AP Physics C EM MC Study Guide For Units 1,2,3
A thin, nonconducting rod of length L is positioned on the x-axis with its left end at x = 0. The rod is charged and has a linear charge density of 5x^3. Which of the following represents the total charge on the rod?
(5/4)L^4
A particle of charge +Q is at point A, a distance rA from the center of a sphere of charge +Q. The particle is moved to point B, a distance rB from the center of the sphere. Which of the following expressions represents the electric potential difference between the two points due to the charge on the sphere? Responses
(Q/4piε)(1/rB - 1/rA)
A solid, nonconducting sphere of radius R has a uniform charge distribution throughout its volume. The electric field at a point a distance r from the center of the sphere is E = kq/r^2, where r > R. Which of the following is a correct illustrates a correct use of Gauss's law to determine the electric field at point where r < R ?
(Qr^3)/(εR^3) = E(4pi * r^2)
Small sphere S of mass m = 2.5g and charge q = -1.5uC is released from rest at the position shown in an electric field of magnitude E = 3.0 x 106 that is directed horizontally to the right, as shown above. Points A and B are both 10cm from the original position of the sphere. Which of the following indicates the point the sphere moves toward and the speed of the sphere when it reaches that point?
-0.63 J
Point charges A , B , and C are positioned at the three corners of a square and have the charges shown in the figure. The sides of the square have a length L. The electric potential at the empty corner of the square is
-1.6 KQ/L
Three point charges are arranged at the corners of a square with sides of length d. At point P at the center of the square, the net electric field vector E net points to the right, as shown. If the charge Q1 = -2.0 nC, and Q2 = +2.0 nC, then the charge Q3 must be equal to
-4 nC
Three identical point charges +q form an equilateral triangle with sides of length s, as shown. The magnitude of the net force acting on each point charge is F, and the potential energy of the system of charges is U. One of the three point charges is then replaced by one with a charge -q. Which of the following a correct expression for the potential energy of the system of three point charges in Figure 2?
-U/3
An uncharged parallel-plate capacitor is connected through an open switch to a battery of voltage V. The switch is closed and the capacitor is allowed to charge. As the capacitor is charged, energy is transferred to it from the battery. When the capacitor is fully charged, the energy stored in the capacitor is U1 . The energy stored in the capacitor when the stored charge is q/2 is
.25U
An isolated conducting sphere of radius R is initially uncharged. A point charge +q is placed a distance r from the center C of the sphere, as shown in the figure. Points 1 and 2 are points on the surface of the sphere such that the point charge and points 1, 2, and C all fall on the same line. The electric field at point C due to the point charge and the sphere is
0
Three point charges, each with charge of magnitude q = 5.0 uC, are arranged in a line as shown. If the net force on the middle charge is 0.50 N, what is the approximate value of d ?
0.7 m
A nonideal 12V battery is connected in a circuit with a single resistor of 6Ω resistance . A voltmeter connected across the resistor reads 9V. What is the internal resistance of the battery?
3Ω
The circuit shown consists of a battery and a resistor with the voltage and resistance values shown. Determine the current through the resistor.
4 A
A resistor connected to a 9 Volt battery draws a current of 0.10A. The resistor is 0.20 cm long and has a square cross-section with sides of length 0.10cm as shown. The resistivity of the material of the resistor is most nearly
4.5x10 Ω*m
A wire of cross-sectional area 7.0x10^-5 m^2 is carrying a current. The current density in the wire is 1.8x10^4 A/m^2. The number of electrons that move through a cross section of the wire in one minute is most nearly
4.72x10^20
A parallel plate capacitor with plate area A and plate separation D has a material between its plates with dielectric constant k=2 . When this capacitor is isolated and fully charged, the energy stored in the capacitor is 20J. The material is slowly removed from between the plates. After the material is removed, the energy stored in the capacitor is
40J
Three identical charges of magnitude q=2.0nC are placed on the corners of a square with sides of length L=0.10m. What is the electric potential due to these charges at a point on the fourth corner of the square?
