(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.
(b) Calculate the capacitance for the following capacitors:
(i) Cylindrical capacitor has radii a = 1.5 cm and b = 2.0 cm and the space between the
plates is filled with an inhomogeneous dielectric with &, = (10 + p)/p, where p is in
centimetres.
(i) Parallel capacitors in Figure 3 with &1 = 2.5, 82 = 3.5, d= 20 mm, and S= 25 cm?.
Eri
d/2
Eri
Er2
Er2
d2
S/2
S/2
Figure 3
(i) What is the effective capacitance of the following capacior network?
(ii) Given that the voltage between a and b is 10 volts, What is the charge on the 2 µF and
4 µF capacitors and what is the potential difference across the 6 µF capacitor?
(iii) What is the energy stored in the 6 µF capacitor?
(iv) If a dielectric of K=2 is inserted into the 2 µF capacitor, what is the charge on this
capacitor after that?
2.0 LF
4.0 µF
6.0 µF
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