AP Physics 2 Compilation of circuits problems

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AP Physics B CH 21, 24
NAME ____________________________________
______1. Which two arrangements of resistors shown above have the same resistance between the terminals?
(A) I and II (B) I and IV
(C) II and III (D) II and IV
(E) III and IV
______2. In the circuit shown above, what is the value of the potential difference between points X and Y if the
6-volt battery has no internal resistance?
(A) 1 V (B) 2 V
(C) 3 V
( D) 4 V (E) 6V
______3. One joule of work is needed to move one coulomb of charge from one point to another with no change in
velocity. Which of the following is true between the two points?
(A) The resistance is one ohm.
(B) The current is one ampere.
(C) The potential difference is one volt.
(D) The electric field strength is one newton per coulomb.
(E) The electric field strength is one joule per electron.
______4. A lamp, a voltmeter V, an ammeter A, and a battery with zero internal resistance are connected as shown
above. Connecting another lamp in parallel with the first lamp as shown by the dashed lines would
(A) increase the ammeter reading (B) decrease the ammeter reading
(C) increase the voltmeter reading (D) decrease the voltmeter reading
(E) produce no change in either meter reading
Questions 5 – 6 relate to the five incomplete circuits below composed of resistors R, all of equal resistance, and
capacitors C, all of equal capacitance. A battery that can be used to complete any of the circuits is available.
______5. Into which circuit should the battery be connected to obtain the greatest steady power dissipation?
(A) A
(B) B
(C) C
(D) D
(E) E
______6. Which circuit will retain stored energy if the battery is connected to it and then disconnected?
(A) A
(B) B
(C) C
(D) D
(E) E
______7. The five resistors shown below have the lengths and cross-sectional areas indicated and are made of
material with the same resistivity. Which has the greatest resistance?
______8. Two capacitors are connected in parallel as shown above. A voltage V is applied to the pair. What is the
ratio of charge stored on C1 to the charge stored on C2, when C1 = 1.5C2 ?
(A) 4/9
(B) 2/3
(C) 1
(D) 3/2
(E) 9/4
______9. The circuit shown above left is made up of a variable resistor and a battery with negligible internal
resistance. A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery
is given above right. What is the emf of the battery?
(A) 0.025 V (B) 0.67 V (C) 2.5 V (D) 6.25 V (E) 40 V
______10. The total equivalent resistance between points X and Y in the circuit shown above is
(A) 3 Q
(B) 4 Q
(C) 5 Q
(D) 6 Q
(E) 7 Q
______11. In the circuit shown above, the value of r for which the current I is 0.5 ampere is
(A) 0 
(B) 1 
(C) 5 
(D) 10 
(E) 20 
______12. Which of the following will cause the electrical resistance of certain materials known as superconductors
to suddenly decrease to essentially zero?
(A) Increasing the voltage applied to the material beyond a certain threshold voltage
(B) Increasing the pressure applied to the material beyond a certain threshold pressure
(C) Cooling the material below a certain threshold temperature
(D) Stretching the matenal to a wire of sufficiently small diameter
(E) Placing the material in a sufficiently large magnetic field
______13. Kirchhoff’s loop rule for circuit analysis is an expression of which of the following?
(A) Conservation of charge
(B) Conservation of energy
(C) Ampere's law
(D) Faraday's law
(E) Ohm's law
Questions 14-15 refer to the circuit shown below.
______14. The equivalent capacitance for this network is most nearly
(A) 10/7 F
(B) 3/2 F (C) 7/3 F (D) 7 F (E) 14 F
______15. The charge stored in the 5-microfarad capacitor is most nearly
(A) 360 C
(B) 500 C
(C) 710 C
(D) 1,100 C
(E) 1,800 C
Questions 16-18 relate to the following circuit diagram which shows a battery with an internal resistance of 4.0
ohms connected to a 16-ohm and a 20-ohm resistor in series. The current in the 20-ohm resistor is 0.3 amperes
______16. What is the emf of the battery?
(A) 1..2 V (B) 6.0 V
(C) 10.8 V
(D) 12.0 V
(E) 13.2 V
______17. What is the potential difference across the terminals X and Y of the battery?
(A) 1.2 V
(B) 6.0 V (C) 10.8 V (D) 12.0 V (E) 13.2 V
______18. What power is dissipated by the 4-ohm internal resistance of the battery?
(A) 0.36 W (B) 1.2 W (C) 3.2 W (D) 3.6 W (E) 4.8 W
______19. The product
2 amperes x 2 volts x 2 seconds
is equal to
(A) 8 coulombs
(B) 8 newtons
(C) 8 joules
(D) 8 calories
(E) 8 newton-amperes
______20. A certain coffeepot draws 4.0 A of current when it is operated on 120 V household lines. If electrical
energy costs 10 cents per kilowatt-hour, how much does it cost to operate the coffeepot for 2 hours?
