The plates of a parallel plate capacitor are 2 cm wide and 5 cm long. The plates
ID: 1532771 • Letter: T
Question
The plates of a parallel plate capacitor are 2 cm wide and 5 cm long. The plates are separated by a 1.6-mm-thick layer of paper. Calculate the capacitance of the device (in pF) using the dielectric constant of paper from this table. Any dielectric material other than a vacuum has a maximum electric field that can be generated in the dielectric material before it physically or chemically breaks down and begins to conduct. This maximum electric field is called dielectric strength. The dielectric strength for paper is reached at a value of 15 106 V/m. Calculate the maximum charge (in µC) that can be placed on the capacitor at this dielectric strength.
TABLE 17.1 Dielectric constants for various materials at 25°C Material Dielectric constant K 1.0 Vacuum 1.0005 Air at 1.0 atm 2.6 Polystyrene 3.5 Paper 4.7 Pyrex glass Porcelain 6.5 7.0 Nerve membrane 12.0 Silicon Ethanol 25.0 Water 78.5Explanation / Answer
area of plate A = 0.02*0.05 = 0.001 m^2
seperation between plates d = 1.6*10^-3 m
dielectric constant k = 3.5
capacitance C = k*e0*A/d
C = 3.5*8.85*10^-12*0.001/(1.6*10^-3)
C = 19.44*10^-12 F
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Electric field E = Q/(A*e0)
Q = E*A*e0
Q = 15*10^6*0.001*8.85*10^-12
Q = 1.33*10^-8 C
Q = 0.133 uC
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