3. Refer to the diagram here. Four identical parallel-plate capacitors have been
ID: 1518701 • Letter: 3
Question
3. Refer to the diagram here. Four identical parallel-plate capacitors have been connected for a long time as shown to an ideal battery E. The capacitors are therefore fully charged, and the total electric potential energy stored is UE.total.
The plate separation distance in each capacitor is d.
Assume the following known values: E, UE.total, d, me, e0
Calculate the following, expressing your results using only known values.
a. Find the area A of each capacitor plate.
b. Suppose an electron were released from rest at the negative plate of capacitor 3. How long would it take to reach the positive plate?
c. Suppose the plate separation distance were doubled only in capacitor 1. By what percentage would this change UE.total?
3. Refer to the diagram here. Four identical parallel-plate capacitors have been connected for a long time as shown to an ideal battery E. The capacitors are therefore fully charged, and the total electric potential energy stored is UEtotal The plate separation distance in each capacitor is d cap cap Calculate the following, expressing your results using only known values cap Find the area A of each capacitor plate Suppose an electron were released from rest at the negative plate of capacitor 3. How long would it take to reach the positive plate? Suppose the plate separation distance were doubled only in capacitor 1 By what percentage would this change UEiwta a. b. c.Explanation / Answer
Known, E, UE, d, me, epsilon
a) Ceff = 5C/3
UE = 0.5*Ceff*E^2 = 5C*E^2/6
C = 6*UE/5E^2 = A*epsilon/d
A = 6*UE*d/5E^2*epsilon
b) Qeff = Ceff*E = 5C*E/3
Q3 = 5C*E/3 - CE = 2CE/3
V3 = 2E/3
Field = V3/d = 2E/3d
Force = 2qE/3d = m*a
and d = 0.5*2qE*t^2/3d*m
t = sqroot(d*3dm/qE)
c) Net Ceff' = 8C/5
(UEnew - UE)/UE = (1.6C - 1.66C)/1.66C = 3.9961 pc
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