Using Kirchhoffs rules, (a) find the current in each

Is a circuit breaker wired (a) in series with the device it is protecting, (b) in parallel, or (c) neither in series or in parallel, or (d) is it impossible to tell?

A battery has some internal resistance. (i) Can the potential difference across the terminals of the battery be equal to its emf? (a) no (b) yes, if the battery is absorbing energy by electrical transmission (c) yes, if more than one wire is connected to each terminal (d) yes, if the current in the battery is zero (e) yes, with no special condition required. (ii) Can the terminal voltage exceed the emf? Choose your answer from the same possibilities as in part (i).

The terminals of a battery are connected across two resistors in series. The resistances of the resistors are not the same. Which of the following statements are correct? Choose all that are correct. (a) The resistor with the smaller resistance carries more current than the other resistor. (b) The resistor with the larger resistance carries less current than the other resistor. (c) The current in each resistor is the same. (d) The potential difference across each resistor is the same. (e) The potential difference is greatest across the resistor closest to the positive terminal.

When operating on a 120-V circuit, an electric heater receives 1.30 3 103 W of power, a toaster receives 1.00 3 103 W, and an electric oven receives 1.54 3 103 W. If all three appliances are connected in parallel on a 120-V circuit and turned on, what is the total current drawn from an external source? (a) 24.0 A (b) 32.0 A (c) 40.0 A (d) 48.0 A (e) none of those answers

If the terminals of a battery with zero internal resistance are connected across two identical resistors in series, the total power delivered by the battery is 8.00 W. If the same battery is connected across the same resistors in parallel, what is the total power delivered by the battery? (a) 16.0 W (b) 32.0 W (c) 2.00 W (d) 4.00 W (e) none of those answers

Several resistors are connected in series. Which of the following statements is correct? Choose all that are correct. (a) The equivalent resistance is greater than any of the resistances in the group. (b) The equivalent resistance is less than any of the resistances in the group. (c) The equivalent resistance depends on the voltage applied across the group. (d) The equivalent resistance is equal to the sum of the resistances in the group. (e) None of those statements is correct.

What is the time constant of the circuit shown in Figure OQ28.7? Each of the five resistors has resistance R, and each of the five capacitors has capacitance C. The internal resistance of the battery is negligible. (a) RC (b) 5RC (c) 10RC (d) 25RC (e) none of those answers

When resistors with different resistances are connected in series, which of the following must be the same for each resistor? Choose all correct answers. (a) potential difference (b) current (c) power delivered (d) charge entering each resistor in a given time interval (e) none of those answers

When resistors with different resistances are connected in parallel, which of the following must be the same for each resistor? Choose all correct answers. (a) potential difference (b) current (c) power delivered (d) charge entering each resistor in a given time interval (e) none of those answers

The terminals of a battery are connected across two resistors in parallel. The resistances of the resistors are not the same. Which of the following statements is correct? Choose all that are correct. (a) The resistor with the larger resistance carries more current than the other resistor. (b) The resistor with the larger resistance carries less current than the other resistor. (c) The potential difference across each resistor is the same. (d) The potential difference across the larger resistor is greater than the potential difference across the smaller resistor. (e) The potential difference is greater across the resistor closer to the battery.

Are the two headlights of a car wired (a) in series with each other, (b) in parallel, or (c) neither in series nor in parallel, or (d) is it impossible to tell?

In the circuit shown in Figure OQ28.12, each battery is delivering energy to the circuit by electrical transmission. All the resistors have equal resistance. (i) Rank the electric potentials at points a, b, c, d, and e from highest to lowest, noting any cases of equality in the ranking. (ii) Rank the magnitudes of the currents at the same points from greatest to least, noting any cases of equality.

Several resistors are connected in parallel. Which of the following statements are correct? Choose all that are correct. (a) The equivalent resistance is greater than any of the resistances in the group. (b) The equivalent resistance is less than any of the resistances in the group. (c) The equivalent resistance depends on the voltage applied across the group. (d) The equivalent resistance is equal to the sum of the resistances in the group. (e) None of those statements is correct.

A circuit consists of three identical lamps connected to a battery as in Figure OQ28.14. The battery has some internal resistance. The switch S, originally open, is closed. (i) What then happens to the brightness of lamp B? (a) It increases. (b) It decreases somewhat. (c) It does not change. (d) It drops to zero. For parts (ii) to (vi), choose from the same possibilities (a) through (d). (ii) What happens to the brightness of lamp C? (iii) What happens to the current in the battery? (iv) What happens to the potential difference across lamp A? (v) What happens to the potential difference across lamp C? (vi) What happens to the total power delivered to the lamps by the battery?

