College Physics

# Problems & Exercises

College PhysicsProblems & Exercises

## 21.1Resistors in Series and Parallel

Note: Data taken from figures can be assumed to be accurate to three significant digits.

1.

(a) What is the resistance of ten $275-Ω275-Ω size 12{"275"- %OMEGA } {}$ resistors connected in series? (b) In parallel?

2.

(a) What is the resistance of a $1.00×102-Ω1.00×102-Ω$, a $2.50-kΩ2.50-kΩ$, and a $4.00-kΩ4.00-kΩ size 12{4 "." "00""-k" %OMEGA } {}$ resistor connected in series? (b) In parallel?

3.

What are the largest and smallest resistances you can obtain by connecting a $36.0-Ω36.0-Ω$, a $50.0-Ω50.0-Ω size 12{"50" "." 0- %OMEGA } {}$, and a $700-Ω700-Ω size 12{"700"- %OMEGA } {}$ resistor together?

4.

An 1800-W toaster, a 1400-W electric frying pan, and a 75-W lamp are plugged into the same outlet in a 15-A, 120-V circuit. (The three devices are in parallel when plugged into the same socket.). (a) What current is drawn by each device? (b) Will this combination blow the 15-A fuse?

5.

Your car’s 30.0-W headlight and 2.40-kW starter are ordinarily connected in parallel in a 12.0-V system. What power would one headlight and the starter consume if connected in series to a 12.0-V battery? (Neglect any other resistance in the circuit and any change in resistance in the two devices.)

6.

(a) Given a 48.0-V battery and $24.0-Ω24.0-Ω size 12{"24" "." 0- %OMEGA } {}$ and $96.0-Ω96.0-Ω size 12{"96" "." 0- %OMEGA } {}$ resistors, find the current and power for each when connected in series. (b) Repeat when the resistances are in parallel.

7.

Referring to the example combining series and parallel circuits and Figure 21.6, calculate $I3I3 size 12{I rSub { size 8{3} } } {}$ in the following two different ways: (a) from the known values of $II size 12{I} {}$ and $I2I2 size 12{I rSub { size 8{2} } } {}$; (b) using Ohm’s law for $R3R3 size 12{R rSub { size 8{3} } } {}$. In both parts explicitly show how you follow the steps in the Problem-Solving Strategies for Series and Parallel Resistors.

8.

Referring to Figure 21.6: (a) Calculate $P3P3 size 12{P rSub { size 8{3} } } {}$ and note how it compares with $P3P3 size 12{P rSub { size 8{3} } } {}$ found in the first two example problems in this module. (b) Find the total power supplied by the source and compare it with the sum of the powers dissipated by the resistors.

9.

Refer to Figure 21.7 and the discussion of lights dimming when a heavy appliance comes on. (a) Given the voltage source is 120 V, the wire resistance is $0.400Ω0.400Ω size 12{0 "." "800" %OMEGA } {}$, and the bulb is nominally 75.0 W, what power will the bulb dissipate if a total of 15.0 A passes through the wires when the motor comes on? Assume negligible change in bulb resistance. (b) What power is consumed by the motor?

10.

A 240-kV power transmission line carrying $5.00×102A5.00×102A$ is hung from grounded metal towers by ceramic insulators, each having a $1.00×109-Ω1.00×109-Ω size 12{1 "." "00"´"10" rSup { size 8{9} } - %OMEGA } {}$ resistance. Figure 21.51. (a) What is the resistance to ground of 100 of these insulators? (b) Calculate the power dissipated by 100 of them. (c) What fraction of the power carried by the line is this? Explicitly show how you follow the steps in the Problem-Solving Strategies for Series and Parallel Resistors.

Figure 21.51 High-voltage (240-kV) transmission line carrying $5.00×102A5.00×102A$ is hung from a grounded metal transmission tower. The row of ceramic insulators provide $1.00×109Ω1.00×109Ω size 12{1 "." 0 times "10" rSup { size 8{9} } %OMEGA } {}$ of resistance each.
11.

