Hey guys, I'm totally stumped with this question:Given that you possess the following materials:(i) two sheets of copper of uniform thickness;(ii) one sheet of mica of uniform thickness 0.10 mm and dielectric constant κ 6;(iii) one sheet of glass of uniform thickness 2.0 mm and dielectric constant κ 7;(iv) one sheet of paraffin wax of uniform thickness 1.0 cm and dielectric constantκ 2;determine which sheet, or combination of sheets, will produce a parallel plate capacitor ofthe largest capacitance when placed between the copper sheets. Assume that all sheetshave the same shape.I just can't seem to find an equation to find equivelant capacitances of multiple dielectrics in a capacitorThanks!!
They are completely different fluids/liquids. Not related whatsoever. Transmission fluid is a pinkish red and is quite oily.
Transmission fluid tank. Good one haha
They're not close at all. Edit to add: Transmission fluid is usally red. Coolant is usually green sometimes orange. But never red.
the basic formula is C (e)(A) / (x) e (eo) * (k) e (8.85E - 12) * (k) eo is permittivity of vacuum e is permittivity of insulating material k is dielectric constant of material for multiple dielectric, for better illustration lets change the format of the equation C (e)(A) /(x) C 1 / [ (A)(x) / (e) ] C 1 / [ (V) / (e) ] above is the general equation of capacitor V is the volume of material that the electrons have to travel for capacitor with parallel plates (V) / (e) (A)(x1) / (ea) + (A)(x2) / (eb) + (A)(x3) / (ec) x1 permittivity ea of x1 thickness x2 permittivity eb of x2 thickness x3 permittivity ec of x3 thickness for capacitor of tubular form, the effective value of dielectric is more complicated, the V has to be integrated due to changes of area with respect to radius, and thats where the natural log comes in (V) / (e) (2 pi L) Ln (R2 - R1) / (ea) + (2 pi L) Ln (R3 - R2) / (eb) + (2 pi L) Ln (R4 - R3) / (ec) where R1 is the innermost radius R2 2nd radius R3 3rd radius R4 outermost radius ea is permittivity between R1 and R2 eb is permittivity between R2 and R3 ec is permittivity betwwen R3 and R4 the effective value of dielectric constant follow the rules of sum of the inversed values, basically it is the same as the effective value of thermal conductivity in heat transfer, and the effective value of electrical conductivity in the calculation of a resistor
Capacitance is proportional to κ and inversely proportional to thickness d. So just find the material with the largest κ/d ratio. Note that you'd never want more than 1 sheet. That would be like adding another capacitor in series.
They are completely different fluids/liquids. Not related whatsoever. Transmission fluid is a pinkish red and is quite oily.
Transmission fluid tank. Good one haha
They're not close at all. Edit to add: Transmission fluid is usally red. Coolant is usually green sometimes orange. But never red.
the basic formula is C (e)(A) / (x) e (eo) * (k) e (8.85E - 12) * (k) eo is permittivity of vacuum e is permittivity of insulating material k is dielectric constant of material for multiple dielectric, for better illustration lets change the format of the equation C (e)(A) /(x) C 1 / [ (A)(x) / (e) ] C 1 / [ (V) / (e) ] above is the general equation of capacitor V is the volume of material that the electrons have to travel for capacitor with parallel plates (V) / (e) (A)(x1) / (ea) + (A)(x2) / (eb) + (A)(x3) / (ec) x1 permittivity ea of x1 thickness x2 permittivity eb of x2 thickness x3 permittivity ec of x3 thickness for capacitor of tubular form, the effective value of dielectric is more complicated, the V has to be integrated due to changes of area with respect to radius, and thats where the natural log comes in (V) / (e) (2 pi L) Ln (R2 - R1) / (ea) + (2 pi L) Ln (R3 - R2) / (eb) + (2 pi L) Ln (R4 - R3) / (ec) where R1 is the innermost radius R2 2nd radius R3 3rd radius R4 outermost radius ea is permittivity between R1 and R2 eb is permittivity between R2 and R3 ec is permittivity betwwen R3 and R4 the effective value of dielectric constant follow the rules of sum of the inversed values, basically it is the same as the effective value of thermal conductivity in heat transfer, and the effective value of electrical conductivity in the calculation of a resistor
Capacitance is proportional to κ and inversely proportional to thickness d. So just find the material with the largest κ/d ratio. Note that you'd never want more than 1 sheet. That would be like adding another capacitor in series.
