Problem 76
A 2.36-\(\mu\)F capacitor that is initially uncharged is connected in series with a 5.86-\(\Omega\) resistor and an emf source with \(\varepsilon =\) 120 V and negligible internal resistance. (a) Just after the connection is made, what are (i) the rate at which electrical energy is being dissipated in the resistor; (ii) the rate at which the electrical energy stored in the capacitor is increasing; (iii) the electrical power output of the source? How do the answers to parts (i), (ii), and (iii) compare? (b) Answer the same questions as in part (a) at a long time after the connection is made. (c) Answer the same questions as in part (a) at the instant when the charge on the capacitor is one-half its final value.
Problem 77
A 224-\(\Omega\) resistor and a 589-\(\Omega\) resistor are connected in series across a 90.0-V line. (a) What is the voltage across each resistor? (b) A voltmeter connected across the 224-\(\Omega\) resistor reads 23.8 V. Find the voltmeter resistance. (c) Find the reading of the same voltmeter if it is connected across the 589-\(\Omega\) resistor. (d) The readings on this voltmeter are lower than the "true" voltages (that is, without the voltmeter present). Would it be possible to design a voltmeter that gave readings \(higher\) than the "true" voltages? Explain.
Problem 78
A resistor with \(R =\) 850 \(\Omega\) is connected to the plates of a charged capacitor with capacitance \(C =\) 4.62 \(\mu\)F. Just before the connection is made, the charge on the capacitor is 6.90 mC. (a) What is the energy initially stored in the capacitor? (b) What is the electrical power dissipated in the resistor just after the connection is made? (c) What is the electrical power dissipated in the resistor at the instant when the energy stored in the capacitor has decreased to half the value calculated in part (a)?
Problem 82
The electronics supply company where you work has two different resistors, \(R_1\) and \(R_2\), in its inventory, and you must measure the values of their resistances. Unfortunately, stock is low, and all you have are \(R_1\) and \(R_2\) in parallel and in series-and you can't separate these two resistor combinations. You separately connect each resistor network to a battery with emf 48.0 V and negligible internal resistance and measure the power \(P\) supplied by the battery in both cases. For the series combination, \(P =\) 48.0 W; for the parallel combination, \(P =\) 256 W. You are told that \(R_1\) \(R_2\). (a) Calculate \(R_1\) and \(R_2\). (b) For the series combination, which resistor consumes more power, or do they consume the same power? Explain. (c) For the parallel combination, which resistor consumes more power, or do they consume the same power?
Problem 86
Assume that a typical open ion channel spanning an axon's membrane has a resistance of 1 \(\times\) 10\(^{11}\) \(\Omega\). We can model this ion channel, with its pore, as a 12-nm-long cylinder of radius 0.3 nm. What is the resistivity of the fluid in the pore? (a) 10 \(\Omega\) \(\cdot\) m; (b) 6 \(\Omega\) \(\cdot\) m; (c) 2 \(\Omega\) \(\cdot\) m; (d) 1 \(\Omega\) \(\cdot\) m.
