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Which of the following do not affect capacitance?

(a) Area of the plates.

(b) Separation of the plates.

(c) Material between the plates.

(d) Charge on the plates.

(e) Energy stored in the capacitor.

Can two equipotential lines cross? Explain.

In the dynamic random access memory (DRAM) of a computer, each memory cell contains a capacitor for charge storage. Each of these cells represents a single binary bit value of 鈥�1鈥� when its 35-fF capacitor \(\left( {{\bf{1}}\;{\bf{fF = 1}}{{\bf{0}}^{{\bf{ - 15}}}}\;{\bf{F}}} \right)\) is charged at 1.5 V, or 鈥�0鈥� when uncharged at 0 V.

(a) When fully charged, how many excess electrons are on a cell capacitor鈥檚 negative plate?

(b) After charge has been placed on a cell capacitor鈥檚 plate, it slowly 鈥渓eaks鈥� off at a rate of about \({\bf{0}}{\bf{.30}}\;{\bf{fC/s}}\). How long does it take for the potential difference across this capacitor to decrease by 2.0% from its fully charged value? (Because of this leakage effect, the charge on a DRAM capacitor is 鈥渞efreshed鈥� many times per second.) Note: A DRAM cell is shown in Fig. 21鈥�29.

In the DRAM computer chip of Problem 94, suppose the two parallel plates of one cell鈥檚 35-fF capacitor are separated by a 2.0-nm-thick insulating material with dielectric constant K= 25.

(a) Determine the area A\(\left( {{\bf{\mu }}{{\bf{m}}^{\bf{2}}}} \right)\)of the cell capacitor鈥檚 plates.

(b) If the plate area A accounts for half of the area of each cell, estimate how many megabytes of memory can be placed on a\({\bf{3}}\;{\bf{c}}{{\bf{m}}^{\bf{2}}}\)silicon wafer.\(\left( {{\bf{1}}\;{\bf{byte = 8}}\;{\bf{bits}}{\bf{.}}} \right)\)

A parallel-plate capacitor with plate area\({\bf{A = 2}}{\bf{.0}}\;{{\bf{m}}{\bf{2}}}\)and plate separation\({\bf{d = 3}}{\bf{.0}}\;{\bf{mm}}\)is connected to a 35-V battery (Fig. 17鈥�51a).

(a) Determine the charge on the capacitor, the electric field, the capacitance, and the energy stored in the capacitor.

(b) With the capacitor still connected to the battery, a slab of plastic with dielectric strength K =3.2 is placed between the plates of the capacitor, so that the gap is completely filled with the dielectric (Fig. 17鈥�51b). What are the new values of charge, electric field, capacitance, and the energy stored in the capacitor?\(\left( {{\bf{1}}\;{\bf{byte = 8}}\;{\bf{bits}}{\bf{.}}} \right)\)

FIGURE 17-51 Problem 96

A battery establishes a voltage Von a parallel-plate capacitor.After the battery is disconnected, the distance between the plates is doubled without loss of charge. Accordingly,the capacitance _________ and the voltage between theplates _________.

(a) increases; decreases.

(b) decreases; increases.

(c) increases; increases.

(d) decreases; decreases.

(e) stays the same; stays the same.

Draw in a few equipotential lines in Fig. 16鈥�32b and c.

FIGURE 16-32