Essential University Physics
4th Edition
ISBN: 9780134988566
Author: Wolfson, Richard
Publisher: Pearson Education,
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Textbook Question
Chapter 25, Problem 72P
Show that only half the total energy drawn from a battery in charging an RC circuit ends up stored in the capacitor. (Hint: What happens to the rest? You’ll need to integrate.)
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Chapter 25 Solutions
Essential University Physics
Ch. 25.1 - The figure shows three circuits. Which are...Ch. 25.2 - Rank front highest to lowest the voltages across...Ch. 25.2 - The figure shows all four possible combinations of...Ch. 25.2 - The figure shows a circuit with three identical...Ch. 25.3 - Which circuit(s) cannot be analyzed using series...Ch. 25.4 - All resistors in the figure have the same value...Ch. 25.5 - A capacitor is charged to 12 V and then connected...Ch. 25 - Are household electrical outlets connected in...Ch. 25 - Can the voltage across a batterys terminals differ...Ch. 25 - Can the voltage across a batterys terminals he...
Ch. 25 - When the switch in Fig. 25.25 is open, whats the...Ch. 25 - Two identical resistors in series dissipate equal...Ch. 25 - When a large electric load such as a washing...Ch. 25 - How would you connect a pair of equal resistors...Ch. 25 - You have a battery whose voltage and internal...Ch. 25 - A student whos confused about voltage and current...Ch. 25 - A student whos confused about voltage and current...Ch. 25 - Sketch a circuit diagram for a circuit that...Ch. 25 - Sketch a diagram for a circuit consisting of two...Ch. 25 - Resistors R1 and R2 are in series, and the series...Ch. 25 - Whats the emf of a battery that delivers 27 J of...Ch. 25 - A 1.5-V battery stores 4.5 kJ of energy. How long...Ch. 25 - If you accidentally leave your car headlights...Ch. 25 - A 47-k resistor and a 39-k resistor are in...Ch. 25 - What resistance should you place in parallel with...Ch. 25 - A defective starter motor draws 285 A from a car's...Ch. 25 - Find the internal resistance of the battery in...Ch. 25 - When a 9-V battery is temporarily short-circuited,...Ch. 25 - You have a 1.0-, a 2.0-, and a 3.0- resistor. What...Ch. 25 - Find all three currents in the circuit of Fig....Ch. 25 - Prob. 24ECh. 25 - Find all three currents in the circuit of Fig....Ch. 25 - Prob. 26ECh. 25 - An ammeter with 100- resistance is inserted in the...Ch. 25 - A new mechanic foolishly connects an ammeter with...Ch. 25 - Show that the quantity RC has the units of time...Ch. 25 - If capacitance is in F, what will he the units of...Ch. 25 - Show that a capacitor is charged to approximately...Ch. 25 - An uncharged 10-F capacitor and a 470-k resistor...Ch. 25 - Find an expression for the voltage across the...Ch. 25 - Rework Example 25.3. changing the 4.0- Ω resistor...Ch. 25 - Example 25.3: In the circuit of Example 25.3, take...Ch. 25 - Example 25.3: In Fig. 25.27, take R1 = R2 = 33.0 Ω...Ch. 25 - Example 25.3 In Fig. 25.27, take R1 = 220 Ω, R2 =...Ch. 25 - A professional-grade camera flash gets its energy...Ch. 25 - You're reengieering the camera flash of the...Ch. 25 - Defibrillators restore normal heart rhythm by...Ch. 25 - Example 25.5: You’re designing a defibrillator as...Ch. 25 - In Fig. 25.28, all resistors have the same value,...Ch. 25 - In Fig. 25.28, take all resistors to be 1 k Find...Ch. 25 - Three 1.5-V batteries, with internal resistances...Ch. 25 - Prob. 45PCh. 25 - You company is designing a battery-based backup...Ch. 25 - In the circuit of Fig. 25.30, find (a) the current...Ch. 25 - In Fig. 25.30, how much power is dissipated in the...Ch. 25 - Whats the ammeter reading in Fig. 25.31? FIGURE...Ch. 25 - Find all three currents in the circuit of Fig....Ch. 25 - In Example 25.4. ε2, is taken to be +9 V in the...Ch. 25 - The voltage across the 30-k resistor in Fig. 25.33...Ch. 25 - In Fig. 25.34, what are the meter readings when an...Ch. 25 - Prob. 55PCh. 25 - The voltage across a charging capacitor in an RC...Ch. 25 - Youre designing an external defibrillator that...Ch. 25 - A capacitor is charged until it holds 5.0 J of...Ch. 25 - A capacitor is charged until it holds 5.0 J of...Ch. 25 - In Fig. 25.35 the 2.0-F capacitor is charged to...Ch. 25 - For the circuit of Example 25.6, take = 100 V,...Ch. 25 - In Fig. 25.36, the switch is initially open and...Ch. 25 - Prob. 63PCh. 25 - An ammeter with resistance 1.42 is connected...Ch. 25 - In Fig. 25.37, take 1 = 12.0 V, 2 = 6.00 V, 3 =...Ch. 25 - With all values except 2 as given in the preceding...Ch. 25 - The voltage on a charged capacitor is monitored...Ch. 25 - Find the resistance needed in an RC circuit to...Ch. 25 - Suppose the currents into and out of a circuit...Ch. 25 - Show that a battery delivers the most power when...Ch. 25 - Youre writing the instruction manual for a stereo...Ch. 25 - Show that only half the total energy drawn from a...Ch. 25 - Find the equivalent resistance between A and B for...Ch. 25 - Prob. 74PCh. 25 - Obtain an expression for the rate of increase...Ch. 25 - The circuit in Fig. 25.39 extends forever to the...Ch. 25 - Figure 25.40 on the next page shows the voltage...Ch. 25 - Figure 25.41 shows a portion of a circuit used to...Ch. 25 - An electrochemical impulse traveling along the...Ch. 25 - In Fig. 25.27, take R1 = 47 Ω and R2 = 150 Ω....Ch. 25 - Write the node and loop equations for the circuit...Ch. 25 - Youre about to purchase a battery. Normally,...Ch. 25 - In the circuit of Fig. 25.42 the switch is...Ch. 25 - BIO Stray voltage is a serious problem on dairy...Ch. 25 - BIO Stray voltage is a serious problem on dairy...Ch. 25 - BIO Stray voltage is a serious problem on dairy...Ch. 25 - BIO Stray voltage is a serious problem on dairy...
