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- Referring to Figure CQ28.6, describe what happens to the lightbulb after the switch is closed. Assume the capacitor has a large capacitance and is initially uncharged. Also assume the light illuminates when connected directly across the battery terminals.A heart defibrillator being used on a patient has an RC time constant of 10.0 ms due to the resistance of the patient and the capacitance of the defibrillator, (a) If the defibrillator has a capacitance of 8.00F , what is theresistance of the path through the patient? (You may neglect the capacitance of the patient and the resistance of the defibrillator.) (b) If the initial voltage is 12.0 kV, how long does it take to decline to 6.00102V ?(a) Determine the equilibrium charge on the capacitor in the circuit of Figure P27.46 as a function of R. (b) Evaluate the charge when R = 10.0 . (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? (c) Is it experimentally meaningful to take R = ? Explain your answer. If so, what charge magnitude does it imply? Figure P27.46
- Consider the circuit shown in Figure P28.21 on page 860. (a) Find the voltage across the 3.00-0 resistor, (b) Find the current in the 3.00-12 resistor.An uncharged series RC circuit is to be connected across a battery. For each of the following changes, determine whether the time for the capacitor to reach 90% of its final charge would increase, decrease, or remain unchanged. Indicate your answers with I, D, or U, respectively. (a) The RC time constant is doubled. (b) The battery voltage is doubled. (c) A second resistor is added in series with the original resistor.Unreasonable Results (a) Calculate the capacitance needed to get an RC time constant of 1,00x103 s with a 0.100- resistor, (b) What is unreasonable about this result? (c) Which assumptions are responsible?
- The duration of a photographic flash is related to an RC time constant, which is 0.100 s for a certain camera, (a) If the resistance of the flash lamp is 0.0400 during discharge, 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 800k ?The circuit in Figure P21.59 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?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 1.83 102.2
- Figure P27.48 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=12[(4RTRL+RT2)1/2+RT] 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. Figure P27.48Integrated Concepts A flashing lamp in a Christmas earring is based on an RC discharge of a capacitor through its resistance. The effective duration of the flash is 0.250 s, during which it produces in average 0.500 W from an average 3.00 V. (a) What energy does it dissipate? (b) How much charge moves through the lamp? (c) Find the capacitance. (d) What is the resistance of the lamp?A 50resistor is connected across the emf v(t)=(160V)sin(120t) . Write an expression for the current throug1 the resistor.