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AP Physics C Electricity and Magnetism

AP Physics C Electricity and Magnetism Practice Test: Practice Test 11

Practice Test 11 for AP Physics C Electricity and Magnetism: real questions and explanations from the Varsity Tutors practice-test pool.

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Question 1 of 25

Three resistors R1, R2, and R3 and the capacitor, C, are connected to an ideal battery V to complete the circuit as shown.

Ps0_capacitorcircuit

After the circuit has been connected for a very long time, the currents in each branch of the circuit are measured to be some values , , and , and the charge on the capacitor some value .

Which of the following equations is a correct expression regarding the voltage of the circuit after a long time?

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Question 1

Three resistors R1, R2, and R3 and the capacitor, C, are connected to an ideal battery V to complete the circuit as shown.

Ps0_capacitorcircuit

After the circuit has been connected for a very long time, the currents in each branch of the circuit are measured to be some values , , and , and the charge on the capacitor some value .

Which of the following equations is a correct expression regarding the voltage of the circuit after a long time?

  1. (correct answer)

Explanation: Identifying the sum of the voltage drops and rises (Kirchoff's Loop Law) around the three possible loops of this circuit is the key to answering this question correctly. The following signs can be assigned to each of the circuit elements based on the direction of the currents given. Ps0_capacitorcircuit_2 Use Ohm's law and the equation for capacitance to derive terms for the voltage across each element of the circuit. There are three possible paths through the circuit, resulting in three correct equations that could be derived: Only one of the given answer options matches up correctly to these.

Question 2

Which would decrease the capacitance of a parallel-plate capacitor?

  1. Replacing the material between the plates with a material of a lower dielectric constant (correct answer)
  2. Moving the plates closer together
  3. Increasing the area of the plates
  4. Replacing the material between the plates with a material of a higher dielectric constant
  5. Increasing the voltage across the capacitor

Explanation: The capacitance of a parallel-plate capacitor is given by C = εA⁄d. Changing the voltage across the capacitor will not affect its capacitance - the capacitance is an inherent quality of the geometry and construction of the capacitor. Moving the plates closer together, increasing the area of the plates, and replacing the material between the plates with a material of a higher dielectric constant would all increase the capacitance. The correct answer is replacing the material between the plates with a material of a lower dielectric constant.

Question 3

Ap physics c e m potential problems 2 6 16 1

Two point charges and are separated by a distance . Calculate the potential at point P, a distance from charge in the direction perpendicular to the line connecting the two charges.

  1. (correct answer)

Explanation: By the Pythagorean theorem, the distance from point P to charge is . Because point P is also from charge , it follows that the potential is

Question 4

A point charge of exerts a force of on another charge with . How far apart are the two charges?

  1. (correct answer)

Explanation: To find the distance between the two charges, use Coulomb's Law. Since we want to find distance, , we solve for . We know the values of the force and the two charges. We can plug in these values and solve for the distance.

Question 5

Ap physics c e m potential problems 2 6 16 1 1

A uniformly charged hollow disk has inner radius and outer radius , and carries a total charge . Calculate the potential a distance from the center, on the axis of the disk.

  1. (correct answer)

Explanation: Use a polar coordinate system with surface charge density and area element . The distance from the point of interest to a point a distance from the center is , so the potential is

Question 6

A wire loop of area is placed in a magnetic field whose magnitude varies with time according to the equation . The loop is held in place, perpendicular to the field. If the wire has resistance , what is the magnitude of the maximum instantaneous current induced in the loop?

  1. (correct answer)

Explanation: Relevant equations: Write the expression for the flux using the given expression for the magnetic field strength: Take the derivative of this flux to find the induced emf: Determine the maximum value of , and replace with this value, to find the maximum induced emf: Plug this maximum induced emf into , to find the maximum induced current:

Question 7

A parallel plate capacitor has a capacitance of . If the plates are apart, what is the area of the plates?

  1. (correct answer)

Explanation: The relationship between capacitance, distance, and area is . We can rearrange this equation to solve for area. Now, we can use the values given in teh question to solve.

Question 8

We have a point charge of . Determine the electric field at a distance of away from that charge.