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- When discharging a capacitor, as discussed in conjunction with Figure 21.39, how long does it take for the voltage on the capacitor to reach zero? Is this a problem?arrow_forwardCheck Your Understanding If you place a wire directly across the two terminal of a battery, effectively shorting out the terminals, the battery will begin to get hot. Wiry do you suppose this happens?arrow_forwardSome camera flashes use flash tubes that requite a high voltage. They obtain a high voltage by charging capacitors in parallel and then internally changing the connections of the capacitors to place diem in series. Consider a circuit that uses four AAA batteries connected in series to charge six 10-mF capacitors through an equivalent resistance of 100 . The connections are thenswitched internally to place the capacitors in series. The capacitors discharge through a lamp with a resistance of 100 . (a) What is the RC time constant and the initialcurrent out of the batteries while they are connected in parallel? (b) How long does it take for the capacitors to charge to 90% of the terminal voltages of the batteries? (c) What is the RC time constant and the initial current of the capacitors connected in series assuming it discharges at 90% of full charge? (d) How long does it rake the current to decrease to 10% of the initial value?arrow_forward
- A 4.00F capacitor and a 6.00F capacitor are connected in parallel across a 600-V supply line, (a) Find the charge on each capacitor and voltage across each, (b) The charged capacitors are disconnected from the line and from each other. They are then reconnected to each other with terminals of unlike sign together. Find the final charge on each capacitor and the voltage across each.arrow_forwardAssume a length of axon membrane of about 0.10 m is excited by an action potential (length excited = nerve speed pulse duration = 50.0 m/s 2.0 103 s = 0.10 m). In the resting state, the outer surface of the axon wall is charged positively with K+ ions and the inner wall has an equal and opposite charge of negative organic ions, as shown in Figure P18.43. Model the axon as a parallel-plate capacitor and take C = 0A/d and Q = C V to investigate the charge as follows. Use typical values for a cylindrical axon of cell wall thickness d = 1.0 108 m, axon radius r = 1.0 101 m, and cell-wall dielectric constant = 3.0. (a) Calculate the positive charge on the outside of a 0.10-m piece of axon when it is not conducting an electric pulse. How many K+ ions are on the outside of the axon assuming an initial potential difference of 7.0 102 V? Is this a large charge per unit area? Hint: Calculate the charge per unit area in terms of electronic charge e per squared (2). An atom has a cross section of about 1 2 (1 = 1010 m). (b) How much positive charge must flow through the cell membrane to reach the excited state of + 3.0 102 V from the resting state of 7.0 102 V? How many sodium ions (Na+) is this? (c) If it takes 2.0 ms for the Na+ ions to enter the axon, what is the average current in the axon wall in this process? (d) How much energy does it take to raise the potential of the inner axon wall to + 3.0 102 V, starting from the resting potential of 7.0 102 V? Figure P18.43 Problem 43 and 44.arrow_forwardTwo capacitors, C1 = 18.0 F and C2 = 36.0 F, are connected in series, and a 12.0-V battery is connected across the two capacitors. Find (a) the equivalent capacitance and (b) the energy stored in this equivalent capacitance. (c) Find the energy stored in each individual capacitor. (d) Show that the sum of these two energies is the same as the energy found in part (b). (e) Will this equality always be true, or docs it depend on the number of capacitors and their capacitances? (f) If the same capacitors were connected in parallel, what potential difference would be required across them so that the combination stores the same energy as in part (a)? (g) Which capacitor stores more energy in this situation, C1 or C2?arrow_forward
- If three unequal capacitors, initially uncharged, are connected in series across a battery, which of the following statements is true? (a) The equivalent capacitance is greater than any of the individual capacitances, (b) The largest voltage appeal's across the smallest capacitance, (c) The largest voltage appears across the largest capacitance. (d) The capacitor with the largest capacitance has the greatest charge, (e) The capacitor with the smallest capacitance has the smallest charge.arrow_forwardA 1-megabit computer memory chip contains many 60.0 1015-F capacitors. Each capacitor has a plate area of 21.0 1012 m2. Determine the plate separation of such a capacitor. (Assume a parallel-plate configuration.) The diameter of an atom is on the order of 1010 m = 1 . Express the plate separation in angstroms.arrow_forwardFind the total capacitance of the combination of capacitors shown in Figure 19.34. Figure 19.34 A combination of series and parallel connections of capacitors.arrow_forward
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