquid (see Module 18-4)

The current density in a wire is uniform and has magnitude 2.0 106 A/m2 , the wires length is 5.0 m, and the density of conduction electrons is 8.49 $ 1028 m#3 . How long does an electron take (on the average) to travel the length of the wire?

A certain x-ray tube operates at a current of 7.00 mA and a potential difference of 80.0 kV.What is its power in watts?

A current is established in a gas discharge tube when a sufficiently high potential difference is applied across the two electrodes in the tube. The gas ionizes; electrons move toward the positive terminal and singly charged positive ions toward the negative terminal. (a) What is the current in a hydrogen discharge tube in which 3.1 $ 1018 electrons and 1.1 $ 1018 protons move past a crosssectional area of the tube each second? (b) Is the direction of the current density toward or away from the negative terminal?

In Fig. 26-37, a resistance coil, wired to an external battery, is placed inside a thermally insulated cylinder fitted with a frictionless piston and containing an ideal gas. A current i ! 240 mA flows through the coil, which has a resistance R ! 550 0. At what speed v must the piston, of mass m ! 12 kg, move upward in order that the temperature of the gas remains unchanged?

An insulating belt moves at speed 30 m/s and has a width of 50 cm. It carries charge into an experimental device at a rate corresponding to 100 mA. What is the surface charge density on the belt?

In a hypothetical fusion research lab, high temperature helium gas is completely ionized and each helium atom is separated into two free electrons and the remaining positively charged nucleus, which is called an alpha particle. An applied electric field causes the alpha particles to drift to the east at 25.0 m/s while the electrons drift to the west at 88.0 m/s.The alpha particle density is 2.80 $ 1015 cm#3 . What are (a) the net current density and (b) the current direction?

When a metal rod is heated, not only its resistance but also its length and cross-sectional area change. The relation R ! rL/A suggests that all three factors should be taken into account in measuring r at various temperatures. If the temperature changes by 1.0 C, what percentage changes in (a) L, (b) A, and (c) R occur for a copper conductor? (d) What conclusion do you draw? The coefficient of linear expansion is 1.70 $ 10#5 K#1

A beam of 16 MeV deuterons from a cyclotron strikes a copper block. The beam is equivalent to current of 15 mA. (a) At what rate do deuterons strike the block? (b) At what rate is thermal energy produced in the block?

A linear accelerator produces a pulsed beam of electrons.The pulse current is 0.50 A, and the pulse duration is 0.10 ms. (a) How many electrons are accelerated per pulse? (b) What is the average current for a machine operating at 500 pulses/s? If the electrons are accelerated to an energy of 50 MeV, what are the (c) average power and (d) peak power of the accelerator?

An electric immersion heater normally takes 100 min to bring cold water in a well-insulated container to a certain temperature, after which a thermostat switches the heater off. One day the line voltage is reduced by 6.00% because of a laboratory overload. How long does heating the water now take? Assume that the resistance of the heating element does not change.

A 400 W immersion heater is placed in a pot containing 2.00 L of water at 20/C. (a) How long will the water take to rise to the boiling temperature, assuming that 80% of the available energy is absorbed by the water? (b) How much longer is required to evaporate half of the water?

A 30 mF capacitor is connected across a programmed power supply. During the interval from t ! 0 to t ! 3.00 s the output voltage of the supply is given by V(t) ! 6.00 % 4.00t # 2.00t 2 volts. At t ! 0.500 s find (a) the charge on the capacitor, (b) the current into the capacitor, and (c) the power output from the power supply.