(II) For commonly used CMOS (complementary metal oxide semiconductor) digital circuits, the charging of the component capacitors C to their working potential difference V accounts for the major contribution of its energy input requirements. Thus, if a given logical operation requires such circuitry to charge its capacitors N times, we can assume that the operation requires an energy of N ( 1 2 C V 2 ) . In the past 20 years, the capacitance in digital circuits has been reduced by a factor of about 20 and the voltage to which these capacitors are charged has been reduced from 5.0 V to 1.5 V. Also, present-day alkaline batteries hold about five times the energy of older batteries. Two present-day AA alkaline cells, each of which measures 1 cm diameter by 4 cm long, can power the logic circuitry of a hand-held personal digital assistant (PDA) with its display turned off for about two months. If an attempt was made to construct a similar PDA (i.e., same digital capabilities so N remains constant) 20 years ago, how many (older) AA batteries would have been required to power its digital circuitry for two months? Would this PDA fit in a pocket or purse?
(II) For commonly used CMOS (complementary metal oxide semiconductor) digital circuits, the charging of the component capacitors C to their working potential difference V accounts for the major contribution of its energy input requirements. Thus, if a given logical operation requires such circuitry to charge its capacitors N times, we can assume that the operation requires an energy of N ( 1 2 C V 2 ) . In the past 20 years, the capacitance in digital circuits has been reduced by a factor of about 20 and the voltage to which these capacitors are charged has been reduced from 5.0 V to 1.5 V. Also, present-day alkaline batteries hold about five times the energy of older batteries. Two present-day AA alkaline cells, each of which measures 1 cm diameter by 4 cm long, can power the logic circuitry of a hand-held personal digital assistant (PDA) with its display turned off for about two months. If an attempt was made to construct a similar PDA (i.e., same digital capabilities so N remains constant) 20 years ago, how many (older) AA batteries would have been required to power its digital circuitry for two months? Would this PDA fit in a pocket or purse?
(II) For commonly used CMOS (complementary metal oxide semiconductor) digital circuits, the charging of the component capacitors C to their working potential difference V accounts for the major contribution of its energy input requirements. Thus, if a given logical operation requires such circuitry to charge its capacitors N times, we can assume that the operation requires an energy of
N
(
1
2
C
V
2
)
. In the past 20 years, the capacitance in digital circuits has been reduced by a factor of about 20 and the voltage to which these capacitors are charged has been reduced from 5.0 V to 1.5 V. Also, present-day alkaline batteries hold about five times the energy of older batteries. Two present-day AA alkaline cells, each of which measures 1 cm diameter by 4 cm long, can power the logic circuitry of a hand-held personal digital assistant (PDA) with its display turned off for about two months. If an attempt was made to construct a similar PDA (i.e., same digital capabilities so N remains constant) 20 years ago, how many (older) AA batteries would have been required to power its digital circuitry for two months? Would this PDA fit in a pocket or purse?
(b) A student has three capacitors. Two of the capacitors have a capacitance of 4.0 µF and one
has a capacitance of 8.0 µF.
Draw labelled circuit diagrams, one in each case, to show how the three capacitors may be
connected to give a total capacitance of:
(i) 1.6uF
(ii) 10µF.
A number of capacitors, each of capacitance 1 uF and each one of which gets punctured if a
potential difference just exceeding 500 volt is applied, are provided. Then an arrangement
suitable for giving a capacitor of capacitance 3 µF across which 2000 volt may be applied
requires at least :
(1) 4 component capacitors
(3) 48 component capacitors
(2) 12 component capacitors
(4) 16 component capacitors
Find the energy which may be stored in capacitors of 2μF and 4μF when taken (a) singly, (b) in series, and (c) in parallel when a potential difference of 100V is available.
Chapter 24 Solutions
Physics for Scientists and Engineers with Modern Physics
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