487 N/C
An air-filled 6.0mF capacitor is connected to a 9.0-volt battery. While keeping the capacitor connected to the battery, a material with dielectric constant k=3 is inserted between the plates. The increase in the energy stored on the capacitor by inserting the material is most nearly
490 mJ
In an experiment, students connect a capacitor to a battery of constant voltage V. Different material of dielectric constant ki can be inserted between the plates as shown. The dielectric constants for three materials that will be inserted between the plates are k1 ,K2, and k3. Which of the following sets of data of the final charge on the capacitor for each dielectric material supports the claim that K3 > K2 > K1?
4mC, 8mC, 12mC
A small sphere of mass 4.0 g and charge of -6.0 uC is traveling in an electric field. The sphere has a speed of 5.0 I at point A, where the electric potential is 5.0 kV. What will the speed of the sphere be at point B, where the electric potential is 8.0 kV?
5.8 m/s
The circuit shown above consists of three capacitors, a resistor, a switch, and an ideal battery. The capacitors are all initially uncharged, and the switch is in the open position. The switch is then closed. Calculate the total energy stored in the circuit a long time after the switch is closed.
5/4 Ce^2
An electron is placed at point A in a uniform electric field of magnitude E directed to the right, as shown above. A short time later, the electron is at point B. Which of the following statements describes the relationship between the electric field and the motion of the electron?
A force not associated with the electric field moves the electron from point A to point B. The electric field does negative work on the electron in the process.
The circuit shown above consists of a resistor R and capacitor C in series with a battery V and a switch. The switch is initially open. A student wishes to measure the potential difference across the resistor, but the voltmeter has a much lower resistance than ideal. Which of the following indicates how the lower resistance will affect the voltmeter's ability to correctly measure the potential difference across the resistor R immediately after the switch is closed and explains why?
It will have no effect because the resistor will have the same potential difference as the battery.
The figure shows the electric potential along the x-axis in a region of space. Which of the following graphs best represents the electric field along the x-axis in the same region of space?
Starts at negative, rises to positive, falls to negative. The slopes are not straight up or straight down
Two point charges are held at rest on the x-axis of a coordinate system as shown above. The first point charge is located at X = -0.20 m and has a charge of q1 = -10 uC. The second point charge is located at x = +0.20 m and has a charge of q2 = +5.0 uC. Where must a third point charge with charge q3 = -2.5 uC be placed so that the net force on it is zero?
+1.17 m
The electric potential V in a region of space is given as a function of positions x by the equation V = 6x - 4x^2, where V is in volts and x is in meters. The magnitude of the electric field at the point (3, 0) is equal to
+18 N/C
In the five figures above, a battery is to be connected in various ways to one, two, or three resistors. All batteries have voltage , and all resistors have resistance . In which figure is the battery supplying the most power?
3, they're all in parallel
In the laboratory, two resistors, R1 and R2, are connected in series in a circuit. The total measured resistance of the circuit, Rt, is varied, and the results are plotted above. Which of the following is closest to the resistance of R1?
100kΩ
A sphere of mass 0.50 g and charge 2.0 uC is released from rest near the surface of Earth in a region where there is a uniform horizontal electric field of magnitude 2.0 . The magnitude of the initial acceleration of the sphere is most nearly
12.7 m/s^2
The figure shows a uniform line of positive charge of magnitude 3.0uC and length 75 cm. The equation for the electric field a distance x along the perpendicular bisector from the line of length L is E = kq/(x^2(x^2 + (.5L)^2)^(1/2)). Point R is 5.0 cm from the line of charge and is positioned along a perpendicular bisector of the line. Point S is also along the bisector and is 7.5 cm from the line. The potential difference between points R and S is most nearly
13.5V
Three identical point charges +q form an equilateral triangle with sides of length s, as shown. The magnitude of the net force acting on each point charge is F, and the potential energy of the system of charges is U. One of the three point charges is then replaced by one with a charge -q. If q = 2 uC and s = 2 cm, what is the magnitude of the net force on the -q point charge?