Show that if two resistors $R1R1 size 12{R rSub { size 8{1} } } {}$ and $R2R2 size 12{R rSub { size 8{2} } } {}$ are combined and one is much greater than the other ($R1>>R2R1>>R2 size 12{R rSub { size 8{1} } ">>"R rSub { size 8{2} } } {}$): (a) Their series resistance is very nearly equal to the greater resistance $R1R1 size 12{R rSub { size 8{1} } } {}$. (b) Their parallel resistance is very nearly equal to smaller resistance $R2R2 size 12{R rSub { size 8{2} } } {}$.

12.

Unreasonable Results

Two resistors, one having a resistance of $145 Ω145 Ω size 12{1"45 " %OMEGA } {}$, are connected in parallel to produce a total resistance of $150Ω150Ω size 12{150 %OMEGA } {}$. (a) What is the value of the second resistance? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

13.

Unreasonable Results

Two resistors, one having a resistance of $900 kΩ900 kΩ size 12{9"00 k" %OMEGA } {}$, are connected in series to produce a total resistance of $0.500 MΩ0.500 MΩ size 12{0 "." "500 M" %OMEGA } {}$. (a) What is the value of the second resistance? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

## 21.2Electromotive Force: Terminal Voltage

14.

Standard automobile batteries have six lead-acid cells in series, creating a total emf of 12.0 V. What is the emf of an individual lead-acid cell?

15.

Carbon-zinc dry cells (sometimes referred to as non-alkaline cells) have an emf of 1.54 V, and they are produced as single cells or in various combinations to form other voltages. (a) How many 1.54-V cells are needed to make the common 9-V battery used in many small electronic devices? (b) What is the actual emf of the approximately 9-V battery? (c) Discuss how internal resistance in the series connection of cells will affect the terminal voltage of this approximately 9-V battery.

16.

What is the output voltage of a 3.0000-V lithium cell in a digital wristwatch that draws 0.300 mA, if the cell’s internal resistance is $2.00Ω2.00Ω size 12{2 "." "00" %OMEGA } {}$?

17.

(a) What is the terminal voltage of a large 1.54-V carbon-zinc dry cell used in a physics lab to supply 2.00 A to a circuit, if the cell’s internal resistance is $0.100 Ω0.100 Ω size 12{0 "." "100" %OMEGA } {}$? (b) How much electrical power does the cell produce? (c) What power goes to its load?

18.

What is the internal resistance of an automobile battery that has an emf of 12.0 V and a terminal voltage of 15.0 V while a current of 8.00 A is charging it?

19.

(a) Find the terminal voltage of a 12.0-V motorcycle battery having a $0.600-Ω0.600-Ω size 12{0 "." "600"- %OMEGA } {}$ internal resistance, if it is being charged by a current of 10.0 A. (b) What is the output voltage of the battery charger?

20.

A car battery with a 12-V emf and an internal resistance of $0.050Ω0.050Ω size 12{0 "." "050" %OMEGA } {}$ is being charged with a current of 60 A. Note that in this process the battery is being charged. (a) What is the potential difference across its terminals? (b) At what rate is thermal energy being dissipated in the battery? (c) At what rate is electric energy being converted to chemical energy? (d) What are the answers to (a) and (b) when the battery is used to supply 60 A to the starter motor?

21.

The hot resistance of a flashlight bulb is $2.30Ω2.30Ω size 12{2 "." "30" %OMEGA } {}$, and it is run by a 1.58-V alkaline cell having a $0.100-Ω0.100-Ω size 12{0 "." "100"- %OMEGA } {}$ internal resistance. (a) What current flows? (b) Calculate the power supplied to the bulb using $I2RbulbI2Rbulb size 12{I rSup { size 8{2} } R rSub { size 8{"bulb"} } } {}$. (c) Is this power the same as calculated using $V2RbulbV2Rbulb size 12{ { {V rSup { size 8{2} } } over {R rSub { size 8{"bulb"} } } } } {}$?

