Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 29, Problem 53PQ
To determine
Find the time constant of discharging a node.
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Switch S in in the figure is closed at time t = 0, to begin charging an initially uncharged capacitor of capacitance C = 17.2 μF through a resistor of resistance R = 21.2 Ω. At what time is the potential across the capacitor equal to that across the resistor?
In an RC circuit where the capacitor starts uncharged, what proportion of the battery voltage, or emf, is across the resistor after three time constants?
a. 5.0%
b. 63.2%
c. 36.8%
d. 95.0%
13.Consider an electric circuit containing a capacitor, resistor, and battery; see Figure 1.2.3. The charge Q(t) on the capacitor satisfies the equation R(dQ/dt)+Q/C=V,where R is the resistance, C is the capacitance, and V is the constant voltage supplied by the battery.
a.If Q(0) = 0, find Q(t) at any time t, and sketch the graph of Q versus t.
b.Find the limiting value QL that Q(t) approaches after a long time.
c.Suppose that Q(t1) = QL and that at time t = t1 the battery is removed and the circuit is closed again. Find Q(t) for t > t1 and sketch its graph.
figure1.2.3The electric circuit of Problem 13.
Chapter 29 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 29.1 - What are the SI units of ?Ch. 29.1 - Prob. 29.2CECh. 29.2 - Prob. 29.3CECh. 29.4 - Prob. 29.5CECh. 29.4 - Prob. 29.6CECh. 29.5 - Prob. 29.7CECh. 29 - Study the symbols in Table 29.2. Then, without...Ch. 29 - Prob. 2PQCh. 29 - Prob. 3PQCh. 29 - Suppose you need to measure the potential...
Ch. 29 - Prob. 5PQCh. 29 - Prob. 6PQCh. 29 - A real battery (modeled as an ideal emf device in...Ch. 29 - Prob. 8PQCh. 29 - Two circuits made up of identical ideal emf...Ch. 29 - Prob. 10PQCh. 29 - Prob. 11PQCh. 29 - Prob. 12PQCh. 29 - Eight real batteries, each with an emf of 5.00 V...Ch. 29 - Prob. 14PQCh. 29 - Prob. 15PQCh. 29 - Prob. 16PQCh. 29 - Prob. 17PQCh. 29 - Prob. 18PQCh. 29 - Prob. 19PQCh. 29 - An ideal emf device with emf is connected to two...Ch. 29 - Prob. 21PQCh. 29 - Prob. 22PQCh. 29 - Prob. 23PQCh. 29 - Prob. 24PQCh. 29 - Prob. 25PQCh. 29 - Prob. 26PQCh. 29 - Determine the currents through the resistors R2,...Ch. 29 - The emf devices in the circuits shown in Figure...Ch. 29 - Prob. 29PQCh. 29 - Prob. 30PQCh. 29 - Prob. 31PQCh. 29 - Prob. 32PQCh. 29 - Prob. 33PQCh. 29 - Prob. 34PQCh. 29 - A Figure P29.35 shows a combination of six...Ch. 29 - A Each resistor shown in Figure P29.36 has...Ch. 29 - Each resistor shown in Figure P29.36 has a...Ch. 29 - Prob. 38PQCh. 29 - Prob. 39PQCh. 29 - The emf in Figure P29.40 is 4.54 V. The...Ch. 29 - Figure P29.41 shows three resistors (R1 = 14.0 ,...Ch. 29 - Figure P29.42 shows five resistors and two...Ch. 29 - The emfs in Figure P29.43 are 1 = 6.00 V and 2 =...Ch. 29 - Prob. 44PQCh. 29 - Figure P29.45 shows five resistors connected...Ch. 29 - Figure P29.46 shows a circuit with a 12.0-V...Ch. 29 - Two ideal emf devices are connected to a set of...Ch. 29 - Two ideal emf devices are connected to a set of...Ch. 29 - Three resistors with resistances R1 = R/2 and R2 =...Ch. 29 - Prob. 51PQCh. 29 - Prob. 52PQCh. 29 - Prob. 53PQCh. 29 - Prob. 55PQCh. 29 - At time t = 0, an RC circuit consists of a 12.0-V...Ch. 29 - A 210.0- resistor and an initially uncharged...Ch. 29 - Prob. 58PQCh. 29 - A real battery with internal resistance 0.500 and...Ch. 29 - Figure P29.60 shows a simple RC circuit with a...Ch. 29 - Prob. 61PQCh. 29 - Prob. 62PQCh. 29 - Prob. 63PQCh. 29 - Ralph has three resistors, R1, R2, and R3,...Ch. 29 - Prob. 65PQCh. 29 - An ideal emf device is connected to a set of...Ch. 29 - Prob. 67PQCh. 29 - An ideal emf device (24.0 V) is connected to a set...Ch. 29 - Prob. 69PQCh. 29 - What is the equivalent resistance between points a...Ch. 29 - A capacitor with initial charge Q0 is connected...Ch. 29 - Prob. 73PQCh. 29 - Prob. 74PQCh. 29 - Prob. 75PQCh. 29 - Prob. 76PQCh. 29 - Figure P29.77 shows a circuit with two batteries...Ch. 29 - In the RC circuit shown in Figure P29.78, an ideal...Ch. 29 - Prob. 79PQCh. 29 - Calculate the equivalent resistance between points...Ch. 29 - In Figure P29.81, N real batteries, each with an...Ch. 29 - Prob. 82PQCh. 29 - Prob. 83PQCh. 29 - Prob. 84PQCh. 29 - Figure P29.84 shows a circuit that consists of two...Ch. 29 - Prob. 86PQCh. 29 - Prob. 87PQCh. 29 - Prob. 88PQCh. 29 - Prob. 89PQCh. 29 - Prob. 90PQCh. 29 - Prob. 91PQCh. 29 - Prob. 92PQCh. 29 - Prob. 93PQCh. 29 - Prob. 94PQCh. 29 - Prob. 95PQ