  1. (correct answer)

Explanation: Coulomb's law for the electric field from point charges is , where we know the values of the following variables. Using these values, we can solve for the electric field.

Question 9

A proton moves in a straight line for a distance of . Along this path, the electric field is uniform with a value of . Find the work done on the proton by the electric field.

The charge of a proton is .

  1. (correct answer)

Explanation: Work done by an electric field is given by the product of the charge of the particle, the electric field strength, and the distance travelled. We are given the charge (), the distance (), and the field strength (), allowing us to calculate the work.

Question 10

A battery is measured to have a potential of 5V. When connected to a wire with no resistors or other components, the voltage measured is 4.9V.

Why was the potential of the battery measured differently when the wire was connected?

  1. The wire has a slight internal resistance and caused a potential drop (correct answer)
  2. Once the current is distributed across the wire, there is less charge per unit length of the circuit and so the voltage is lower
  3. The wire is causing electrons to be lost to the air, which lowers the potential measured
  4. The difference in potential measured is small enough to be disregarded
  5. The wire connected to the battery must be connected to something else where this potential is being lost

Explanation: All wires have at least some internal resistance. The most likely explanation for this is that the wire is displaying slight resistance, and therefore caused the measured potential to be less than it was before.

Question 11

Starting from rest, a skateboarder travels down a 25o incline that's 22m long. Using conservation of energy, calculate the skateboarder's speed when he reaches the bottom. Ignore friction.

  1. (correct answer)

Explanation: Conservation of energy states that . The skateboarder starts from rest; thus, and . At the bottom of the incline, and . Solve for v. Using trigonometry, .

Question 12

An object of mass 0.5 kg is accelerating with a vector (2, 4). A drag force of (-1, 3) is acting upon this object. Which of the following represents the vector of the other agent acting upon the object?

  1. (2, -1) (correct answer)
  2. (1, 7)
  3. (-3, -1)
  4. (-1, 2)
  5. (3, 1)

Explanation: To figure out the force vector of the other agent acting on the object, let's recall Newton's Second Law of Motion:(-1, 3) + (x1, y1) = 0.5(2, 4)(x1 - 1, y1 + 3) = (1, 2)x1 - 1 = 1x1 = 2y1 + 3 = 2y1 = -1So the force vector of the other agent acting on the object is (2, -1).

Question 13

A mass oscillates on a spring with period . If the mass is doubled, what is the new period of oscillation?

  1. (correct answer)

Explanation: The formula for the period of oscillation is . When we double the mass, we get: Because the new factor of 2 is under the square root sign, and also in the numerator, the new period will be increased by .

Question 14

If a particle moves with a constant velocity of 6 meters per second, find the position function if the particle begins at position x = 10 meters.

  1. x(t) = 6t + 10 (correct answer)
  2. x(t) = 6t - 10
  3. x(t) = 10t - 6
  4. x(t) = 10t + 6
  5. x = 6t

Explanation: To find the position function when given a velocity function, we need to integrate the velocity function and apply the initial condition to the antiderivative. The antiderivative of a constant velocity function of 6 meters per second is 6t. Applying the initial condition that x(0) = 10, we find that x(t) = 6t + 10.

Question 15

Three point charges are arranged around the origin, as shown.

Ps0_threechargepotential

Calculate the total electric potential at the origin due to the three point charges.

  1. (correct answer)

Explanation: Electric potential is a scalar quantity given by the equation: To find the total potential at the origin due to the three charges, add the potentials of each charge.

Question 16

Three resistors and a battery form the following circuit.

Circuit_1

Calculate the equivalent resistance if the resistors have the following values.

  1. (correct answer)

Explanation: First, calculate the equivalent resistance of and . Since these two resistors are arranged in series, we just take the sum of their values. With resistors 2 and 3 combined together in a single value, the following circuit is formed. Circuit_2 Notice that and are arranged in parallel. To calculate the equivalent resistance of this parallel pair, we use the following equation. Plug in the values, and solve for . This is just like the circuit shown below. Circuit_3

Question 17

The plates of a parallel plate capacitor are apart and in area. A potential difference of is applied across the capacitor. Find the capacitance.

  1. (correct answer)

Explanation: Capacitance is related to plate area and distance by the equation . Given the area and distance, we can solve for capacitance. The voltage, in this case, is irrelevant.