22.

The label on a portable radio recommends the use of rechargeable nickel-cadmium cells (nicads), although they have a 1.25-V emf while alkaline cells have a 1.58-V emf. The radio has a $3.20-Ω3.20-Ω size 12{3 "." "20"- %OMEGA } {}$ resistance. (a) Draw a circuit diagram of the radio and its batteries. Now, calculate the power delivered to the radio. (b) When using Nicad cells each having an internal resistance of $0.0400 Ω0.0400 Ω size 12{0 "." "0400" %OMEGA } {}$. (c) When using alkaline cells each having an internal resistance of $0.200 Ω0.200 Ω size 12{0 "." "200" %OMEGA } {}$. (d) Does this difference seem significant, considering that the radio’s effective resistance is lowered when its volume is turned up?

23.

An automobile starter motor has an equivalent resistance of $0.0500Ω0.0500Ω size 12{0 "." "0500" %OMEGA } {}$ and is supplied by a 12.0-V battery with a $0.0100-Ω0.0100-Ω size 12{0 "." "0100"- %OMEGA } {}$ internal resistance. (a) What is the current to the motor? (b) What voltage is applied to it? (c) What power is supplied to the motor? (d) Repeat these calculations for when the battery connections are corroded and add $0.0900Ω0.0900Ω size 12{0 "." "0900" %OMEGA } {}$ to the circuit. (Significant problems are caused by even small amounts of unwanted resistance in low-voltage, high-current applications.)

24.

A child’s electronic toy is supplied by three 1.58-V alkaline cells having internal resistances of $0.0200Ω0.0200Ω size 12{0 "." "0200" %OMEGA } {}$ in series with a 1.53-V carbon-zinc dry cell having a $0.100-Ω0.100-Ω size 12{0 "." "100"- %OMEGA } {}$ internal resistance. The load resistance is $10.0Ω10.0Ω size 12{"10" "." 0 %OMEGA } {}$. (a) Draw a circuit diagram of the toy and its batteries. (b) What current flows? (c) How much power is supplied to the load? (d) What is the internal resistance of the dry cell if it goes bad, resulting in only 0.500 W being supplied to the load?

25.

(a) What is the internal resistance of a voltage source if its terminal voltage drops by 2.00 V when the current supplied increases by 5.00 A? (b) Can the emf of the voltage source be found with the information supplied?

26.

A person with body resistance between his hands of $10.0 kΩ10.0 kΩ size 12{"10" "." 0" k" %OMEGA } {}$ accidentally grasps the terminals of a 20.0-kV power supply. (Do NOT do this!) (a) Draw a circuit diagram to represent the situation. (b) If the internal resistance of the power supply is $2000Ω2000Ω size 12{"2000" %OMEGA } {}$, what is the current through his body? (c) What is the power dissipated in his body? (d) If the power supply is to be made safe by increasing its internal resistance, what should the internal resistance be for the maximum current in this situation to be 1.00 mA or less? (e) Will this modification compromise the effectiveness of the power supply for driving low-resistance devices? Explain your reasoning.

27.

Electric fish generate current with biological cells called electroplaques, which are physiological emf devices. The electroplaques in the South American eel are arranged in 140 rows, each row stretching horizontally along the body and each containing 5000 electroplaques. Each electroplaque has an emf of 0.15 V and internal resistance of $0.25Ω0.25Ω size 12{0 "." "25" %OMEGA } {}$. If the water surrounding the fish has resistance of $800Ω800Ω size 12{"800" %OMEGA } {}$, how much current can the eel produce in water from near its head to near its tail?

28.

Integrated Concepts

A 12.0-V emf automobile battery has a terminal voltage of 16.0 V when being charged by a current of 10.0 A. (a) What is the battery’s internal resistance? (b) What power is dissipated inside the battery? (c) At what rate (in $ºC/minºC/min size 12{°"C/min"} {}$) will its temperature increase if its mass is 20.0 kg and it has a specific heat of $0.300 kcal/kg⋅ºC0.300 kcal/kg⋅ºC size 12{0 "." "300"" kcal/kg" cdot °C} {}$, assuming no heat escapes?