156 N
The parallel plate capacitor represented above was used by students in an experiment. The electric potential is set to zero at plate D, and the electric potential at the other positions is measured. The distance between the difference positions is also measure, and the data are shown in the table. Based on the data provided, which of the following gives the correct magnitude and direction of the electric field inside the plates of the capacitor?
2000 N/C to the right
Students use the experimental setup shown to determine power dissipated in a circuit. The circuit consists of two ohmic resistors of unknown resistance and an ideal battery of unknown voltage. Which of the following indicates two meters whose reading the students should use to determine the power dissipated by R1?
A3 and V2
A capacitor is connected to a battery as shown above. The plates of the capacitor are pulled apart using insulating handles while the capacitor remains connected to the battery. Will the capacitance and energy stored in the capacitor increase, decrease, or remain the same?
Both will decrease
In the circuit shown above, all three lightbulbs are identical and the switch is initially open. When the switch is closed, which of the following best describes the relative brightness of the bulbs?
Bulb 1 is brighter than both bulbs 2 and 3.
The circuit above consists of a battery and three identical bulbs. Which of the following best describes how the three bulbs are connected to each other?
Bulbs B and C are connected in parallel to each other, and that combination is connected in series to bulb A.
An isolated parallel-plate capacitor with plate spacing of d has capacitance C when it has a dielectric constant k. The plate separation is increased to 2d, and the dielectric is replaced with material of dielectric constant 2k. The new capacitance of the capacitor is
C
A positively charged conducting spherical shell of radius r is a distance D away from a second positively charged conducting spherical shell of radius R, where D >> R > r. The two shells are connected by a thin metal wire, and the equilibrium is established. At equilibrium, the small shell carries a charge +q and the large shell carries a charge +Q, as shown. Points A, B, and C in the vicinity of the shells are shown in the figure. Points A and C are just outside the surface of each sphere, and point B is equidistant from both spheres. Which of the following indicates the point at which the magnitude of the electric field is greatest and supplies evidence for the claim?
II and III
An air-filled parallel-plate capacitor of capacitance C is connected to a battery of voltage V. When fully charged, the capacitor stores a charge Q and the electric field between the plates is E. While the capacitor is connected to the battery, a material with a dielectric constant of 2 is inserted into the space between the plates of the capacitor. As a result, the magnitudes of the charge stored on the capacitor and the electric field between the plates are
Charge stored: 2Q Electric Field: E
A positive test charge is brought near to, but not touching, a conducting sphere that is connected to the ground. Both objects remain at rest in the positions shown above. Charge begins to flow from the ground to the sphere. Which of the following statements best describes when charge stops flowing, and provides justification for the claim?
Charge will flow from the ground to the sphere until the potential is the same everywhere within the sphere, because then the net force on all charges on the surface of the sphere will be zero.
A ring with charge +Q uniformly distributed on it is centered at the origin of the coordinate system. The ring lies in the xy-plane. Which claim below best characterizes the electric field along the z-axis? Responses
Components of the electric field perpendicular to the central axis cancel out, and there is only a component along the central axis. This component is always directed away from the center of the ring, except for the point at the center of the ring where the electric field is zero.
In an experiment, students are asked to determine the power dissipated by an unknown electronic device. The students connect the device to a battery, as shown, and make the necessary measurements. The figure shows four labeled points, a voltmeter, and an ammeter. Which of the following describes the proper connections for the meters to make measurements to determine the power dissipated?
Connect the voltmeter between points B and C, and insert the ammeter at point A.
Four identical resistors are connected in the circuit above. Several points in the circuit have been labeled. Students use a voltmeter and an ammeter to make measurements of the potential differences between two points and the current present at any point, respectively. Which of the following would create the greatest amount of error in a measurement?
Connecting the ammeter between points A and D.
A semicircular wire has a uniform positive linear charge density Q/L=Q/(pi * R), where Q is the total charge of the wire, L is the length of the wire, and R is the radius of the semicircle. Which of the following claims about the electric field at point P is correct and gives supporting evidence?
It is directed vertically downward because the charge is positive, and horizontal components of the electric field contributed from elements of charge on opposite sides of the semicircle cancel each other.
