1: Four capacitors are connected as shown in the figure below. What is the equiv

Question

1: Four capacitors are connected as shown in the figure below. What is the equivalent capacitance? (Take C1 = 16 ?F, C2 = 4.3 ?F, C3 = 13 ?F, and C4 = 3.6 ?F.)

2: A parallel-plate capacitor has square plates of edge length 1.1 cm and a plate spacing of 0.11 mm. If the gap between the plates is filled with mica, what is the capacitance?

3: A cell membrane is composed of lipid molecules and is approximately 16 nm thick. If the dielectric constant of a lipid is

? ? 6, what is the approximate capacitance of a spherical cell that has a diameter of 12 ?m?

Explanation / Answer

Solution 1

Figure not given

Solution 2

Capacitance = k x ?0 x area / separation

C = k * 8.854 10^-12 * 0.0036 / 0.0034 = 9.3748235 pF ( k=1 air )

k coeff dielectric :
pyrex glass =5.1
polystyrene= 2.6
k moy = (5.1 +2.6 ) / 2 = 3.85

C = k * 9.3748235 = 3.85 * 9.3748235 = 36.093 pF

U= 1/2 C V^2 = 0.5 * 36.093 10^-12 * 76 ^2 = 1.0423 10^-7 J
Q = 36.093 10^-12 * 76 = 2.743 nC

Solution 3

r = 9.58 * 10 ^ -6 / 2 m
T = 9.58 * 10 ^ -9 m
eo = 8.85 * 10 ^ -12
k = 5
Since r >>T:
c = k*eo*A/T
c = 4 * pi * k * eo * r ^ 2 / T
c ? 1.33176712485E-12 F
c ? 1.33pF

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