Determine the capacitance of this capacitor. Determine the area of each plate.

Question

The electric field between the plates of a paper-separated (K=3.75) capacitor is 8.25×104 V/m. The plates are 2.15 mm apart, and the charge on each plate is 0.670 μC.

 

(a) Determine the capacitance of this capacitor.

(b) Determine the area of each plate.

Answer 1

Since the electric field is 8,25 x 10⁴  V/m and the plate separation is 2.15 x 10^-3 m,    the electric potential across the device is the product of these ;  V =  177.375 V.     Since   Q =   V C,     C =  .670 x 10 ^-6 / 177.375 =   3.77 x 10^-9 F.

 

The equation for the capacitance   C  =   K ε₀ A / d   ( ε₀ = 8.854 x 10^-12 ) can be used to solve for   A.  The result is

  A =  .245 m² .