(A) 2.4 cents
(B) 4.8 cents
(C) 8.0 cents
(D) 9.6 cents
(E) 16 cents
______21. The total resistance of a wire loop of radius b is R. What is the resistance of the wire loop of radius 2b?
(A) R/4
(B) R/2
(C) R
(D) 2R
(E) 4R
______22. In the diagrams above, resistors R1 and R2 are shown in two different connections to the same source of
emf  that has no internal resistance. How does the power dissipated by the resistors in these two cases
compare?
(A) It is greater for the series connection.
(B) It is greater for the parallel connection.
(C) It is the same for both connections.
(D) It is different for each connection, but one must know the values of R1 and R2 to know which is greater.
(E) It is different for each connection, but one must know the value of  to know which is greater.
Questions 22-23 refer to the following diagram that shows part of a closed electrical circuit.
______23. The electrical resistance of the part of the circuit shown between point X and point Y is
(A) 4/3 
(B) 2 
(C) 2.75 
(D) 4 
(E) 6 
______24. When there is a steady current in the circuit, the amount of charge passing a point per unit of time is
(A) the same everywhere in the circuit
(B) greater at point X than at point Y
(C) greater in the 1  resistor than in the 2  resistor(D) greater in the 1  resistor than in the 3  resistor
(E) greater in the 2  resistor than in the 3  resistor
Extra Credit:
Name as many items you can think of, that are drawn(represented) on a circuit.
AP Physics B CH 21, 24 Testb
NAME _____________________________________
1) (10 points) In the circuit shown above, A, B. C, and D are identical lightbulbs. Assume that the battery maintains a
constant potential difference between its terminals (i.e., the internal resistance of the battery is assumed to be negligible)
and the resistance of each lightbulb remains constant.
a. Draw a diagram of the circuit in the box below, using the following symbols to represent the components in your
diagram. Label the resistors A, B. C, and D to refer to the corresponding lightbulbs.
b.
List the bulbs in order of their brightnesses, from brightest to least bright. If any two or more bulbs have the same
brightness, state which ones. Justify your answer.
c.
Bulb D is then removed from its socket.
i. Describe the change in the brightness, if any, of bulb A when bulb D is removed from its socket. Justify your answer.
ii.
Describe the change in the brightness, if any, of bulb B when bulb D is removed from its socket. Justify your answer.
2) (15 points) Three identical resistors, each of resistance 30  are connected in a circuit to heat water in a glass beaker.
24 V battery with negligible internal resistance provides the power.
a. The three resistors may be connected in series or in parallel.
i. If they are connected in series, what power is developed in the circuit?
ii. If they are connected in parallel, what power is developed in the circuit?
b. Using the battery and one or more of the resistors, design a circuit that will heat the water at the fastest rate when the
resistor(s) are placed in the water. Include an ammeter to measure the current in the circuit and a voltmeter to
measure the total potential difference of the circuit. Assume the wires are insulated and have no resistance. Draw a
diagram of the circuit in the box below, using the following symbols to represent the components in your diagram.
c. The resistor(s) in the circuit in part (b) are now immersed in a 0.5 kg sample of water, which is initially at 298 K. The
specific heat of water is 4,200 J/kg.K. Assume that all of the heat produced is absorbed by the water.
i. Calculate the amount of time it takes for the water to begin to boil.
ii. Under actual experimental conditions, would the time taken for the water to boil be longer or
shorter than the calculated time in part (c) i ? Justify your answer.
d. As the circuit continues to provide energy to the water, vapor is formed at the same temperature as the boiling water.
Where has the energy used to boil the water gone?
3) (15 points) A student is provided with a 12.0-V battery of negligible internal resistance and four resistors with the
following resistances: 100 , 30 , 20 , and 10 . The student also has plenty of wire of negligible resistance
available to make connections as desired.
a. Using all of these components, draw a circuit diagram in which each resistor has nonzero current flowing through it, but
in which the current from the battery is as small as possible.
b.
Using all of these components, draw a circuit diagram in which each resistor has nonzero current flowing through it, but
in which the current from the battery is as large as possible (without short circuiting the battery).
The battery and resistors are now connected in the circuit shown above.
c. Determine the following for this circuit.
i. The current in the 10- resistor
ii.
d.
The total power consumption of the circuit
Assuming that the current remains constant, how long will it take to provide a total of 10 kJ of electrical energy to the
circuit?
4) (15 points) A battery with an emf of 24 volts and an internal resistance of 1ohm is connected to an external circuit as
shown above. Determine each of the following:
a. the equivalent resistance of the combination of the 4-ohm, 8-ohm, and 12-ohm resistors
b. the current in the 5-ohm resistor
c. the terminal voltage, VAC of the battery
d. the rate at which energy is dissipated in the 12-ohm resistor
e. the magnitude of the potential difference VBC
f. the power delivered by the battery to the external circuit
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