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College Physics for AP® Courses 2e

Test Prep for AP® Courses

College Physics for AP® Courses 2eTest Prep for AP® Courses

21.1 Resistors in Series and Parallel

1.
A circuit is shown as a rectangle with an extra line connecting the top and bottom having resistor Y. The top of this circuit has a 2-volt battery to the left of the Y resistor line, the left side of this circuit has a point P marked and then a 14-volt battery, the bottom has a resistor X to the left of the Y resistor line, and the right side has a resistor Z.
Figure 21.54

The figure above shows a circuit containing two batteries and three identical resistors with resistance R. Which of the following changes to the circuit will result in an increase in the current at point P? Select two answers.

  1. Reversing the connections to the 14 V battery.
  2. Removing the 2 V battery and connecting the wires to close the left loop.
  3. Rearranging the resistors so all three are in series.
  4. Removing the branch containing resistor Z.
2.

In a circuit, a parallel combination of six 1.6-kΩ resistors is connected in series with a parallel combination of four 2.4-kΩ resistors. If the source voltage is 24 V, what will be the percentage of total current in one of the 2.4-kΩ resistors?

  1. 10%
  2. 12%
  3. 20%
  4. 25%
3.

If the circuit in the previous question is modified by removing some of the 1.6 kΩ resistors, the total current in the circuit is 24 mA. How many resistors were removed?

  1. 1
  2. 2
  3. 3
  4. 4
4.
A circuit is shown that has nothing on the top or bottom, a battery to the left, and 2R resistor on the right. Additionally, there is an R resistor connecting the top and bottom of the circuit between the left and right sides of the circuit.
Figure 21.55

Two resistors, with resistances R and 2R are connected to a voltage source as shown in this figure. If the power dissipated in R is 10 W, what is the power dissipated in 2R?

  1. 1 W
  2. 2.5 W
  3. 5 W
  4. 10 W
5.

In a circuit, a parallel combination of two 20-Ω and one 10-Ω resistors is connected in series with a 4-Ω resistor. The source voltage is 36 V.

  1. Find the resistor(s) with the maximum current.
  2. Find the resistor(s) with the maximum voltage drop.
  3. Find the power dissipated in each resistor and hence the total power dissipated in all the resistors. Also find the power output of the source. Are they equal or not? Justify your answer.
  4. Will the answers for questions (a) and (b) differ if a 3 Ω resistor is added in series to the 4 Ω resistor? If yes, repeat the question(s) for the new resistor combination.
  5. If the values of all the resistors and the source voltage are doubled, what will be the effect on the current?

21.2 Electromotive Force: Terminal Voltage

6.

Suppose there are two voltage sources – Sources A and B – with the same emfs but different internal resistances, i.e., the internal resistance of Source A is lower than Source B. If they both supply the same current in their circuits, which of the following statements is true?

  1. External resistance in Source A’s circuit is more than Source B’s circuit.
  2. External resistance in Source A’s circuit is less than Source B’s circuit.
  3. External resistance in Source A’s circuit is the same as Source B’s circuit.
  4. The relationship between external resistances in the two circuits can’t be determined.
7.

Calculate the internal resistance of a voltage source if the terminal voltage of the source increases by 1 V when the current supplied decreases by 4 A? Suppose this source is connected in series (in the same direction) to another source with a different voltage but same internal resistance. What will be the total internal resistance? How will the total internal resistance change if the sources are connected in the opposite direction?

21.3 Kirchhoff’s Rules

8.

An experiment was set up with the circuit diagram shown. Assume R1 = 10 Ω, R2 = R3 = 5 Ω, r = 0 Ω and E = 6 V.

A circuit is drawn with points a, b, and c across the top from left to right and points h, g, and f across the bottom from left to right. Segment ah from top to bottom has a battery with voltage E and a resistor with resistance r. Segment bg from top to bottom has point i, a resistor marked R1, and point j. Segment cf from top to bottom has resistor with resistance R2, point d, point e, and a resistor with resistance R3.
Figure 21.56

  1. One of the steps to examine the set-up is to test points with the same potential. Which of the following points can be tested?

    1. Points b, c and d.
    2. Points d, e and f.
    3. Points f, h and j.
    4. Points a, h and i.

  2. At which three points should the currents be measured so that Kirchhoff’s junction rule can be directly confirmed?

    1. Points b, c and d.
    2. Points d, e and f.
    3. Points f, h and j.
    4. Points a, h and i.

  3. If the current in the branch with the voltage source is upward and currents in the other two branches are downward, i.e. Ia = Ii + Ic, identify which of the following can be true? Select two answers.

    1. Ii = Ij - If
    2. Ie = Ih - Ii
    3. Ic = Ij - Ia
    4. Id = Ih - Ij

  4. The measurements reveal that the current through R1 is 0.5 A and R3 is 0.6 A. Based on your knowledge of Kirchoff’s laws, confirm which of the following statements are true.

    1. The measured current for R1 is correct but for R3 is incorrect.
    2. The measured current for R3 is correct but for R1 is incorrect.
    3. Both the measured currents are correct.
    4. Both the measured currents are incorrect.

  5. The graph shown in the following figure is the energy dissipated at R1 as a function of time.

    Plot of t versus E with a solid line drawn from the origin O to (E1, t1).
    Figure 21.57

    Which of the following shows the graph for energy dissipated at R2 as a function of time?

    1. Plot of t versus E with a solid line drawn from the origin O to (2E1, t1).
      Figure 21.58
    2. Plot of t versus E with a solid line drawn from the origin O to (E1, t1).
      Figure 21.59
    3. Plot of t versus E with a solid line drawn from the origin O to (E1/2, t1).
      Figure 21.60
    4. Plot of t versus E with a solid line drawn from the origin O to (E1/4, t1).
      Figure 21.61
9.