A parallel-plate capacitor has capacitance C . Which of the following is a modification, with correct reasoning, that will decrease the capacitance of the capacitor to 0.5C?
Decrease the area of the plates by a factor of two, because then half as much charge will deposit on the plates when the same potential difference is applied.
Two point charges with charges +2q and +q are separated by distance d. Several equipotential lines near the point charges and labeled points A, B, C, and D are shown in the figure. Which of the following correctly ranks the magnitudes of the electric field at the four labeled points from largest to smallest?
EA > EB > ED > EC
A lightbulb glows brightly when it is connected across a certain battery. The battery will maintain a constant potential difference even as its output current increases. Four more identical bulbs are then connected across the same battery, so that all five bulbs are in parallel. How does the brightness of each of the five bulbs in parallel compare to the original bulb?
Each of the five bulbs is equally as bright as the original bulb.
A charged sphere of radius 30 cm is isolated in the center of a large room. The sphere carries a charge of 1.0 uC. The magnitudes of the electric field at the surface of the sphere and at a distance of 1 m away from the surface of the sphere are most nearly
Electric Field at Surface 1.0 x 10^5 N/C Electric Field 1m from Surface 5.3 x 10^3 N/C
The figures shown represent the electric fields near four different objects. Figure A represents two positive point charges, figure B represents two oppositely charged plates, figure C represents a negatively charged ring, and figure D represents a positively charged disk. Which figure, if any, has an error in its representation of the direction of the electric field?
Figure C
An isolated, nonconducting sphere is positioned on the x-axis between positions 1 and x2, as shown. The sphere has charge +Q uniformly distributed throughout its volume. Which of the following pairs of graphs could represent the magnitude of the electric field and the electric potential as functions of x ?
First graph: absolute value function between x1 and x2 Second graph: -x^2 function between x1 and x2
The figure shows an uncharged conducting cubic shell and a positive point charge Q outside the shell. There are two lettered points W and X inside the shell where the electric field can be measured. The electric field at points W and X are Ew and Ex, respectively. Point W is at the center of the cubic shell. Outside the shell are points Y and Z where the charge Q can be placed. All four points are along the same line. Which of the following statements is correct?
If the point charge is placed at point Z, Ew = Ex.
A ring with charge −Q uniformly distributed around its circumference is centered on the axis of the xy-coordinate plane, as shown. Which of the following best describes the direction of the electric field at point P due to the ring, and provides correct reasoning to support this direction?
In the -z-direction , because contributions from all parts of the ring produce a -z-component, with x- and y-components canceling out
A parallel-plate capacitor of capacitance C has plate area A, and the plates are a distance d apart. The capacitor is connected to a battery of voltage V. When fully charged, the capacitor stores a charge Q. Which of the following claims is true?
Increasing the area of the plates to 4A will increase the capacitance of the capacitor to 4C.
In a lab activity, a battery of voltage V is connected to a variable resistor R. Data are obtained for the power P supplied by the battery for various values of R. Which of the following relationships would yield a straight line graph for the data?
P as a function of 1/R.
Small sphere S of mass m = 2.5g and charge q = -1.5uC is released from rest at the position shown in an electric field of magnitude E = 3.0 x 10^6 N/C that is directed horizontally to the right, as shown above. Points A and B are both 10cm from the original position of the sphere. Which of the following indicates the point the sphere moves toward and the speed of the sphere when it reaches that point?
Point A with speed 19 m/s
A positively charged conducting spherical shell of radius r is a distance D away from a second positively charged conducting spherical shell of radius R, where D >> R > r. The two shells are connected by a thin metal wire, and the equilibrium is established. At equilibrium, the small shell carries a charge +q and the large shell carries a charge +Q, as shown. Points A, B, and C in the vicinity of the shells are shown in the figure. Points A and C are just outside the surface of each sphere, and point B is equidistant from both spheres. Which of the following indicates the point at which the magnitude of the electric field is greatest and supplies evidence for the claim?
Point A, because r is less than R.