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- 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 = 10.0 M 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 lime, where t = 0 represents the instant at which the switch is thrown to position b. (a) Construct a graph of In (/v) versus I 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. v(V) t(s) In (/v) 6.19 0 5.56 4.87 4.93 11.1 4.34 19.4 3.72 30.8 3.09 46.6 2.47 67.3 1.83 102.2arrow_forwardThe values of the components in a simple series RC circuit containing a switch (Fig. P21.53) are C = 1.00 F, R = 2.00 106 , and = 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.arrow_forwardDraw two graphs of charge versus time on a capacitor. Draw one for charging an initially uncharged capacitor in series with a resistor, as in the circuit in Figure 21.38, starting from t = 0. Draw the other for discharging a capacitor through a resistor, as in the circuit in Figure 21.39, starting at t = 0, with an initial charge Q0. Show at least two intervals of t.arrow_forward
- In Figure P29.81, N real batteries, each with an emf and internal resistance r, are connected in a closed ring. A resistor R can be connected across any two points of this ring, causing there to be n real batteries in one branch and N n resistors in the other branch. Find an expression for the current through the resistor R in this case.arrow_forwardA capacitor of capacitance C = 4.5 uF is initially uncharged. It is connected in series with a switch of negligible resistance, a resistor of resistance R = 8.5 kOhm, and a battery which provides a potential difference of VB = 105V. (a) Calculate the time constant t for the circuit in seconds. (b) After a very long time after the switch has been closed, what is the voltage drop VC across the capacitor in terms of VB? (c) Calculate the charge Q on the capacitor a very long time after the switch has been closed in C. (d) Calculate the current I a very long time after the switch has been closed in A. (e) Calculate the time t after which the current through the resistor in one-third of its maximum value in s. (f) Calculate the cahrge Q on the capacitor when the current in the resistor equals one third its maximum value in C.arrow_forwardThe figure displays two circuits with a charged capacitor that is to be discharged through a resistor when a switch is closed. In figure (a) below, R1 = 21.9 Ω and C1 = 5.26 μF. In figure (b) below, R2 = 10.9 Ω and C2 = 8.08 μF. The ratio of the initial charges on the two capacitors is q02/q01 = 1.64. At time t = 0, both switches are closed. At what time t do the two capacitors have the same charge?arrow_forward
- An initially uncharged capacitor with a capacitance of C = 5.00 µF is connected in series with a resistor with a resistance of R = 4.5 k. If this series combination of circuit elements is attached to an ideal battery with an emf of Ɛ = 450 V by means of a switch S that is closed at time t = 0, then answer the following questions. (a) What is the time constant of this circuit? (b) How long will it take for the capacitor to reach 75% of its final charge? (c) What is the final charge on the capacitor?arrow_forwardYou connect a battery, resistor, and capacitor as in the figure, where R = 16.0 Ω and C = 8.00 ×10−6 F. The switch S is closed at t = 0. When the current in the circuit has magnitude 3.00 A, the charge on the capacitor is 40.0 × 10−6 C. (a) What is the emf of the battery? (b) At what time t after the switch is closed is the charge on the capacitor equal to 40.0×10−6 C? (c) When the current has magnitude 3.00 A, at what rate is energy being stored in the capacitor? (d) When the current has magnitude 3.00 A, at what rate is energy being supplied by the battery?arrow_forwardThe figure 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. The resistor has a resistance of 284 kΩΩ. (a) What is the time constant? s ( ± 0.1 s) (b) How long will it take to reduce the voltage on the capacitor to 1.0% of its full value once discharge begins? s ( ± 1 s) (c) If the capacitor is charged to a voltage ?0V0 through a 109 ΩΩ resistance, calculate the time it takes to rise to 0.9?0V0 (This is close to two time constants, but you should calculate it precisely.) ms ( ± 0.1 ms)arrow_forward
- A simple RC circuit consists of a 1 microF capacitor in series with a 3,000 ohm resistor connected to a 6V battery and an open switch. Initially the capacitor is discharged. Once the switch is closed, determine the time it takes for the voltage in the capacitor to be 3.8 V. a. 3s b. 0.003s c. 3x10^9s d. 3x10^-9s e. 3x10^-8 sarrow_forwardYou connect a battery, a resistor, and a capacitor as shown in Figure 4, in that e = 36.0 V, C = 5.0 uF and R = 120 Ohms C. The switch S is closed at t = 0. (a) When the voltage across the capacitor is 8.00 V, what is the magnitude of the current in the circuit? (b) At what time t after the switch is closed the voltage across the capacitor is equal to 8.00 V? (c) When the voltage across the capacitor equals 8.00 V, at what speed is energy being stored in the capacitor? Translation: "Chave aberta" = switch openarrow_forwardA capacitor, initially at 21 V, is discharged using an 19 Ω resistor. After 155 s there are 4.2 V across the capacitor. What is the capacitance of the capacitor? (in F) a. 36.6 F b. 13.1 F c. 8.16 F d. 5.07 Farrow_forward
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