Solved: A real battery is not just an emf. We can model a

The tip of a flashlight bulb is touching the top of a 3 V battery as shown in Figure Q23. l. Does the bulb light? Why or why not?

A fl ashlight bulb is connected to a battery and is glowing; the circuit is shown in Figure Q23.2. Is c urrent /2 greater than, less than, or equal to c urrent /1? Explain.

Current /;0 flows into three resistors connected together one after the other as shown in Figure Q23.3. The accompanying graph shows the value of the potential as a funct ion of position. a. Is lout greater than, less than, or equal to /;0? Explain. b. Rank in order, from largest to smallest, the three resistances R1, R2, and R3. Explain.

The circuit in Figure Q23.4 has two resistors, with R1 > R2 . Which resistor dissipates the larger amount of power? Explain.

The circuit in Figure Q23.S has a battery and two resis tors, with R1 > R2 Which resistor dissipates the larger amount of power? Explain.

In the circuit shown in Figure Q23.6, bulbs A and B are glowing. Then the switc h is closed . What happens to each bulb? Does it get brighter, stay the same, get dimmer, or go out? Explain.

Figure Q23.7 shows two c ircuits. The two batteries are identical and the four resistors all have exactly the same resistance. a. Is 6.Vab larger than, smaller than, or equal to 6.V:,d? Explain. b. Rank in order, from largest to smallest, the currents / 1, 12, and /3 . Explain.

Figure Q23.8 shows two circuits. The two batteries are identical and the four resistors all have exactly the same resistance. a. Compare 6.Vab 6.Vcd and 6.Vef Are they all the same? If not, rank them in order from largest to smallest. Explain. b. Rank in order, from largest to smallest, the five currents /1 to 15 . Explain.

a. ln Figure Q23.9, what fraction of current I goes through the 3 n resistor? b. If the 9 n resistor is replaced with a larger resistor, will the fraction of current going through the 3 n resistor increase, decrease, or stay the same?

Two of the three resistors in Figure Q23.10 are unknown but equa l. Is the total resistance be tween points a and b less than, greater than, or equa l to 50 fl? R Explain.

Two of the three resistors in Figure Q23. l 1 are unknown but equal. Is the total resistance between points a and b less than, greater than, or equal to 200 fl? Explai n.

Rank in order, from largest to smallest, the c urrents /1, / 2, and /3 in the circuit diagram in Figure Q23. l 2.

The three bulbs in Figure Q23. l 3 are identical. Rank the bulbs from brightest to dimmest. Explain.

The four bulbs in Figure Q23.L4 ar.c identical. Rank the bulbs from brightest to dimmest. Explain.

Figure Q23. 15 shows five identical bulbs connected to a battery. All the bulbs are glowing. Rank the bulbs from brightest to dimmest. Explain.

a. The three bulbs in Figure Q23. l 6 are identical. Rank the bulbs from brightest to dimmest. Explain. b. Suppose a wire is connected between points 1 and 2. What happens to each bulb? Does it get brighter, stay the same, get dimmer, or go out? Explain.

Initially, bulbs A and Bin Figure Q23.17 are both glowing. Bulb B is then removed from its socket. Does removing bulb B cause the potential difference ~Vi 2 between points 1 and 2 to increase, decrease, stay the same, or become zero? Explain.

a. Consider the points a and b in Figure Q23. l 8. Is the potential di fference ~ Vab between points a and b zero? ff so, why? ff not, which point is more positive? b. If a wire is connected between points a and b, does it carry a c urrent? If so, in which direction- to the right or to the left? Explain.

When the switch in Figure Q23. l 9 is closed, a. Does the current through the battery increase, decrease, or stay the same? Explain. b. Does the current through R 1 increase, dec rease, or stay the same? Explain.

A voltmeter is (incorrectly) inserted into a circuit as shown in Figure Q23.20. a. What is the current in the circuit? b. What does the voltmeter read? c. How would you change the circuit to correctly connect the voltmeter to measure the potential difference across the resistor?

An ammeter is (incorrectly) inserted into a circuit as shown in Figure Q23.2 l . a. What is the current through the 5.0 f1 resistor? b. How would you change the circuit to correctly connect the ammeter to measure the current through the 5.0 f1 resistor?