A series circuit consists of three identical lamps connected to a battery as shown in Figure OQ28.15. The switch S, originally open, is closed. (i) What then happens to the brightness of lamp B? (a) It increases. (b) It decreases somewhat. (c) It does not change. (d) It drops to zero. For parts (ii) to (vi), choose from the same possibilities (a) through (d). (ii) What happens to the brightness of lamp C? (iii) What happens to the current in the battery? (iv) What happens to the potential difference across lamp A? (v) What happens to the potential difference across lamp C? (vi) What happens to the total power delivered to the lamps by the battery?

Four resistors are connected to a battery as shown in Figure P28.16. (a) Determine the potential difference across each resistor in terms of e. (b) Determine the current in each resistor in terms of I. (c) What If? If R3 is increased, explain what happens to the current in each of the resistors. (d) In the limit that R3 S `, what are the new values of the current in each resistor in terms of I, the original current in the battery?

Consider the combination of resistors shown in Figure P28.17. (a) Find the equivalent resistance between points a and b. (b) If a voltage of 35.0 V is applied between points a and b, find the current in each resistor.

For the purpose of measuring the electric resistance of shoes through the body of the wearer standing on a metal ground plate, the American National Standards Institute (ANSI) specifies the circuit shown in Figure P28.18. The potential difference DV across the 1.00-MV resistor is measured with an ideal voltmeter. (a) Show that the resistance of the footwear is Rshoes 5 50.0 V 2 DV DV (b) In a medical test, a current through the human body should not exceed 150 mA. Can the current delivered by the ANSI-specified circuit exceed 150 mA? To decide, consider a person standing barefoot on the ground plate.

Calculate the power delivered to each resistor in the circuit shown in Figure P28.19.

Why is the following situation impossible? A technician is testing a circuit that contains a resistance R. He realizes that a better design for the circuit would include a resistance 7 3R rather than R. He has three additional resistors, each with resistance R. By combining these additional resistors in a certain combination that is then placed in series with the original resistor, he achieves the desired resistance.

Consider the circuit shown in Figure P28.21 on page 860. (a) Find the voltage across the 3.00-V resistor. (b) Find the current in the 3.00-V resistor.

In Figure P28.22, show how to add just enough ammeters to measure every different current. Show how to add just enough voltmeters to measure the potential difference across each resistor and across each battery

The circuit shown in Figure P28.22 is connected for 2.00 min. (a) Determine the current in each branch of the circuit. (b) Find the energy delivered by each battery. (c) Find the energy delivered to each resistor. (d) Identify the type of energy storage transformation that occurs in the operation of the circuit. (e) Find the total amount of energy transformed into internal energy in the resistors.

For the circuit shown in Figure P28.24, calculate (a) the current in the 2.00-V resistor and (b) the potential difference between points a and b.

What are the expected readings of (a) the ideal ammeter and (b) the ideal voltmeter in Figure P28.25?

The following equations describe an electric circuit: 2I1 (220 V) 1 5.80 V 2 I2 (370 V) 5 0 1I2 (370 V) 1 I3 (150 V) 2 3.10 V 5 0 I1 1 I3 2 I2 5 0 (a) Draw a diagram of the circuit. (b) Calculate the unknowns and identify the physical meaning of each unknown.

Taking R 5 1.00 kV and e 5 250 V in Figure P28.27, determine the direction and magnitude of the current in the horizontal wire between a and e.

Jumper cables are connected from a fresh battery in one car to charge a dead battery in another car. Figure P28.28 shows the circuit diagram for this situation. While the cables are connected, the ignition switch of the car with the dead battery is closed and the starter is activated to start the engine. Determine the current in (a) the starter and (b) the dead battery. (c) Is the dead battery being charged while the starter is operating?

The ammeter shown in Figure P28.29 reads 2.00 A. Find (a) I1, (b) I2, and (c) e.

In the circuit of Figure P28.30, determine (a) the current in each resistor and (b) the potential difference across the 200-V resistor.

