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 83PQ
To determine
The time constant
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a. List some applications of RC circuits. For the RC circuit shown in Figure, the capacitor with initial charge
qo is discharged through the resistor. What multiple of the time constant t gives the time the capacitor takes
to lose the first one-third of its charge.
This problem involves analyzing an RC circuit. See the circuit diagram below.
Switch closes
at t = 0 s.
А.
When the switch closes at t = 0, the capacitor will begin to charge. What is AVc a
very long time after the switch has closed? After a very long time, what is the maximum charge
on the capacitor, Qmax in terms of a combination of problem variables Ɛ, C or R?
%3D
Apply Kirchhoff's loop law starting clockwise from the lower left corner. Write down the loop
equation for this circuit. How is the current through the resistor related to the instantaneous
capacitor charge? Is I = + dQ/dt or I = – dQ/dt? Explain.
|
В.
The Kirchhoff loop equation from part (A) should be a differential equation in terms
of dQ/dt. Using the differential equation technique “separation of variables" show that charge
as a function of time is given by Q(t) = Qmax(1 – e-t/t).
С.
Using the result of part (B) determine and expression for the current as a function of
time 1(t).
Sketch Q (t) and I(t) from t = 0 to t…
b. About how many time constants does it take to charge a capacitor in an RC circuit to 50% of its
maximum value?
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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- A 500 resistor, an uncharged 1.50F capacitor,and a 6.16-V emf are connected in series, (a) What is the initial current? (b) What is the RC time constant? (c) What is the current after one time constant? (d) What is the voltage on the capacitor after one time constant?arrow_forwardThe duration of a photographic flash is related to an RC time constant, which is 0.100F for a certain camera, (a) If the resistance of the flash lamp is 0.0400 duringdischarge, 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 k ?arrow_forwardAt time t = 0, an RC circuit consists of a 12.0-V emf device, a 60.0- resistor, and a 150.0-F capacitor that is fully charged. The switch is thrown so that the capacitor begins to discharge. a. What is the time constant t of this circuit? b. How much charge is stored by the capacitor at t = 0.5, 2, and 4?arrow_forward
- Consider a series RC circuit as in Figure P18.35 for which R = 1.00 M, C = 5.00 F, and = 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. Figure P18.35 Problem 35 and 38.arrow_forward(a) What is the average power output of a heart defibrillator that dissipates 400 J of energy in 10.0 ms? (b) Considering the high-power output, why doesn’t the defibrillator produce serious bums?arrow_forwardb. Would adding another capacitor in parallel to an RC circuit increase, decrease, or not change its time constant?arrow_forward
- b. A capacitor in a RC circuit is charged for a long time as shown in the Figure below, where the battery voltage V=6V. The switch s is flipped from a to b and the capacitor discharges through the R = 4 MQ resistor. 4 seconds after the switch is flipped to discharge the capacitor, the voltage across the capacitor is 3 V. What are (a) The time constant of this circuit (b) The capacitance of the capacitor (c) The current in the circuit and the charge on the capacitor just before the switch is flipped from a to b. (d) The current in the circuit immediately after the switch is flipped from a to barrow_forwarda. Write your understanding about the time constant for RC circuit. A capacitor is discharging through a resistor. If it takes a time T for the charge on a capacitor to drop to half its initial value, how long (in terms of T) does it take for the stored energy to drop to half its initial value? -e b. A 10-m-long wire has a resistance equal to 0.20 Q and carries a current equal to 5.0 A. (a) What is the potential difference across the entire length of the wire? (b) What is the electric-field strength in the wire?arrow_forwardIn the RC circuit shown in figure 2, the switch is closed at time t = 0. If the resistance and capacitance are R = 1Ω and C = 5µF respectively, calculate the time at which the charge on the capacitor reaches 2/3 of its final value.arrow_forward
- An RC circuit is connected across a DC voltage source through an open switch. The switch is closed at t = 0 s. Which of the following is a correct statement regarding the circuit? O The resistor and the capacitor share the applied voltage equally as a function of time. O Once the capacitor is fully charged, there is no current in the circuit. The capacitor charges to its maximum value in one time constant. O The current flows through the circuit even after the capacitor is fully charged. The capacitor charges to its maximum value in two time constants.arrow_forwardA cook plugs a 400 W crockpot and a 1000 w kettle into a 240 V power supply, all operating on directc When we compare the two, we find that Select one: a. I Crockpot > I Kettle and R Crockpot I kettle and Rcrockpot =R kettle. C. I crockpot R kettle. d. I Crockpot = I Kettle and R Crockpot = R Kettle. %3D Previous page Finish attempt Shot by Hisense H12arrow_forwardUsing your data, answer the following questions: a. To three decimal places, what fraction of the total charge does a capacitor in an RC circuit have after charging for 4.15 time constants; the fraction f such that q(4.15t) = fQmaxarrow_forward
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