Rank in order, from largest to smallest, the equi valent capacitances (Ce,;J i to (Ccq)4 of the four groups of capacitors shown in Figure Q23.22.

Figure Q23.23 shows a c ircuit consist ing of a battery, a switch, two identical lightbulbs, and a capacitor that is initially uncharged. a. Immediately after the switch is closed, are either or both bulbs glowing? Explain.b. If both bulbs are glowing, which FIGURE 023.23 is brighter? Or are they equally bright? Explain. c. For any bulb (A or B or both) that lights up immediate ly after the switch is closed, does its brightness increase with time, decrease with time, or remain unchanged? Explain.

Figure Q23.24 shows the volt- AVc age as a function of time across a capaci tor as it is discharged (separately) through three different resistors. Rank in order, from largest to smallest, the values of the resistances R 1 to R3

A c harged capacitor could be connected to two identical resistors in either of the two ways shown in Figure Q23.25. Which configuration wi ll discharge the capacitor in the shortest time once the switch is closed? Explain.

A flashing light is controlled by the cbarging and discharging of an RC circuit. If the light is flashing too rapidly, describe two changes that you could make to the c ircuit to reduce the flash rate.

A device to make an e lectrical measurement of skin moisture has electrodes that form two plates of a capacitor; the skin is the dielectric between the plates. Adding moisture to the skin means adding water, which has a large dielectric constant. lf a ci rcuit repeatedly charges and discharges the capacitor to determine the capacitance, how will an increase in skin moisture affect the charging and discharging time? Explain.

Consider the model of nerve conduction in myelinated axons BIO pre sented in the c hapter. Suppose the d is tance between the nodes of Ranvier was halved for a particular axon. a. How would this affect the resistance and the capaci tance of one segment of the axon? b. How would this affect the time constant for the charging of one segment? c. How would thi s affect the signal propagation speed for the axon?

Adding a myelin sheath to an axon results in faster signal propagation. It also means that less energy is required for a signal to propagate down the axon. Explain why this is so.

What is the current in the circuit of Figure Q23.30? A. 1.0 A B. 1.7 A C. 2.5 A D. 4.2A

Which resistor in Figure Q23.30 dissipates the most power? . A. The 4.0 f! resisto r. B. The 6.0 f! resistor. C. Both dissipate the same power

Normally, household lightbulbs are connected in paralle l to a power supply. Suppose a 40 W and a 60 W lightbulb are , instead, connected in series, as shown in Figure Q23.32. Which bulb is brighter? A. The 60 W bulb. B. The 40 W bulb. C. The bulbs are equally bright.

A metal wire of resistance R is cut into two pieces of equal length. The two pieces are connected together side by side. What is the resistance of the two connected wires? A. R/4 B. R/2 C. R D. 2R E. 4R

What is the value of resistor R in Figure Q23.34? A. 4.0f! B. 12 !1 c. 36 !1 ~V= 8.0V IOfl D. n n E. 96 !1

Two capacitors are connected in series. They are then reconnected to be in FIGURE parallel. The capacitance of the parallel combination A. Is less than that of the series combination. B. Is more than that of the series combination. C. Is the same as that of the series combination. D. Could be more or less than that of the series combination depending on the values of the c apacitances.

If a cell's membrane thickness doubles but the cell stays the BIO same size, how do the resistance and the ca1:>acitance of the cell membrane change? A. The resistance and the capacitance increase. B. The resistance increases, the capacitance decreases. C. The resistance decreases, the capacitance increase s. D. The resistance and the capacitance decrease.

If a cell's diameter is reduced by 50% without changing the membrane thickness, how do the resistance and capacitance of the cell membrane c hange? A. The resistance and the capacitance increase. B. The resistance increases, the capacitance decrease s. C. The resistance decreases, the capacitance increase s. D. The resistance and the capacitance decrease.

For the circuit of Figure P23.38, a. What is the equivalent capacitance? b. How much charge flows through the battery as the capacitors are being charged?

For the circuit of Figure P23.39, a. What is the equivalent capacitance? b. What is the charge of each of the capacitors?

