Parallel plate capacitor question?

Question

A parallel plate capacitor is constructed using plates of area A and a spacing between the plates d with air in the region between. That capacitor has a capacitance of 37pF. A graduate student attempts to make a copy but mistakenly uses inches rather than centimeters for all the dimensions, so all dimensions are 2.54 times larger than the original. What is the capacitance of the graduate student's capacitor (in pF)?

billrussell42 · Accepted Answer

Parallel plate cap 
C = ε₀εᵣ(A/d) in Farads
   ε₀ is vacuum permittivity, 8.854e-12 F/m
   εᵣ is dielectric constant or relative permittivity 
    of the material (vacuum = 1)
   A and d are area of plate in m² and separation in m

C₁ = ε₀εᵣ(A₁/d₁)
C₂ = ε₀εᵣ(A₂/d₂)
A₂ = (2.54)²A₁
d₂ = (2.54)d₁
C₂ = ε₀εᵣ( (2.54)²A₁ / (2.54)d₁)
C₂ = ε₀εᵣ(2.54)(A₁ / d₁) = (2.54)C₁  = 94 pF

Parallel plate capacitor question?

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