29.

Unreasonable Results

A 1.58-V alkaline cell with a $0.200-Ω0.200-Ω size 12{0 "." "200"- %OMEGA } {}$ internal resistance is supplying 8.50 A to a load. (a) What is its terminal voltage? (b) What is the value of the load resistance? (c) What is unreasonable about these results? (d) Which assumptions are unreasonable or inconsistent?

30.

Unreasonable Results

(a) What is the internal resistance of a 1.54-V dry cell that supplies 1.00 W of power to a $15.0-Ω15.0-Ω size 12{"15" "." 0- %OMEGA } {}$ bulb? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

## 21.3Kirchhoff’s Rules

31.

Apply the loop rule to loop abcdefgha in Figure 21.25.

32.

Apply the loop rule to loop aedcba in Figure 21.25.

33.

Verify the second equation in Example 21.5 by substituting the values found for the currents $I1I1 size 12{I rSub { size 8{1} } } {}$ and $I2I2 size 12{I rSub { size 8{2} } } {}$.

34.

Verify the third equation in Example 21.5 by substituting the values found for the currents $I1I1 size 12{I rSub { size 8{1} } } {}$ and $I3I3 size 12{I rSub { size 8{3} } } {}$.

35.

Apply the junction rule at point a in Figure 21.52.

Figure 21.52
36.

Apply the loop rule to loop abcdefghija in Figure 21.52.

37.

Apply the loop rule to loop akledcba in Figure 21.52.

38.

Find the currents flowing in the circuit in Figure 21.52. Explicitly show how you follow the steps in the Problem-Solving Strategies for Series and Parallel Resistors.

39.

Solve Example 21.5, but use loop abcdefgha instead of loop akledcba. Explicitly show how you follow the steps in the Problem-Solving Strategies for Series and Parallel Resistors.

40.

Find the currents flowing in the circuit in Figure 21.47.

41.

Unreasonable Results

Consider the circuit in Figure 21.53, and suppose that the emfs are unknown and the currents are given to be $I1=5.00 AI1=5.00 A$, $I2=3.0 AI2=3.0 A size 12{I rSub { size 8{2} } =3 "." 0" A"} {}$, and $I3=–2.00 AI3=–2.00 A size 12{I rSub { size 8{3} } "=-"2 "." "00"" A"} {}$. (a) Could you find the emfs? (b) What is wrong with the assumptions?

Figure 21.53

## 21.4DC Voltmeters and Ammeters

42.

What is the sensitivity of the galvanometer (that is, what current gives a full-scale deflection) inside a voltmeter that has a $1.00-MΩ1.00-MΩ size 12{1 "." "00""-M" %OMEGA } {}$ resistance on its 30.0-V scale?

43.

What is the sensitivity of the galvanometer (that is, what current gives a full-scale deflection) inside a voltmeter that has a $25.0-kΩ25.0-kΩ size 12{"25" "." 0"-k" %OMEGA } {}$ resistance on its 100-V scale?

44.

Find the resistance that must be placed in series with a $25.0-Ω25.0-Ω size 12{"25" "." 0- %OMEGA } {}$ galvanometer having a $50.0-μA50.0-μA size 12{"50" "." 0-μA} {}$ sensitivity (the same as the one discussed in the text) to allow it to be used as a voltmeter with a 0.100-V full-scale reading.

45.

Find the resistance that must be placed in series with a $25.0-Ω25.0-Ω size 12{"25" "." 0- %OMEGA } {}$ galvanometer having a $50.0-μA50.0-μA size 12{"50" "." 0-μA} {}$ sensitivity (the same as the one discussed in the text) to allow it to be used as a voltmeter with a 3000-V full-scale reading. Include a circuit diagram with your solution.

