42. The voltage across the 30-kΩresistor in Fig. 28-60 is measured with (a) a 50-kΩvoltmeter, (b) a 250-kΩvoltmeter, and (c) a digital meter with 10-MΩresistance. To two significant figures, what does each read? 43. In Fig. 28-61 what are the meter readings when (a) an ideal voltmeter or (b) an ideal ammeter is connected between
666 CHAPTER 28 points A and B ? + – 30 V 10 k Ω 20 k Ω A B FIGURE 28-61 Problem 43. Solution (a) An ideal voltmeter has infinite resistance, so AB is still an open circuit (as shown on Fig. 28-61) when such a voltmeter is connected. The meter reads the voltage across the 20 k Ω resistor (part of a voltage divider), or ( ) ( ) 30 20 20 10 V = = 20 V (see Equation 28-2a or b). (b) An ideal ammeter has zero resistance, and thus measures the current through the points A and B when short-circuited (i.e., no current flows through the 20 k Ω resistor). In Fig. 28-61, this would be I AB = 30 10 3 V mA. = Ω = (Such a connection does not measure the current in the original circuit, since an ammeter should be connected in series with the current to be measured.) Problem 45. Show that the quantity RC has the units of time (seconds). Solution The SI units for the time constant, RC , are ( )( ) ( )( ) ( )( ) , Ω F V A C V s C C s = = = = = = as stated. Problem 47. Show that a capacitor is charged to approximately 99% of the applied voltage in five time constants. Solution After five time constants, Equation 28-6 gives a voltage of V e C =E ' = - = - × - - 1 1 6 74 10 99 3% 5 3 . . of the applied voltage. Problem 49. Figure 28-62 shows the voltage across a capacitor that is charging through a 4700- Ω resistor in the circuit of Fig. 28-29. Use the graph to determine (a) the battery voltage, (b) the time constant, and (c) the capacitance.
CHAPTER 28 667 FIGURE 28-62 Problem 49 Solution. Solution (a) For the circuit considered, the voltage across the capacitor asymptotically approaches the battery voltage after a long time (compared to the time constant). In Fig. 28-62, this is about 9 V. (b) The time constant is the time it takes the capacitor voltage to reach 1 63 2% 1 - = - e . of its asymptotic value, or 5.69 V in this case. From the graph, τ ' 15 . . ms (c) The time constant is RC , so C = = 15 4700 0 319 . . . ms F = Ω μ Problem
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- Winter '14
- Volt, Resistor, Electrical resistance, Series and parallel circuits, resistor R1