Using Kirchhoffs rules, (a) find the current in each resistor shown in Figure P28.31 and (b) find the potential difference between points c and f

In the circuit of Figure P28.32, the current I1 5 3.00 A and the values of e for the ideal battery and R are unknown. What are the currents (a) I2 and (b) I3? (c) Can you find the values of e and R? If so, find their values. If not, explain.

In Figure P28.33, find (a) the current in each resistor and (b) the power delivered to each resistor.

For the circuit shown in Figure P28.34, we wish to find the currents I1, I2, and I3. Use Kirchhoffs rules to obtain equations for (a) the upper loop, (b) the lower loop, and (c) the junction on the left side. In each case, suppress units for clarity and simplify, combining the terms. (d) Solve the junction equation for I3. (e) Using the equation found in part (d), eliminate I3 from the equation found in part (b). (f) Solve the equations found in parts (a) and (e) simultaneously for the two unknowns I1 and I2. (g) Substitute the answers found in part (f) into the junction equation found in part (d), solving for I3. (h) What is the significance of the negative answer for I2?

Find the potential difference across each resistor in Figure P28.35.

(a) Can the circuit shown in Figure P28.36 be reduced to a single resistor connected to a battery? Explain. Calculate the currents (b) I1, (c) I2, and (d) I3.

An uncharged capacitor and a resistor are connected in series to a source of emf. If e 5 9.00 V, C 5 20.0 mF, and R 5 100 V, find (a) the time constant of the circuit, (b) the maximum charge on the capacitor, and (c) the charge on the capacitor at a time equal to one time constant after the battery is connected.

Consider a series RC circuit as in Figure P28.38 for which R 5 1.00 MV, C 5 5.00 mF, and e 5 30.0 V. Find (a) the time constant of the circuit and (b) the maximum charge on the capacitor after the switch is thrown closed. (c) Find the current in the resistor 10.0 s after the switch is closed.

A 2.00-nF capacitor with an initial charge of 5.10 mC is discharged through a 1.30-kV resistor. (a) Calculate the current in the resistor 9.00 ms after the resistor is connected across the terminals of the capacitor. (b) What charge remains on the capacitor after 8.00 ms? (c) What is the maximum current in the resistor?

A 10.0-mF capacitor is charged by a 10.0-V battery through a resistance R. The capacitor reaches a potential difference of 4.00 V in a time interval of 3.00 s after charging begins. Find R.

In the circuit of Figure P28.41, the switch S has been open for a long time. It is then suddenly closed. Take e 5 10.0 V, R1 5 50.0 kV, R2 5 100 kV, and C 5 10.0 mF. Determine the time constant (a) before the switch is closed and (b) after the switch is closed. (c) Let the switch be closed at t 5 0. Determine the current in the switch as a function of time.

In the circuit of Figure P28.41, the switch S has been open for a long time. It is then suddenly closed. Determine the time constant (a) before the switch is closed and (b) after the switch is closed. (c) Let the switch be closed at t 5 0. Determine the current in the switch as a function of time.

The circuit in Figure P28.43 has been connected for a long time. (a) What is the potential difference across the capacitor? (b) If the battery is disconnected from the circuit, over what time interval does the capacitor discharge to one-tenth its initial voltage?

Show that the integral e` 0 e 22t/RC dt in Example 28.11 has the value 1 2RC.

A charged capacitor is connected to a resistor and switch as in Figure P28.45. The circuit has a time constant of 1.50 s. Soon after the switch is closed, the charge on the capacitor is 75.0% of its initial charge. (a) Find the time interval required for the capacitor to reach this charge. (b) If R 5 250 kV, what is the value of C?

An electric heater is rated at 1.50 3 103 W, a toaster at 750 W, and an electric grill at 1.00 3 103 W. The three appliances are connected to a common 120-V household circuit. (a) How much current does each draw? (b) If the circuit is protected with a 25.0-A circuit breaker, will the circuit breaker be tripped in this situation? Explain your answer.

A heating element in a stove is designed to receive 3 000 W when connected to 240 V. (a) Assuming the resistance is constant, calculate the current in the heating element if it is connected to 120 V. (b) Calculate the power it receives at that voltage.

Turn on your desk lamp. Pick up the cord, with your thumb and index finger spanning the width of the cord. (a) Compute an order-of-magnitude estimate for the current in your hand. Assume the conductor inside the lamp cord next to your thumb is at potential , 102 V at a typical instant and the conductor next to your index finger is at ground potential (0 V). The resistance of your hand depends strongly on the thickness and the moisture content of the outer layers of your skin. Assume the resistance of your hand between fingertip and thumb tip is , 104 V. You may model the cord as having rubber insulation. State the other quantities you measure or estimate and their values. Explain your reasoning. (b) Suppose your body is isolated from any other charges or currents. In orderof-magnitude terms, estimate the potential difference between your thumb where it contacts the cord and your finger where it touches the cord.