46.

Find the resistance that must be placed in parallel with a $25.0-Ω25.0-Ω size 12{"25" "." 0- %OMEGA } {}$ galvanometer having a $50.0-μA50.0-μA size 12{"50" "." 0-μA} {}$ sensitivity (the same as the one discussed in the text) to allow it to be used as an ammeter with a 10.0-A full-scale reading. Include a circuit diagram with your solution.

47.

Find the resistance that must be placed in parallel with a $25.0-Ω25.0-Ω size 12{"25" "." 0- %OMEGA } {}$ galvanometer having a $50.0-μA50.0-μA size 12{"50" "." 0-μA} {}$ sensitivity (the same as the one discussed in the text) to allow it to be used as an ammeter with a 300-mA full-scale reading.

48.

Find the resistance that must be placed in series with a $10.0-Ω10.0-Ω size 12{"10" "." 0- %OMEGA } {}$ galvanometer having a $100-μA100-μA size 12{"100"-μA} {}$ sensitivity to allow it to be used as a voltmeter with: (a) a 300-V full-scale reading, and (b) a 0.300-V full-scale reading.

49.

Find the resistance that must be placed in parallel with a $10.0-Ω10.0-Ω size 12{"10" "." 0- %OMEGA } {}$ galvanometer having a $100-μA100-μA size 12{"100"-μA} {}$ sensitivity to allow it to be used as an ammeter with: (a) a 20.0-A full-scale reading, and (b) a 100-mA full-scale reading.

50.

Suppose you measure the terminal voltage of a 1.585-V alkaline cell having an internal resistance of $0.100Ω0.100Ω size 12{0 "." "100" %OMEGA } {}$ by placing a $1.00-kΩ1.00-kΩ size 12{1 "." "00""-k" %OMEGA } {}$ voltmeter across its terminals. (See Figure 21.54.) (a) What current flows? (b) Find the terminal voltage. (c) To see how close the measured terminal voltage is to the emf, calculate their ratio.

Figure 21.54
51.

Suppose you measure the terminal voltage of a 3.200-V lithium cell having an internal resistance of $5.00Ω5.00Ω size 12{5 "." "00" %OMEGA } {}$ by placing a $1.00-kΩ1.00-kΩ size 12{1 "." "00""-k" %OMEGA } {}$ voltmeter across its terminals. (a) What current flows? (b) Find the terminal voltage. (c) To see how close the measured terminal voltage is to the emf, calculate their ratio.

52.

A certain ammeter has a resistance of $5.00×10−5Ω5.00×10−5Ω size 12{5 "." "00"´"10" rSup { size 8{-5} } %OMEGA } {}$ on its 3.00-A scale and contains a $10.0-Ω10.0-Ω size 12{"10" "." 0- %OMEGA } {}$ galvanometer. What is the sensitivity of the galvanometer?

53.

A $1.00-MΩ1.00-MΩ size 12{1 "." "00""-M" %OMEGA } {}$ voltmeter is placed in parallel with a $75.0-kΩ75.0-kΩ size 12{"75" "." 0"-k" %OMEGA } {}$ resistor in a circuit. (a) Draw a circuit diagram of the connection. (b) What is the resistance of the combination? (c) If the voltage across the combination is kept the same as it was across the $75.0-kΩ75.0-kΩ size 12{"75" "." 0"-k" %OMEGA } {}$ resistor alone, what is the percent increase in current? (d) If the current through the combination is kept the same as it was through the $75.0-kΩ75.0-kΩ size 12{"75" "." 0"-k" %OMEGA } {}$ resistor alone, what is the percentage decrease in voltage? (e) Are the changes found in parts (c) and (d) significant? Discuss.

54.

