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- Why do we need to be careful about work done on the system versus work done by the system in calculations?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.A large household air conditioner may consume 15.0 kW of power. What is the cost of operating this air conditioner 3.00 h per day for 30.0 d if the cost of electricity is $0.110 per kW h?
- Consider the RC high-pass filler circuit shown in Figure P33.53. (a) Find an expression for the ratio of the amplitude of the output volt age to that of the input voltage in terms of R, C, and the AC source frequency . (b) What value does this ratio approach as the frequency decreases toward zero? (c) What value does this ratio approach as the frequency increases without limit?Power P0 = I0 V0 is delivered to a resistor of resistance R0. If the resistance is doubled (Rnew = 2R0) while the voltage is adjusted such that the current is constant, what are the ratios (a) Pnew/P0 and (b) Vnew/V0? If, instead, the resistance is held constant while Pnew = 2P0, what are the ratios (c) Vnew/V0, and (d) Inew/I0?Assume 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.
- The power dissipated in a resistor is given by P = V2/R, which means power decreases if resistance increases. Yet this power is also given by P = I2R, which means power increases if resistance increases. Explain why there is no contradiction here.In this chapter, most examples and problems involved direct current (DC). DC circuits have the current flowing in one direction, from positive to negative. When the current was changing, it was changed linearly from I=ImaxtoI=+Imax and the voltage changed linearly from V=Vmax to V=+Vmax where Vmax=ImaxR .Suppose a voltage source is placed in series with a resistor of R = 10 that supplied a current that alternated as a sine wave, for example, I(t)=(3.00A)sin(24.00st) . (a) What would a graph of the voltage drop across the resistor V(t) versus time look like? (b) What would a plot of V(t) versus I(t) for one period look like? (Hint: If you are not sure, try plotting V(t) versus I(t) using a spreadsheet.)(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?
- If you were to design an electric heater using Nichrome wire as the heating element, what parameters of the wire could you vary to meet a specific power output such as 1 000 W?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.The timing device in an automobile’s intermittent wiper system is based on an RC time constant and utilizes 0.5.00F capacitor and available resistor. Over what range must R be made to vary to achieve time constants from 2.00 to 15.0 s?