Assume you have a battery of emf e and three identical lightbulbs, each having constant resistance R. What is the total power delivered by the battery if the lightbulbs are connected (a) in series and (b) in parallel? (c) For which connection will the lightbulbs shine the brightest?

Find the equivalent resistance between points a and b in Figure P28.50.

Four 1.50-V AA batteries in series are used to power a small radio. If the batteries can move a charge of 240 C, how long will they last if the radio has a resistance of 200 V?

Four resistors are connected in parallel across a 9.20-V battery. They carry currents of 150 mA, 45.0 mA, 14.0 mA, and 4.00 mA. If the resistor with the largest resistance is replaced with one having twice the resistance, (a) what is the ratio of the new current in the battery to the original current? (b) What If? If instead the resistor with the smallest resistance is replaced with one having twice the resistance, what is the ratio of the new total current to the original current? (c) On a February night, energy leaves a house by several energy leaks, including 1.50 3 103 W by conduction through the ceiling, 450 W by infiltration (airflow) around the windows, 140 W by conduction through the basement wall above the foundation sill, and 40.0 W by conduction through the plywood door to the attic. To produce the biggest saving in heating bills, which one of these energy transfers should be reduced first? Explain how you decide. Clifford Swartz suggested the idea for this problem.

The circuit in Figure P28.53 has been connected for several seconds. Find the current (a) in the 4.00-V battery, (b)in the 3.00-V resistor, (c) in the 8.00-V battery, and (d) in the 3.00-V battery. (e) Find the charge on the capacitor

The circuit in Figure P28.54a consists of three resistors and one battery with no internal resistance. (a) Find the current in the 5.00-V resistor. (b) Find the power delivered to the 5.00-V resistor. (c) In each of the circuits in Figures P28.54b, P28.54c, and P28.54d, an additional 15.0-V battery has been inserted into the circuit. Which diagram or diagrams represent a circuit that requires the use of Kirchhoffs rules to find the currents? Explain why. (d) In which of these three new circuits is the smallest amount of power delivered to the 10.0-V resistor? (You need not calculate the power in each circuit if you explain your answer.)

For the circuit shown in Figure P28.55, the ideal voltmeter reads 6.00 V and the ideal ammeter reads 3.00 mA. Find (a) the value of R, (b) the emf of the battery, and (c) the voltage across the 3.00-kV resistor.

The resistance between terminals a and b in Figure P28.56 is 75.0 V. If the resistors labeled R have the same value, determine R.

(a) Calculate the potential difference between points a and b in Figure P28.57 and (b) identify which point is at the higher potential.

Why is the following situation impossible? A battery has an emf of e 5 9.20 V and an internal resistance of r 5 1.20 V. A resistance R is connected across the battery and extracts from it a power of P 5 21.2 W.

A rechargeable battery has an emf of 13.2 V and an internal resistance of 0.850 V. It is charged by a 14.7-V power supply for a time interval of 1.80 h. After charging, the battery returns to its original state as it delivers a constant current to a load resistor over 7.30 h. Find the efficiency of the battery as an energy storage device. (The efficiency here is defined as the energy delivered to the load during discharge divided by the energy delivered by the 14.7-V power supply during the charging process.)

Find (a) the equivalent resistance of the circuit in Figure P28.60, (b) the potential difference across each resistor, (c) each current indicated in Figure P28.60, and (d) the power delivered to each resistor.

When two unknown resistors are connected in series with a battery, the battery delivers 225 W and carries a total current of 5.00 A. For the same total current, 50.0 W is delivered when the resistors are connected in parallel. Determine the value of each resistor.

. When two unknown resistors are connected in series with a battery, the battery delivers total power Ps and carries a total current of I. For the same total current, a total power Pp is delivered when the resistors are connected in parallel. Determine the value of each resistor.

The pair of capacitors in Figure P28.63 are fully charged by a 12.0-V battery. The battery is disconnected, and the switch is then closed. After 1.00 ms has elapsed, (a) how much charge remains on the 3.00-mF capacitor? (b) How much charge remains on the 2.00-mF capacitor? (c)What is the current in the resistor at this time?