A $0.0200-Ω0.0200-Ω$ ammeter is placed in series with a $10.00-Ω10.00-Ω size 12{"10" "." "00"- %OMEGA } {}$ resistor in a circuit. (a) Draw a circuit diagram of the connection. (b) Calculate the resistance of the combination. (c) If the voltage is kept the same across the combination as it was through the $10.00-Ω10.00-Ω size 12{"10" "." "00"- %OMEGA } {}$ resistor alone, what is the percent decrease in current? (d) If the current is kept the same through the combination as it was through the $10.00-Ω10.00-Ω size 12{"10" "." "00"- %OMEGA } {}$ resistor alone, what is the percent increase in voltage? (e) Are the changes found in parts (c) and (d) significant? Discuss.

55.

Unreasonable Results

Suppose you have a $40.0-Ω40.0-Ω size 12{"40" "." 0- %OMEGA } {}$ galvanometer with a $25.0-μA25.0-μA size 12{"25" "." 0-mA} {}$ sensitivity. (a) What resistance would you put in series with it to allow it to be used as a voltmeter that has a full-scale deflection for 0.500 mV? (b) What is unreasonable about this result? (c) Which assumptions are responsible?

56.

Unreasonable Results

(a) What resistance would you put in parallel with a $40.0-Ω40.0-Ω size 12{"40" "." 0- %OMEGA } {}$ galvanometer having a $25.0-μA25.0-μA$ sensitivity to allow it to be used as an ammeter that has a full-scale deflection for $10.0-μA 10.0-μA size 12{"10" "." 0 μA} {}$? (b) What is unreasonable about this result? (c) Which assumptions are responsible?

## 21.5Null Measurements

57.

What is the $emfxemfx size 12{"emf" rSub { size 8{x} } } {}$ of a cell being measured in a potentiometer, if the standard cell’s emf is 12.0 V and the potentiometer balances for $Rx=5.000ΩRx=5.000Ω size 12{R rSub { size 8{x} } =5 "." "000" %OMEGA } {}$ and $Rs=2.500ΩRs=2.500Ω size 12{R rSub { size 8{s} } =2 "." "500" %OMEGA } {}$?

58.

Calculate the $emfxemfx size 12{"emf" rSub { size 8{x} } } {}$ of a dry cell for which a potentiometer is balanced when $Rx=1.200ΩRx=1.200Ω size 12{R rSub { size 8{x} } =1 "." "200" %OMEGA } {}$, while an alkaline standard cell with an emf of 1.600 V requires $Rs=1.247ΩRs=1.247Ω size 12{R rSub { size 8{s} } =1 "." "247" %OMEGA } {}$ to balance the potentiometer.

59.

When an unknown resistance $RxRx size 12{R rSub { size 8{x} } } {}$ is placed in a Wheatstone bridge, it is possible to balance the bridge by adjusting $R3R3 size 12{R rSub { size 8{3} } } {}$ to be $2500Ω2500Ω size 12{"2500" %OMEGA } {}$. What is $RxRx size 12{R rSub { size 8{x} } } {}$ if $R2R1=0.625R2R1=0.625 size 12{ { {R rSub { size 8{2} } } over {R rSub { size 8{1} } } } =0 "." "625"} {}$?

60.

To what value must you adjust $R3R3 size 12{R rSub { size 8{3} } } {}$ to balance a Wheatstone bridge, if the unknown resistance $RxRx size 12{R rSub { size 8{x} } } {}$ is $100Ω100Ω size 12{"100" %OMEGA } {}$, $R1R1 size 12{R rSub { size 8{1} } } {}$ is $50.0Ω50.0Ω size 12{"50" "." 0 %OMEGA } {}$, and $R2R2 size 12{R rSub { size 8{2} } } {}$ is $175Ω175Ω size 12{"175" %OMEGA } {}$?

61.