In an experiment, students connect a parallel plate capacitor with square conducting plates of side length L to a battery of potential difference AVB. A dielectric slab of constant k > 1 with square faces of side length L is slowly inserted between the plates at short intervals of distance, pausing at each interval so that the capacitor reaches a steady state. The students measure the charge stored on the capacitor each time steady state is reached. The process is repeated until the dielectric is completely inside the capacitor. The students use the data to create a graph of the charge Q stored on the capacitor as a function of the distance x that the dielectric has been inserted into the capacitor. Which of the graphs correctly represents the data collected from the experiment?
Positive linear graph
Students design an experiment to test the effect of changing the plate area A on the capacitance C of a parallel plate capacitor. They use two sheets of aluminum foil and separate them with foam. They measure the capacitance of the capacitor and then begin to reduce the areas of the foil plates. Which of the following graphs would reasonably show the capacitance as a function of area for their data?
Positive, linear graph
Point charges 1 and 2 have charges Q1 and Q2 and are held 3.0 mm apart. The point charges exert an attractive force of 16 N on each other. Which of the following are possible values for the charges?
Q1=+1.0x10^-7C and Q2 =- 1.6×10^-7C
For the circuits shown, identical capacitors are connected to identical batteries and to three resistors. The values of the resistances are , , and , as shown. Which of the following correctly ranks the charge stored on the capacitors after they are fully charged?
Q1=Q2=Q3
Charged spheres A and B are near each other and isolated from all other charges. Three Gaussian surfaces are shown in the region surrounding the spheres: surface 1 around sphere A, surface 2 around sphere B, and surface 3 around both spheres. The net flux through surface 2 has twice the magnitude as the net flux through surface 1. The net flux through surface 3 has a magnitude equal to the net flux through surface 1. Which of the following are possible values of the charges Q A and QB, the charges on spheres A and B, respectively?
Qa = -q & Qb = +2q
Two resistors, R1 and R2, are connected in series with a battery, as shown above. In an experiment, the voltage of the battery is varied, and the potential difference across is measured. The results of this experiment are shown in the graph below. Which of the following could be the values of the resistances of R1 and R2?
R1 = 1000Ω, R2 = 33Ω
The circuit shown consists of three resistors with R1<R2<R3, an ideal battery, and four switches. Which of the following combinations of closed switches will maximize the current in the circuit?
S1,S2, and S4
An ammeter is connected in series with a resistor of unknown resistance and a DC power supply of known . A student uses the ammeter to measure the current and calculates the power dissipated by the resistor using and . The student later discovers that the ammeter is not an ideal ammeter. Which of the following correctly compares the actual power dissipated by the resistor to the value of power calculated by the student and explains why?
The actual power dissipated by the resistor is less than P because the ammeter had some resistance.
A parallel plate capacitor is charged by connecting it to a battery. After the steady state is reached, the electric energy stored in the capacitor is Ue. Which of the following makes a correct claim about the amount of work needed to charge the capacitor and gives evidence to support this claim?
The amount of work needed to charge the capacitor is Ue, because, when integrating the equation W=∫qdV with the correct limits yields the equation for the energy stored on a capacitor, Ue=(1/2)qV.
An uncharged parallel-plate capacitor is connected through an open switch to a battery of voltage V. The switch is closed and the capacitor is allowed to charge. The charge on the capacitor is measured at various times while it is charging. The data yield the graph shown. Which of the following could be determined using values obtained from the graph?
The capacitance C of the capacitor
An isolated parallel plate capacitor is constructed with a removable piece of dielectric material between two parallel conducting plates. Which of the following correctly predicts the effect inserting the dielectric material will have on the capacitance of the capacitor and the magnitude of the electric field between the plates of the capacitor?
The capacitance will increase, and the magnitude of the electric field will decrease.
A capacitor is connected to an ideal battery, and the capacitor is allowed to charge completely. The capacitor is then isolated from the battery, and a material with a dielectric constant of 3 is slowly inserted between the plates of the capacitor. Which of the following correctly describes the process of inserting the material?
