A mica capacitor has square plates that are 3.8cm on a sideand separated by 2.5m

Question

A mica capacitor has square plates that are 3.8cm on a sideand separated by 2.5mils. what is the capacitance? what size capacitor is capable of storing 10mj of energy with100v across its plates? A studen wants to constrcut a 1 F capacitor out of two squareplates for a science fair project. He palns to use a paperdielectric (r= 2.5) that is 8x10-5 m thick. Thescience fair is to be held in Astrodonem. Will his capacitor fit inthe Astrodome? What would be the size of the plates if itcould be constructed? please show all work for all thanks A mica capacitor has square plates that are 3.8cm on a sideand separated by 2.5mils. what is the capacitance? what size capacitor is capable of storing 10mj of energy with100v across its plates? A studen wants to constrcut a 1 F capacitor out of two squareplates for a science fair project. He palns to use a paperdielectric (r= 2.5) that is 8x10-5 m thick. Thescience fair is to be held in Astrodonem. Will his capacitor fit inthe Astrodome? What would be the size of the plates if itcould be constructed? please show all work for all thanks

Explanation / Answer

(a) For a parallel plate capacitor , withplate area A and distance between the plates = d

Capacitance C =Ar0 /d

:where r = Relativepermittivity of material in between plates.

0 = 8.85x10-12F/m

For mica , r =7

Therefore for A = (3.8cm)*(3.8cm) = 0.001444 m2 and

d = 2.5mils =2.5 milliinches = 2.5 * (0.0254 mm) = 0.0635 x 10-3m

      C = (0.001444) (7x8.85x10-12) /(0.0635x10-3) F

   => C = 1.40875 x 10-9 F =1.409 nF

(b) Energy stored in acapacitor with capacitance C and voltage across it Vis

      E = (1/2) CV2

Therefore C =2E/ V2 = 2* ( 10x10-3J) /(100V)2 = 2x10-6 F = 2F

(c Let us first determine the areaof plates A required for capacitor.

    As shown in part (a) , C = Ar0/ d

      =>    A = Cd / r0

Now , given C= 1 F , d = 8x10-5m , r = 2.5 , 0 =8.85x10-12 F /m

Hence A = 1x8x10-5 / (2.5x8.85x10-12) m2

        => A = 3.616 x 106m2

Now aswe can see A is very large .

If a square plate capacitor is tomade then the

length of a side of square L= A

         =(3.616x106) m

   Thediameter of Astrodomeis about 710 feet ( = 236m)

   SinceL >> 236 m , The said1 F capacitor cannot fit in theAstrodome.

I hope this helpsyou

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