(a) What is the unknown $emfxemfx size 12{"emf" rSub { size 8{x} } } {}$ in a potentiometer that balances when $RxRx size 12{R rSub { size 8{x} } } {}$ is $10.0Ω10.0Ω size 12{"10" "." 0 %OMEGA } {}$, and balances when $RsRs size 12{R rSub { size 8{s} } } {}$ is $15.0Ω15.0Ω size 12{"15" "." 0 %OMEGA } {}$ for a standard 3.000-V emf? (b) The same $emfxemfx size 12{"emf" rSub { size 8{x} } } {}$ is placed in the same potentiometer, which now balances when $RsRs size 12{R rSub { size 8{s} } } {}$ is $15.0Ω15.0Ω size 12{"15" "." 0 %OMEGA } {}$ for a standard emf of 3.100 V. At what resistance $RxRx size 12{R rSub { size 8{x} } } {}$ will the potentiometer balance?

62.

Suppose you want to measure resistances in the range from $10.0Ω10.0Ω size 12{"10" "." 0 %OMEGA } {}$ to $10.0 kΩ10.0 kΩ size 12{"10" "." 0" k" %OMEGA } {}$ using a Wheatstone bridge that has $R2R1=2.000R2R1=2.000 size 12{ { {R rSub { size 8{2} } } over {R rSub { size 8{1} } } } =2 "." "000"} {}$. Over what range should $R3R3 size 12{R rSub { size 8{3} } } {}$ be adjustable?

## 21.6DC Circuits Containing Resistors and Capacitors

63.

The timing device in an automobile’s intermittent wiper system is based on an $RCRC size 12{ ital "RC"} {}$ time constant and utilizes a $0.500-μF0.500-μF size 12{0 "." "500-"μF} {}$ capacitor and a variable resistor. Over what range must $RR size 12{R} {}$ be made to vary to achieve time constants from 2.00 to 15.0 s?

64.

A heart pacemaker fires 72 times a minute, each time a 25.0-nF capacitor is charged (by a battery in series with a resistor) to 0.632 of its full voltage. What is the value of the resistance?

65.

The duration of a photographic flash is related to an $RCRC size 12{ ital "RC"} {}$ time constant, which is $0.100 μs0.100 μs size 12{0 "." "100" μs} {}$ for a certain camera. (a) If the resistance of the flash lamp is $0.0400Ω0.0400Ω size 12{0 "." "0400" %OMEGA } {}$ during discharge, what is the size of the capacitor supplying its energy? (b) What is the time constant for charging the capacitor, if the charging resistance is $800 kΩ800 kΩ size 12{"800"" k" %OMEGA } {}$?

66.

A 2.00- and a $7.50-μF7.50-μF size 12{7 "." "50"-mF} {}$ capacitor can be connected in series or parallel, as can a 25.0- and a $100-kΩ100-kΩ size 12{"100""-k" %OMEGA } {}$ resistor. Calculate the four $RCRC size 12{ ital "RC"} {}$ time constants possible from connecting the resulting capacitance and resistance in series.

67.

After two time constants, what percentage of the final voltage, emf, is on an initially uncharged capacitor $CC size 12{C} {}$, charged through a resistance $RR size 12{R} {}$?

68.

A $500-Ω500-Ω size 12{"500"- %OMEGA } {}$ resistor, an uncharged $1.50-μF1.50-μF size 12{1 "." "50"-mF} {}$ capacitor, and a 6.16-V emf are connected in series. (a) What is the initial current? (b) What is the $RCRC size 12{ ital "RC"} {}$ time constant? (c) What is the current after one time constant? (d) What is the voltage on the capacitor after one time constant?

69.

A heart defibrillator being used on a patient has an $RCRC size 12{ ital "RC"} {}$ time constant of 10.0 ms due to the resistance of the patient and the capacitance of the defibrillator. (a) If the defibrillator has an $8.00-μF8.00-μF size 12{8 "." "00"-mF} {}$ capacitance, what is the resistance of the path through the patient? (You may neglect the capacitance of the patient and the resistance of the defibrillator.) (b) If the initial voltage is 12.0 kV, how long does it take to decline to $6.00×102V6.00×102V$?

70.