What is the time constant for the discharge of the capacitor in Figure P23.40?

What is the time constant for the discharge of the capacitor in Figure P23.4 I?

After how many time constants has the voltage across a discharging capacitor decayed to 0.10% of its initial value?

After how many time constants has the voltage across a (I 20Y) lightbulb screwed into this socket? discharging capacitor decayed to 0.10% of its initial value?

A capacitor charging circuit consists of a battery, an uncharged 20 F capacitor, and a 4.0 kfl resistor. Alt = 0 s, the switch is closed; 0. 15 s later, the current is 0.46 mA. What is the battery's emf?

Tho switch figure P23.45 has been in position a for a long time. It is changed to position b at t = 0 s. What are the charge Q on the capacitor and the current I through the resistor (a) immediately after the switch is closed? b. What fraction of the battery's power is dissipated by the (b) At t = 50 s? (c) At t = 200 s? internal resistance?

A 9.0-nm-thick cell membrane undergoes an action potential that follows the c urve in the table on page 748. What is the strength of the electric field inside the membrane just before the action potential and at the peak of the depolarization?

A cell membrane has a resistance and a capacitance and thus a characteristic time constant. What is the time constant of a 9.0-nmthick membrane surrounding a 0.040-mm-diameter spherical cell?

Changing the thickness of the myelin sheath surrounding an axon changes its capacitance and thus the conduction speed. A myelinated nerve fiber has a conduction speed of 55 mis. If the spacing between nodes is 1.0 mm and the resistance of segments between nodes is 25 Mfl, what is the capacitance of each segment?

A patticular myelinated axon has nodes spaced 0.80 mm apart. The resistance between nodes is 20 Mfl; the capacitance of each insulated segment is 1.2 pf. What is the conduction speed of a nerve impulse along this axon?

To measure signal propagation in a nerve in the arm, the BIO nerve is triggered near the armpit. The peak of the action potential is measured at the elbow and then, 4.0 ms later, 24 cm away from the elbow at the wrist. a. What is the speed of propagation along this nerve? b. A determination of the speed made by measuring the time between the application of a stimulus at the armpit and the peak of an action potential at the elbow or the wrist would be inaccurate. Explain the problem with this approach, and why the noted technique is preferable.

Two 75 W ( 120 V) lightbulbs are wired in series, then the combination is connected to a 120 V supply. How much power is dissipated by each bulb?

How much power is dissipated by each resistor in Figure P23.52?

Two 75 W ( 120 V) lightbulbs are wired in series, then the combination is connected to a 120 V supply. How much power is dissipated by each bulb?

The corroded contacts in a lightbulb socket have 5.0 fl total resistance. How much actual power is dissipated by a 100 W (I 20Y) lightbulb screwed into this socket?

A real battery is not just an emf. We can model a real 1.5 V battery as a 1.5 V emf in series with a resistor known as the "internal resistance," as shown in Figure P23.55. A typical battery has 1.0 fl internal resistance due to imperfections that limit current through the battery. When there's no voltage drop across the internal resistance, the potential difference between its terminals is 1.5 V, the value of the emf. Suppose the terminals of this battery are connected to a 2.0 fl resistor.a. What is the potential difference between the terminals of the battery? b. What fraction of the battery's power is dissipated by the internal resistance.

For the real battery shown in Figure P23.55, calculate the power dissipated by a resistor R connected to the battery when (a) R = 0.25 fl, (b) R = 0.50 fl, (c) R = 1.0 fl , (d) R = 2.0 fl, and (e) R = 4.0 fl. (Your results should suggest that maximum power dissipation is achieved when the external resistance R equals the internal resistance. This is true in general.)

Batteries are recharged by connecting them to a power supply (i.e ., another battery) of greater emf in such a way that the current flows inlo the positive terminal of the battery being recharged, as was shown in Example 23. 1. This reverse current through the battery replenishes its chemicals. The current is kept fairly low so as not to overheat the battery being recharged by dissipati ng energy in its internal resistance. a. Suppose the real battery of Figure P23.55 is rechargeable. What emf power supply should be used for a 0. 75 A recharging cu1Tent? b. Tf this power supply charges the battery for I 0 minutes, how much energy goes into the battery? How much is dissipated as thermal energy in the internal resistance?