For this question, consider the circuit shown in the following figure.

Circuit that across the top from left to right goes point b, battery with voltage E1, point c, resistor with resistance r1, and point d; across the middle goes point a, battery with voltage E2, point k, resistor with resistance r2, point l, resistor with resistance R2, and point e; across the bottom goes point j, battery with voltage E3, point i, resistor with resistance r3, and point h; along the left side from top to bottom goes a resistor with resistance R1, point a, and a resistor with resistance R3; and along the right side goes a resistor with resistance R5, point e, a resistor with resistance r4, point f, a battery with voltage E4, and point g. Additionally, there are three arrows showing the direction of the current: one between point a and the resistor with resistance R1 pointing up; another between point a and the battery with voltage E2 pointing right; and another between point j and the resistor with resistance R3 pointing up.
Figure 21.62

  1. Assuming that none of the three currents (I1, I2, and I3) are equal to zero, which of the following statements is false?

    1. I3 = I1 + I2 at point a.
    2. I2 = I3 - I1 at point e.
    3. The current through R3 is equal to the current through R5.
    4. The current through R1 is equal to the current through R5.

  2. Which of the following statements is true?

    1. E1 + E2 + I1R1 - I2R2 + I1r1 - I2r2 + I1R5 = 0
    2. - E1 + E2 + I1R1 - I2R2 + I1r1 - I2r2 - I1R5 = 0
    3. E1 - E2 - I1R1 + I2R2 - I1r1 + I2r2 - I1R5 = 0
    4. E1 + E2 - I1R1 + I2R2 - I1r1 + I2r2 + I1R5 = 0

  3. If I1 = 5 A and I3 = -2 A, which of the following statements is false?

    1. The current through R1 will flow from a to b and will be equal to 5 A.
    2. The current through R3 will flow from a to j and will be equal to 2 A.
    3. The current through R5 will flow from d to e and will be equal to 5 A.
    4. None of the above.

  4. If I1 = 5 A and I3 = -2 A, I2 will be equal to

    1. 3 A
    2. -3 A
    3. 7 A
    4. -7 A
10.
A circuit with nothing on the top or bottom, but a battery marked E on the left, a resistor marked R1 in the middle, and a resistor marked R2 on the right.
Figure 21.63

In an experiment this circuit is set up. Three ammeters are used to record the currents in the three vertical branches (with R1, R2, and E). The readings of the ammeters in the resistor branches (i.e. currents in R1 and R2) are 2 A and 3 A respectively.

  1. Find the equation obtained by applying Kirchhoff’s loop rule in the loop involving R1 and R2.
  2. What will be the reading of the third ammeter (i.e. the branch with E)? If E were replaced by 3E, how would this reading change?
  3. If the original circuit is modified by adding another voltage source (as shown in the following circuit), find the readings of the three ammeters.
A circuit a battery marked E on the left, a resistor marked R1 in the middle, and a resistor marked R2 on the right. There is nothing on the bottom, and on the top, there is a battery marked 2E between the two resistors.
Figure 21.64
11.
Circuit with a battery with voltage E1 and resistor with resistance r1 across the top from left to right; point A, a resistor with resistance R1, and point B across the middle; and a battery marked E2 and a resistor with resistance r2 across the bottom. Additionally, on the left, from top to bottom there is a resistor with resistance R2 and point A; on the right, from top to bottom there is point B and a resistor with resistance R3.
Figure 21.65

In this circuit, assume the currents through R1, R2 and R3 are I1, I2 and I3 respectively and all are flowing in the clockwise direction.

  1. Find the equation obtained by applying Kirchhoff’s junction rule at point A.
  2. Find the equations obtained by applying Kirchhoff’s loop rule in the upper and lower loops.
  3. Assume R1 = R2 = 6 Ω, R3 = 12 Ω, r1 = r2 = 0 Ω, E1 = 6 V and E2 = 4 V. Calculate I1, I2 and I3.
  4. For the situation in which E2 is replaced by a closed switch, repeat parts (a) and (b). Using the values for R1, R2, R3, r1 and E1 from part (c) calculate the currents through the three resistors.
  5. For the circuit in part (d) calculate the output power of the voltage source and across all the resistors. Examine if energy is conserved in the circuit.
  6. A student implemented the circuit of part (d) in the lab and measured the current though one of the resistors as 0.19 A. According to the results calculated in part (d) identify the resistor(s). Justify any difference in measured and calculated value.

21.6 DC Circuits Containing Resistors and Capacitors

12.

A battery is connected to a resistor and an uncharged capacitor. The switch for the circuit is closed at t = 0 s.

  1. While the capacitor is being charged, which of the following is true?

    1. Current through and voltage across the resistor increase.
    2. Current through and voltage across the resistor decrease.
    3. Current through and voltage across the resistor first increase and then decrease.
    4. Current through and voltage across the resistor first decrease and then increase.

  2. When the capacitor is fully charged, which of the following is NOT zero?

    1. Current in the resistor.
    2. Voltage across the resistor.
    3. Current in the capacitor.
    4. None of the above.
13.

An uncharged capacitor C is connected in series (with a switch) to a resistor R1 and a voltage source E. Assume E = 24 V, R1 = 1.2 kΩ and C = 1 mF.

  1. What will be the current through the circuit as the switch is closed? Draw a circuit diagram and show the direction of current after the switch is closed. How long will it take for the capacitor to be 99% charged?
  2. After full charging, this capacitor is connected in series to another resistor, R2 = 1 kΩ. What will be the current in the circuit as soon as it’s connected? Draw a circuit diagram and show the direction of current. How long will it take for the capacitor voltage to reach 3.24 V?
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