The capacitor will pull the material into the space between the plates, and the potential energy stored between the plates of the capacitor will decrease by a factor of 3.
Two particles of mass m with charges +q and -q are connected to opposite ends of a nonconducting rod of length L. The particle-rod system is held at rest in a uniform electric field of magnitude E, directed to the right, with the rod at an angle theta with the field, as shown. Assume the force of gravity is negligible. Which of the following best describes the motion of the center of mass of the particle-rod system, and its oscillation, if it is released from rest?
The center of mass will remain at rest. The system will rotate clockwise first, then counterclockwise, as it oscillates.
In an experiment to investigate the properties of a capacitor, students connect a parallel plate capacitor to a variable voltage source as shown. Without using the electron emitter, the variable voltage source is set at a fixed value, and the spacing between the plates is gradually increased without disconnecting the capacitor from the voltage source. Which of the following is a correct claim about how this will affect the charge on the plates of the capacitor and provides evidence to support this claim?
The charge on the plates of the capacitor will decrease, because the capacitance decreases.
A parallel plate capacitor with air between its plates is connected to a battery and fully charged. While keeping the charged capacitor connected to the battery, a dielectric material is introduced between the plates. Which of the following is a true statement about how adding the dielectric affects to the capacitor?
The charge stored on the capacitor will increase.
In an experiment to investigate the properties of a capacitor, students connect a parallel plate capacitor to a variable voltage source as shown. To determine how the electric field between the plates of the capacitor changes as the potential difference across the plates changes, the students set up an electron emitter as shown to send a beam of electrons between the plates of the capacitor. When the voltage is turned on, it is observed that the beam is deflected upward. As the voltage is increased, the electrons are deflected more. Which of the following statements is supported by this observation?
The electric field between the plates is directed downward, and its strength increases with increasing voltage.
In an experiment, students study the variation of the capacitance C of a parallel plate capacitor as the distance d between the plates is changed. The students connect the capacitor to a battery and make measurements of d, the charge q stored on the capacitor, and potential difference ∆V across the plates of the capacitor. In an attempt to confirm the equations C = εA/d and C=q/∆V, students construct a graph of q/∆V as a function of 1/d, expecting a straight line trend for the data, but the data are significantly nonlinear. Which of the following could be one potential source of error?
The electric field between the plates of the capacitor becomes significantly nonuniform as the value of d increases.
An electron is moving in the direction shown above and is accelerating toward the disk, which has an electric charge. Which of the following makes a correct claim about the electric field produced by the disk and gives evidence to support this claim?
The electric field is to the right, because the electron accelerates to the left.
A solid nonconducting sphere is inside a solid nonconducting spherical shell, as shown in the figure. A total charge +Q is evenly distributed throughout the sphere and is also evenly distributed throughout the shell. Which of the following statements is a correct claim about the electric field at point X between the sphere and shell and has a valid supporting statement?
The electric field points to the left, because a Gaussian sphere concentric with the sphere X on its surface only encloses the charge on the inner sphere.
Two point charges with charges +2q and +q are separated by distance d. Several equipotential lines near the point charges and labeled points A, B, C, and D are shown in the figure. A third point charges of charge +3q is brought in from a large distance away and placed a distance d from each of the two original point charges, as shown above. Which of the following expressions is correct for the change of electric potential energy from the two-point charges system to the three-point charges system?
The electrical potential energy is increased by (9kq^2)/d
A capacitor with a dielectric of constant k is fully charged and then isolated. The dielectric is then removed from the capacitor. Which of the following claims about removing the dielectric from the isolated capacitor is correct? Responses
The energy stored in the capacitor increases by a factor of k.
A battery with internal resistance is connected to a variable resistor, as shown above. A voltmeter and an ammeter are used to measure the potential difference across the battery and the current in the circuit, respectively. These measurements are made with several different values of the variable resistance in the circuit. The graph above shows the voltmeter reading as a function of the ammeter reading. The experiment is repeated, but this time with a battery with the same voltage but no internal resistance. Which of the following is a change that will be observed in the graph?