Question 18

A charge, , is enclosed by two spherical surfaces of radii and , with . The cross-sectional side view is shown.

Ps0_gauss

Which is the correct relationship between the electric flux passing through the two spherical surfaces around the point charge?

  1. (correct answer)

Explanation: Electric flux is given by either side of the equation of Gauss's Law: Since the charge is the same for both spherical surfaces, even though these surfaces are of different radii, the amounts of electric flux passing through each surface is the same.

Question 19

A spherical asteroid has a hole drilled through the center as diagrammed below:

Hole through planet

Refer to the diagram above. An object that is much smaller than the asteroid is released from rest at the surface of the asteroid, at point a. How do the velocity and acceleration of the object compare at point b at the surface, and point a, located at the center of the asteroid?

  1. and (correct answer)
  2. and
  3. and
  4. and
  5. and

Explanation: Because the gravitational force depends only on the mass beneath the object (which is the gravitational version of Gauss's Law for charge), the acceleration steadily decreases as the object falls, and drops to zero at the center. Nevertheless, the velocity keeps increasing as the object falls, it just does so more slowly.

Question 20

A box of mass 6 kg slides down an inclined ramp with height of 5 m. If the box initially starts at rest, what is the speed of the box as it hits the ground?

  1. 10 m/s (correct answer)
  2. 5 m/s
  3. 6 m/s
  4. 4 m/s
  5. 2 m/s

Explanation: Using the conservation of energy, we know that the final energy is equal to the initial energy. We also know that the initial kinetic energy is 0 because the box starts from rest, and we know that the final potential energy is 0 because the height of the ground is 0. So our new equation for the conservation of energy is:mghinitial = 1⁄2mvfinal22gh = vfinal2(2)(10 m/s2)(5 m) = vfinal2So the velocity of the box as it hits the ground is 10 m/s.

Question 21

The units of the electric field are N⁄C. What are the units of electric potential?

  1. J⁄A⋅s (correct answer)
  2. J⁄A
  3. J
  4. J2
  5. J⋅m⁄s

Explanation: From the electric field equation kq⁄r2 and the potential equation kq⁄r, we can deduce that the units of electric potential are the units of the electric field multiplied by a factor of m (for meters, which is the unit of r in the denominator). Since N⋅m=J, one expression of the dimensions of the electric potential is J⁄C. An ampere is the unit for current, which expresses the flow of charge, and A=C⁄s, so we can write the unit for electric potential as J⁄A⋅s.

Question 22

A battery is measured to have a potential of 5V. When connected to a wire with no resistors or other components, the voltage measured is 4.9V.

If the current through the wire is measured to be 2A, how much thermal energy is being lost per second as soon as the wire is connected to the battery?

  1. (correct answer)

Explanation: First, we must know that the wire has some internal resistance . To calculate this, we need to know the potential drop through the wire, which must be the difference we saw from the initial voltage reading to the second. This value, 0.1V, we plug into Ohm's law to calculate the resistance of the wire. The question asks for energy lost per second; this value is equivalent to the power. Use our values to solve.

Question 23

Ap physics c e m potential problems 2 6 16 1 2

Three equal point charges are placed at the vertices of an equilateral triangle of side length . Calculate the potential at the center of the triangle, labeled P.

  1. (correct answer)

Explanation: Draw a line from the center perpendicular to any side of the triangle. This line divides the side into two equal pieces of length . From the center, draw another line to one of the vertices at the end of this side. This produces a 30-60-90 triangle with longer leg , so the hypotenuse (the distance from the vertex to the center) is . The potential at the center is due to three of these charges, so it must be

Question 24

A point charge of exerts a force of on another charge with . How far apart are the two charges?

  1. (correct answer)

Explanation: To find the distance between the two charges, use Coulomb's Law. Since we want to find distance, , we solve for . We know the values of the force and the two charges. We can plug in these values and solve for the distance.

Question 25

An infinitely long wire has a current of running through it. Calculate the magnetic field at a distance away from the wire.

  1. (correct answer)

Explanation: For infinitely long wires, the formula for the magnetic field is , where is the current and is the distance from the wire. The magnetic field is calculated using our given values.