When two capacitors are connected in parallel and then connected to a battery, t

Question

When two capacitors are connected in parallel and then connected to a battery, the total stored energy is 4.8 times greater than when they are connected in series and then connected to the same battery. What is the ratio of the two capacitances? (Before the battery is connected in each case, the capacitors are fully discharged.) Express your answer using two significant figures. In a dynamic random access memory (DRAM) computer chip, each memory cell chiefly consists of a capacitor for charge storage. Each of these cells represents a single binary-bit value of 1 when its 35-fF capacitor (1 fF = 10^-15 F) is charged at 1.5 V, or 0 when uncharged at 0 V. The cell capacitor's two conducting parallel plates are separated by a 2.0-nm thick insulating material with dielectric constant K = 25. Determine the area A (in mu m^2) of the cell capacitor's plates. Express your answer to two significant figures and include the appropriate units. 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.)Express your answer using two significant figures.

Explanation / Answer

7) 0.5(c1 + c2) v^2 = 4.8*0.5(c1 c2)/(c1 + c2) v^2

  (c1 + c2)^2 = 4.8*(c1 c2)

c1^2 + c2^2 -2.8*c1c2 = 0   

c1 = 2.3798 c2

c1 = 0.4202 c2

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