When two resistors are connected in parallel across a battery of unknown voltage, one resistor carries a current of 3.2 A while the second carries a c urrent of 1.8 A. What c urrent wi II be supplied by the same battery if these two resistors are connected to it in series?

The 10 fl resistor in Figure P23.59 is dissipating 40 W of power. How much power are the other two resistors dissipating?

At this instant, the current in the c irc uit of Figure P23.60 is 20 mA in the direction shown and the capacitor charge is 200 .,C. What is the resistance R?

What is the current through the battery in Figure P23.62 when the switch is (a) open and (b) closed?

What is the ratio ? parallel/ ? series of the total power dissipated by two identical resistors connected in parallel to a battery to the total power when they are connected in series to the same battery?

You have a device that needs a voltage reference of 3.0 V, but you have only a 9.0 V battery. Fottunately, you also have several 10 kfl resistors. Show how you can use the resistors and the battery to make a circuit that provides a potential difference of 3.0 V.

There is a current of 0.25 A in the circuit of Figure P23.65. INT a. What is the direct ion of the current? Explai n. b. What is the value of the resistance R? c. What is the power dissipated by R? d. Make a graph of potential versus position, starting from V = 0 V in the lower left corner and proceeding clockwise. See Figure P23.9 for an example.

A circuit you' re building needs an ammeter that goes from 0 mA to a full-scale reading of 50.0 mA. Unfortunately, the only ammeter in the storeroom goes from 0 ,A to a fullscale reading of only 500 ,A. Fortunately, you can make this ammeter work by putting it in a measuring circuit, as shown in Figure P23.66. This lets a certain fraction of the current pass through the meter; knowing this value, you can deduce the total current. Assume that the ammeter is ideal. a. What value of R must you use so that the meter will go to full scale when the c urrent I is 50.0 mA? Hint: When I = 50.0 mA, the ammeter should be reading its maximum value.b. What is the equivalent resistance of your measuring circuit?

A circuit you're building needs a voltmeter that goes from 0 V to a full -scale reading of 5.0 Y. Unfortunately, the only meter in the storeroom is an ammeter that goes from 0 ,A to a full -scale reading of 500 ,A. It is possible to use this meter to measure voltages by putting it in a measuring circuit as shown in Figure P23.67. What value of R must you use so that the meter will go to full scale when the potential difference ~V is 5.0 V? Assume that the ammeter is ideal.

For the circuit shown in Figure P23.68, find the current through and the potential difference across each resistor. Place your results in a table for ease of reading.

You have three 12 ,F capacitors. Draw diagrams showing how you could arrange all three so that their equivalent capacitance is (a) 4.0 ,F, (b) 8.0 ,F, (c) 18 ,F, and (d) 36 ,F.

Initially, the switch C in Figure P23.70 is in C position a and capacitors C2 and C3 are uncharged. Then the switch is flipped to position b. Afterward, what are the charge on across each capacitor?

The capacitor in an RC cjrcuit with a time constant of 15 ms is charged to I 0 V. The capacitor begins to discharge at t = 0 s. a. At what time will the charge on the capacitor be reduced to half its initial value? b. At what time wi ll the energy stored in the capacitor be reduced to half its initial value?

The capacitor in Figure P23.72 is initially unc harged and the switch, in position c, is not connected to e ither side of the circ uit. The switch is now fl ipped to position a for 10 ms, then to position b for 10 ms, and then brought back to posi tion c. What is the final pote ntial difference across the capacitor?

What value resistor will discharge a 1.0 ,F capacitor to I 0% of its initial charge in 2.0 ms?

The charging circuit for the flash system of a camera uses a 100 ,F capacitor that is charged from a 250 V power supply. What is the most resistance that can be in series with the capac itor if the capacitor is to charge to at least 87% of its final voltage in no more than 8.0 s?

A capacitor is discharged through a I 00 fl resistor. The discharge current decreases to 25% of its in itial value in 2.5 ms. What is the value of the capacitor?

A 50 ,F capacitor that had been charged to 30 V is discharged through a resistor. Figure P23. 76 shows the capacitor voltage as a fu nction of time. What is the value of the resistance?