An ECG monitor must have an $RCRC size 12{ ital "RC"} {}$ time constant less than $1.00×102μs1.00×102μs size 12{"100" ms} {}$ to be able to measure variations in voltage over small time intervals. (a) If the resistance of the circuit (due mostly to that of the patient’s chest) is $1.00 kΩ1.00 kΩ size 12{1 "." 00" k" %OMEGA } {}$, what is the maximum capacitance of the circuit? (b) Would it be difficult in practice to limit the capacitance to less than the value found in (a)?

71.

Figure 21.55 shows how a bleeder resistor is used to discharge a capacitor after an electronic device is shut off, allowing a person to work on the electronics with less risk of shock. (a) What is the time constant? (b) How long will it take to reduce the voltage on the capacitor to 0.250% (5% of 5%) of its full value once discharge begins? (c) If the capacitor is charged to a voltage $V0V0 size 12{V rSub { size 8{0} } } {}$ through a $100-Ω100-Ω size 12{"100"- %OMEGA } {}$ resistance, calculate the time it takes to rise to $0.865V00.865V0 size 12{0 "." "865"`V rSub { size 8{0} } } {}$ (This is about two time constants.)

Figure 21.55
72.

Using the exact exponential treatment, find how much time is required to discharge a $250-μF250-μF size 12{"250"-mF} {}$ capacitor through a $500-Ω500-Ω size 12{"500"- %OMEGA } {}$ resistor down to 1.00% of its original voltage.

73.

Using the exact exponential treatment, find how much time is required to charge an initially uncharged 100-pF capacitor through a $75.0-MΩ75.0-MΩ size 12{"75" "." 0"-M" %OMEGA } {}$ resistor to 90.0% of its final voltage.

74.

Integrated Concepts

If you wish to take a picture of a bullet traveling at 500 m/s, then a very brief flash of light produced by an $RCRC size 12{ ital "RC"} {}$ discharge through a flash tube can limit blurring. Assuming 1.00 mm of motion during one $RCRC size 12{ ital "RC"} {}$ constant is acceptable, and given that the flash is driven by a $600-μF600-μF size 12{"600"-mF} {}$ capacitor, what is the resistance in the flash tube?

75.

Integrated Concepts

A flashing lamp in a Christmas earring is based on an $RCRC size 12{ ital "RC"} {}$ discharge of a capacitor through its resistance. The effective duration of the flash is 0.250 s, during which it produces an average 0.500 W from an average 3.00 V. (a) What energy does it dissipate? (b) How much charge moves through the lamp? (c) Find the capacitance. (d) What is the resistance of the lamp?

76.

Integrated Concepts

A $160-μF160-μF size 12{"160"-mF} {}$ capacitor charged to 450 V is discharged through a $31.2-kΩ31.2-kΩ size 12{31 "." "2-k" %OMEGA } {}$ resistor. (a) Find the time constant. (b) Calculate the temperature increase of the resistor, given that its mass is 2.50 g and its specific heat is $1.67kJkg⋅ºC1.67kJkg⋅ºC size 12{1 "." "67" { {"kJ"} over {"kg" cdot "deg"C} } } {}$, noting that most of the thermal energy is retained in the short time of the discharge. (c) Calculate the new resistance, assuming it is pure carbon. (d) Does this change in resistance seem significant?

77.

Unreasonable Results

(a) Calculate the capacitance needed to get an $RCRC size 12{ ital "RC"} {}$ time constant of $1.00×103s1.00×103s$ with a $0.100-Ω0.100-Ω size 12{0 "." "100"- %OMEGA } {}$ resistor. (b) What is unreasonable about this result? (c) Which assumptions are responsible?

78.

Consider a camera’s flash unit. Construct a problem in which you calculate the size of the capacitor that stores energy for the flash lamp. Among the things to be considered are the voltage applied to the capacitor, the energy needed in the flash and the associated charge needed on the capacitor, the resistance of the flash lamp during discharge, and the desired $RCRC size 12{ ital "RC"} {}$ time constant.

79.