The graph will be horizontal with a -intercept of 12V.
A sphere with charge +q is placed on the x-axis at position x = 3 m, as shown. Which of the following graphs best represents the x- component of the electric field due to the charge as a function of position x ?
The image of a negative vertical asymptote but at x = 3
An infinitely long, thin, nonconducting rod carrying charge −Q is placed inside an infinitely long metal cylinder that has no net charge. The cylinder is not grounded, and the rod does not touch the cylinder. Which of the following describes the distribution of charges on the cylinder?
The inside surface of the cylinder has a charge of +Q, and the outside surface has a charge of −Q, because the electric field inside the metal cylinder must be zero.
Students set up a simple series circuit consisting of a power source and a resistor. The students desire to obtain accurate readings for the potential difference across the resistor and the current through the resistor. Student A sets up an ammeter in series with the resistor, and the voltmeter is set up in parallel with the series combination of the ammeter and the resistor, as shown in the figure on the left below. Student B sets up the ammeter in series with the resistor, and the voltmeter is set up in parallel with just the resistor, as shown in the figure on the right below. Which of the following is the better setup to obtain accurate readings from the meters and explains why.
The setup for student B is better, because the potential difference across the ammeter will not be included in the measurement.
For an experiment, a student wants to maximize the power output for a circuit. The student has three resistors of resistances 5Ω, 10Ω, and 20Ω, and a 5V battery. Which of the following best describes how the students should arrange the resistors so that when they are connected to the battery it will maximize the power output for the circuit, and explains why?
The student should place all resistors in parallel, because the battery supplies more current to a parallel combination than to a series combination.
Students are devising an experiment to determining the effect of changing resistors have on the power supplied by a battery to a circuit. The students create the circuit shown, measure the current with the ammeter A, and determine the power. Which of the following procedures should the students use for their experiment?
Using the circuit with battery 1 and resistor 1, measure the current in the circuit and determine the power supplied by the battery. Then repeat this step substituting resistor 2 for resistor 1. Then repeat this step substituting resistor 3 for resistor 2.
Students perform an experiment using a circuit that contains two parallel plate capacitors. Capacitor C1 = 30uF is fully charged and connected to initially uncharged capacitor C2 = 60uF, as shown in the circuit. Which of the following is a correct hypothesis by the students regarding the relative magnitude of the potential difference V1 and V2 across the plates of capacitors C1 and C2, respectively, when the circuit reaches steady state?
V2 = V1
The four nonconducting rods shown below all have a uniform charge distribution of either Q or −Q on their top and bottom halves. A student claims that two of the rods produce a net electric field at labeled point P that is directed toward the top of the page. Is the student correct, and if so, which two diagrams support the claim?
Yes, figures A and C support the claim.
If the expression for the electric potential due to a small sphere of charge +Q at point P that is a distance D from the center of a small sphere is kQ/D, then the electric potential at a point O that is a distance 2D from the center of the small sphere is
kQ/2D
A positively charged conducting spherical shell of radius r is a distance D away from a second positively charged conducting spherical shell of radius R, where D >> R > r. The two shells are connected by a thin metal wire, and the equilibrium is established. At equilibrium, the small shell carries a charge +q and the large shell carries a charge +Q, as shown. Which of the following is a correct equation relating the radii of the shells and the charges on the shells?
q/r = Q/R
Circuits P and Q shown above consist of identical batteries, resistors, and capacitors. The switch is closed in each circuit. The time it takes for the capacitors in circuit Q to reach half their maximum charge is t. The time it takes for the capacitor in circuit to reach half its maximum charge is
t
An isolated conducting sphere of radius R is initially uncharged. A point charge +q is placed a distance r from the center C of the sphere, as shown in the figure. Points 1 and 2 are points on the surface of the sphere such that the point charge and points 1, 2, and C all fall on the same line. Which of the following is a correct for the potential difference (V1 - V2) between the electric potentials at points 1 and 2 on the surface of the sphere and gives evidence to support this claim?
∆V = 0, because the surface of the sphere is an equipotential surface.
