(II) In the DRAM computer chip of Problem 10, the cell capacitor’s two conducting parallel plates are separated by a 2.0-nm thick insulating material with dielectric constant K = 25. ( a ) Determine the area A (in μ m 2 ) of the cell capacitor’s plates. ( b ) In (older) “planar” designs, the capacitor was mounted on a silicon-wafer surface with its plates parallel to the plane of the wafer. Assuming the plate area A accounts for half of the area of each cell, estimate how many megabytes of memory can be placed on a 3.0-cm 2 silicon wafer with the planar design? (1 byte = 8 bits.)
(II) In the DRAM computer chip of Problem 10, the cell capacitor’s two conducting parallel plates are separated by a 2.0-nm thick insulating material with dielectric constant K = 25. ( a ) Determine the area A (in μ m 2 ) of the cell capacitor’s plates. ( b ) In (older) “planar” designs, the capacitor was mounted on a silicon-wafer surface with its plates parallel to the plane of the wafer. Assuming the plate area A accounts for half of the area of each cell, estimate how many megabytes of memory can be placed on a 3.0-cm 2 silicon wafer with the planar design? (1 byte = 8 bits.)
(II) In the DRAM computer chip of Problem 10, the cell capacitor’s two conducting parallel plates are separated by a 2.0-nm thick insulating material with dielectric constant K = 25. (a) Determine the area A (in μm2) of the cell capacitor’s plates. (b) In (older) “planar” designs, the capacitor was mounted on a silicon-wafer surface with its plates parallel to the plane of the wafer. Assuming the plate area A accounts for half of the area of each cell, estimate how many megabytes of memory can be placed on a 3.0-cm2 silicon wafer with the planar design? (1 byte = 8 bits.)
The square plates of the capacitor have sides " "e and are a distance "d" apart. A material of
dielectric constant "K" is inserted a distance "x" into of the capacitor.
Obtain
IV)
1)
II)
The equivalent capacitance of this device for: l=10 cm, x=4 cm, d=8 mm, k=5.
The energy stored in the capacitor for: l=10 cm, x=4 cm, d=8 mm, K-5, AV=1000 V
The force vector exerted on the dielectric, assuming a constant potential difference
"AV", neglect friction as it is very small.
Evaluate the magnitude of the force, for: 1=5 cm, AV=2 000 volts, d=2 mm, and K=4.5.
dok
T
k
H
AV
(i) Rank the following five capacitors from greatest to smallest capacitance, noting any cases of equality. (Use only ">" or
"=" symbols. Do not include any parentheses around the letters or symbols.)
(a) a 20-uF capacitor with a 4-V potential difference between its plates
(b) a 30-µF capacitor with charges of magnitude 90 µC on each plate
(c) a capacitor with charges of magnitude 80 uC on its plates, differing by 2 V in potential
(d) a 10-µF capacitor storing energy 125 µ)
(e) a capacitor storing energy 250 µ) with a 10-V potential difference
(i) Use Gauss’s law to find the electric field due to a uniformly charged infinite plane sheet. What is the direction of field for positive and negative charge densities?
(ii) Find the ratio of the potential differences that must be applied across the parallel and series combination of two capacitors Cj and C2 with their capacitances in the ratio 1 : 2 so that the energy stored in the two cases becomes the same.
Chapter 24 Solutions
Physics for Scientists and Engineers with Modern Physics
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