Concepts & Calculations

Note: Each of these problems consists of Concept Questions followed by a related quantitative Problem. The Concept Questions involve little or no mathematics. They focus on the concepts with which the problems deal. Recognizing the concepts is the essential initial step in any problem-solving technique.

| 117 | Concept Questions The resistance and the magnitude of the current depend on the path that the current takes. The drawing shows three situations in which the current takes different paths through a piece of material. Rank them according to (a) resistance and (b) current, largest first. Give your reasoning.
Problem Each of the rectangular pieces is made from a material whose resistivity is , and the unit of length in the drawing is L0 = 5.00 cm. If the material is connected to a 3.00-V battery, find (a) the resistance and (b) the current in each case. Verify that your answers are consistent with your answers to the Concept Questions.

| 118 | Concept Questions Each of the four circuits in the drawing consists of a single resistor whose resistance is either R or 2R, and a single battery whose voltage is either V or 2V. Rank the circuits according to (a) the power and (b) the current delivered to the resistor, largest to smallest. Explain your answers.
Problem The unit of voltage in each circuit is V = 12.0 V and the unit of resistance is . Determine (a) the power supplied to each resistor and (b) the current delivered to each resistor. Check to see that your answers are consistent with your answers to the Concept Questions.

| 119 | Concept Questions The drawing shows three different resistors in two different circuits. The resistances are such that R1 > R2 > R3. (a) For the circuit on the left, rank the current through each resistor and the voltage across each one, largest first. (b) Repeat part (a) for the circuit on the right. Justify your answers.
Problem The battery has a voltage of V = 24.0 V, and the resistors have values of . (a) For the circuit on the left, determine the current through and the voltage across each resistor. (b) Repeat part (a) for the circuit on the right. Be sure your answers are consistent with your answers to the Concept Questions.

| 120 | Concept Question The circuit in the drawing contains three identical resistors. Consider the equivalent resistance between the two points a and b, b and c, and a and c. Rank the equivalent resistances in decreasing order. Explain your reasoning.

Problem Each resistor has a value of . Determine the equivalent resistance between the points a and b, b and c, and a and c. Check to see that your answers are consistent with your answer to the Concept Question.

| 121 | Concept Question Parts a and b of the drawing contain a resistor and a battery. Using the direction of the current as a guide, label the ends of each resistor with + and − signs. In both cases, proceed from point A to point B and determine the potential drops and potential rises. Express the drops and rises in terms of the current I, the resistance R, and the battery voltage V.

| Potential drops | Potential rises
Part a |  |
Part b |  |

Problem Using Kirchhoff’s loop rule, find the value of the current I in part c of the drawing.

| 122 | Concept Question Two capacitors, C1 and C2, are connected to a battery whose voltage is V. Recall from Section 19.5 that the electrical energy stored by each capacitor is and , where V1 and V2 are, respectively, the voltages across C1 and C2. If the capacitors are connected in series, is the total energy stored by them greater than, less than, or equal to the total energy stored when they are connected in parallel? Justify your answer.
Problem The battery voltage is V = 60.0 V, and the capacitances are and . Determine the total energy stored by the two capacitors when they are wired (a) in parallel and (b) in series. Check to make sure that your answer is consistent with your answer to the Concept Question.

| 123 | Concept Questions The drawing shows two circuits, and the same battery is used in each. The two resistances RA in circuit A are the same, and the two resistances RB in circuit B are the same. (a) How is the total power delivered by the battery related to the equivalent resistance connected between the battery terminals and to the battery voltage? (b) When two resistors are connected in series, is the equivalent resistance of the combination greater than, smaller than, or equal to the resistance of either resistor alone? (c) When two resistors are connected in parallel, is the equivalent resistance of the combination greater than, smaller than, or equal to the resistance of either resistor alone? (d) The same total power is delivered by the battery in circuits A and B. Is RB greater than, smaller than, or equal to RA?

Problem Knowing that the same total power is delivered in each case, find the ratio RB/RA for the circuits in the drawing. Verify that your answer is consistent with your answer to Concept Question (d).

| 124 | Concept Questions Each resistor in the three circuits in the drawing has the same resistance R, and the batteries have the same voltage V. (a) How is the total power delivered by the battery related to the equivalent resistance connected between the battery terminals and to the battery voltage? (b) Rank the equivalent resistances of the circuits in descending order (largest first). (c) Rank the three values of the total power delivered by the batteries in descending order (largest first).
Problem The values for R and V in the drawing are 9.0 Ω and 6.0 V, respectively. Determine the total power delivered by the battery in each of the three circuits. Be sure that your answer is consistent with your answer to Concept Question (c).

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