A power supply has an open-circuit voltage of 40.0 V and an internal resistance of 2.00 V. It is used to charge two storage batteries connected in series, each having an emf of 6.00 V and internal resistance of 0.300 V. If the charging current is to be 4.00 A, (a) what additional resistance should be added in series? At what rate does the internal energy increase in (b) the supply, (c) in the batteries, and (d) in the added series resistance? (e) At what rate does the chemical energy increase in the batteries?

The circuit in Figure P28.65 contains two resistors, R1 5 2.00 kV and R2 5 3.00 kV, and two capacitors, C1 5 2.00 mF and C2 5 3.00 mF, connected to a battery with emf e 5 120 V. If there are no charges on the capacitors before switch S is closed, determine the charges on capacitors (a) C1 and (b) C2 as functions of time, after the switch is closed.

Two resistors R1 and R2 are in parallel with each other. Together they carry total current I. (a) Determine the current in each resistor. (b) Prove that this division of the total current I between the two resistors results in less power delivered to the combination than any other division. It is a general principle that current in a direct current circuit distributes itself so that the total power delivered to the circuit is a minimum.

The values of the components in a simple series RC circuit containing a switch (Fig. P28.38) are C 5 1.00 mF, R 5 2.00 3 106 V, and e 5 10.0 V. At the instant 10.0 s after the switch is closed, calculate (a) the charge on the capacitor, (b) the current in the resistor, (c) the rate at which energy is being stored in the capacitor, and (d) the rate at which energy is being delivered by the battery.

A battery is used to charge a capacitor through a resistor as shown in Figure P28.38. Show that half the energy supplied by the battery appears as internal energy in the resistor and half is stored in the capacitor

A young man owns a canister vacuum cleaner marked 535 W [at] 120 V and a Volkswagen Beetle, which he wishes to clean. He parks the car in his apartment parking lot and uses an inexpensive extension cord 15.0 m long to plug in the vacuum cleaner. You may assume the cleaner has constant resistance. (a) If the resistance of each of the two conductors in the extension cord is 0.900 V, what is the actual power delivered to the cleaner? (b) If instead the power is to be at least 525 W, what must be the diameter of each of two identical copper conductors in the cord he buys? (c) Repeat part (b) assuming the power is to be at least 532 W.

(a) Determine the equilibrium charge on the capacitor in the circuit of Figure P28.70 as a function of R. (b) Evaluate the charge when R 5 10.0 V. (c) Can the charge on the capacitor be zero? If so, for what value of R ? (d) What is the maximum possible magnitude of the charge on the capacitor? For what value of R is it achieved? (e) Is it experimentally meaningful to take R 5 `? Explain your answer. If so, what charge magnitude does it imply?

Switch S shown in Figure P28.71 has been closed for a long time, and the electric circuit carries a constant current. Take C1 5 3.00 mF, C2 5 6.00 mF, R1 5 4.00 kV, and R2 5 7.00 kV. The power delivered to R2 is 2.40 W. (a) Find the charge on C1. (b) Now the switch is opened. After many milliseconds, by how much has the charge on C2 changed?

Three identical 60.0-W, 120-V lightbulbs are connected across a 120-V power source as shown in Figure P28.72. Assuming the resistance of each lightbulb is constant (even though in reality the resistance might increase markedly with current), find (a) the total power supplied by the power source and (b) the potential difference across each lightbulb.

A regular tetrahedron is a pyramid with a triangular base and triangular sides as shown in Figure P28.73. Imagine the six straight lines in Figure P28.73 are each 10.0-V resistors, with junctions at the four vertices. A 12.0-V battery is connected to any two of the vertices. Find (a) the equivalent resistance of the tetrahedron between these vertices and (b) the current in the battery.

An ideal voltmeter connected across a certain fresh 9-V battery reads 9.30 V, and an ideal ammeter briefly connected across the same battery reads 3.70 A. We say the battery has an open-circuit voltage of 9.30 V and a short-circuit current of 3.70 A. Model the battery as a source of emf e in series with an internal resistance r as in Figure 28.1a. Determine both (a) e and (b) r. An experimenter connects two of these identical batteries together as shown in Figure P28.74. Find (c) the open-circuit voltage and (d) the short-circuit current of the pair of connected batteries. (e) The experimenter connects a 12.0-V resistor between the exposed terminals of the connected batteries. Find the current in the resistor. (f) Find the power delivered to the resistor. (g) The experimenter connects a second identical resistor in parallel with the first. Find the power delivered to each resistor. (h) Because the same pair of batteries is connected across both resistors as was connected across the single resistor, why is the power in part (g) not the same as that in part (f)?