The switch in Figure P23.77 has been closed for a very long time. a. What is the charge on the capacitor? b. The switch is opened at t = 0 s. At what time has the charge on the capacitor decreased to I 0% of its initial value?

Intermittent windshield wipers use a variable resistor in an RC circuit to set the delay between successive passes of the wipers. A typical circuit is shown in Figure P23.78. When the switch closes, the capacitor (initially uncharged) begins to charge and the potential at point b begins to increase. A sensor measures the potential difference between points a and b, triggering a pass of the wipers when Vb= v . (Another part of the c ircuit, not shown, discharges the capacitor at this time so that the cycle can start agai n.) a. What value of the variable resistor will give 12 seconds from the start of a cycle to a pass of the wipers? b. To decrease the time, should the variable resistance be increased or decreased?

In Example 23. 14 we estimated the capacitance of the cell membrane to be 89 pF, and in Example 23.15 we found that approximately 10,000 Na+ ions flow through a n ion c hannel when it ope ns. Based on this information and what you learned in this chapter about the action potential, estimate the total number of sodium ion c hannels in the membrane of a nerve cell.

The giant axon of a squid is 0.5 mm in diameter, 10 cm long, and not mye li nated. Unmyel inated cell membranes INT behave as capacitors with I ,F of capacitance per square centimeter of membrane area. When the axon is charged to the - 70 mY resti ng potential, what is the e nergy stored in this capacitance?

A cell has a 7.0-nm-thick membrane with a total membrane area of 6.0 x I0- 9 m2 a. We can model the cell as a capacitor, as we have seen. What is the magnitude of the charge on each " plate" when the membrane is at its resting potential of-70 mV? b. How many sodium ions does this charge cotTespond to?

Which pair of graphs in Figure P23.82 best represents the capacitor voltage and the c urrent through the torso as a function of time after the switch is closed?

For the values noted in the passage above, what is the time constant for the discharge of the capaci tor? A. 3.2 ,s B. 160 ,s C. 3.2 ms D. 160 ms

If a patient receives a series of j olts, the resistance of the torso may increase. How does such a change affect the initial current and the time constant of subsequent jolts? A. The in itial current and the time constant both increase. B. The initial current decreases, the time constant increases. C. The in itial current increases, the time constant decreases. D. The in itial current and the time constant both decrease.

In some cases, the defib rillator may be charged to a lower voltage. How wi ll this affect the time constant of the discharge? A. The time constant wi ll increase. B. The time constant will not change. C. The time constant will decrease. there is a net potential difference across the cell, as shown in Figure P23.86. Stacks of these cells connected in series can produce a large total voltage. Each stack can produce a small current; for more total current, more stacks are needed, connected in parallel.

In an electric eel, each electrocyte can develop a voltage of ISO mV for a sholt time. For a total voltage of 450 V, how many e lectrocytes must be connected in series? A. 300 B. 450 c. 1500 D. 3000

An electric eel produces a pulse of current of 0.80 A at a voltage of 500 V. For the short time of the pulse, what is the instantaneous power? A. 400W B. SOOW C. 62S W D. 800W

Electric eels live in fresh water. The torpedo ray is an electric fi sh that li ves in salt water. The e lectrocytes in the ray are grouped differently than in the eel; each stack of electrocytes has fewer cells, but there are more stacks in paralle l. Which of the following best explain,-; the ray's electrocyte arrangement? A. The lower resistivity of salt water requires more c urrent but lower voltage. B. The lower resistivity of salt water requires more voltage but lower current. C. The higher resistivity of salt water requires more current but lower voltage. D. The higher resistivity of salt water requires more voltage but lower current.

The electric catfi sh is another electric fi sh that produces a voltage pul se by means of stacks of electrocytes. As the fi sh grows in length, the magnitude of the voltage pulse the fi sh produces grows as well. The best explanation for this change is that, as the fi sh grows, A. The voltage produced by each e lectrocyte increases. B. More e lectrocytes are added to each stack. C. More stacks of electrocytes are added in parallel to the existing stacks. D. The thickness of the electrocytes increases.