In Figure P28.75 on page 866, suppose the switch has been closed for a time interval sufficiently long for the capacitor to become fully charged. Find (a) the steady-state current in each resistor and (b) the charge Q max on the capacitor. (c) The switch is now opened at t 5 0. Write an equation for the current in R2 as a function of time and (d) find the time interval required for the charge on the capacitor to fall to one-fifth its initial value.

Figure P28.76 shows a circuit model for the transmission of an electrical signal such as cable TV to a large number of subscribers. Each subscriber connects a load resistance RL between the transmission line and the ground. The ground is assumed to be at zero potential and able to carry any current between any ground connections with negligible resistance. The resistance of the transmission line between the connection points of different subscribers is modeled as the constant resistance RT . Show that the equivalent resistance across the signal source is Req 5 1 2 3 14RTRL 1 RT 2 2 1/2 1 RT4 Suggestion: Because the number of subscribers is large, the equivalent resistance would not change noticeably if the first subscriber canceled the service. Consequently, the equivalent resistance of the section of the circuit to the right of the first load resistor is nearly equal to Req

The student engineer of a campus radio station wishes to verify the effectiveness of the lightning rod on the antenna mast (Fig. P28.77). The unknown resistance Rx is between points C and E. Point E is a true ground, but it is inaccessible for direct measurement because this stratum is several meters below the Earths surface. Two identical rods are driven into the ground at A and B, introducing an unknown resistance Ry. The procedure is as follows. Measure resistance R1 between points A and B, then connect A and B with a heavy conducting wire and measure resistance R2 between points A and C. (a) Derive an equation for Rx in terms of the observable resistances, R1 and R2. (b) A satisfactory ground resistance would be Rx , 2.00 V. Is the grounding of the station adequate if measurements give R1 5 13.0 V and R2 5 6.00 V? Explain.

The circuit shown in Figure P28.78 is set up in the laboratory to measure an unknown capacitance C in series with a resistance R 5 10.0 MV powered by a battery whose emf is 6.19 V. The data given in the table are the measured voltages across the capacitor as a function of time, where t 5 0 represents the instant at which the switch is thrown to position b. (a) Construct a graph of ln (e/Dv) versus t and perform a linear least-squares fit to the data. (b) From the slope of your graph, obtain a value for the time constant of the circuit and a value for the capacitance.

An electric teakettle has a multiposition switch and two heating coils. When only one coil is switched on, the well-insulated kettle brings a full pot of water to a boil over the time interval Dt. When only the other coil is switched on, it takes a time interval of 2 Dt to boil the same amount of water. Find the time interval required to boil the same amount of water if both coils are switched on (a) in a parallel connection and (b) in a series connection.

A voltage DV is applied to a series configuration of n resistors, each of resistance R. The circuit components are reconnected in a parallel configuration, and voltage DV is again applied. Show that the power delivered to the series configuration is 1/n2 times the power delivered to the parallel configuration.

In places such as hospital operating rooms or factories for electronic circuit boards, electric sparks must be avoided. A person standing on a grounded floor and touching nothing else can typically have a body capacitance of 150 pF, in parallel with a foot capacitance of 80.0 pF produced by the dielectric soles of his or her shoes. The person acquires static electric charge from interactions with his or her surroundings. The static charge flows to ground through the equivalent resistance of the two shoe soles in parallel with each other. A pair of rubbersoled street shoes can present an equivalent resistance of 5.00 3 103 MV. A pair of shoes with special staticdissipative soles can have an equivalent resistance of 1.00 MV. Consider the persons body and shoes as forming an RC circuit with the ground. (a)How long does it take the rubber-soled shoes to reduce a persons potential from 3.00 3 103 V to 100 V? (b) How long does it take the static-dissipative shoes to do the same thing?

The switch in Figure P28.82a closes when DVc . 2 3 DV and opens when DVc , 1 S 3 DV. The ideal voltmeter reads a potential difference as plotted in Figure P28.82b. What is the period T of the waveform in terms of R1, R2, and C ?

The resistor R in Figure P28.83 receives 20.0 W of power. Determine the value of R.