A capacitor holds 200 microcoulombs of charge when a·20V battery is connected to

Question

A capacitor holds 200 microcoulombs of charge when a·20V battery is connected to it in a simple capacitor battery circuit. Whats the capacitance of a capacitor? And if the area of the plates is 0.3m2, what is the distance between the plates? How much energy is stored between the plates? Efield? Energy density? A dielectric of kappa = 3 is inserted between the plates of the capacitor of the previoous problem. What is the new capacitance? Stored energy? Stored charged on each plate? Efield? Energy density?

Explanation / Answer

1.)C=Q/V=200x10^-6/20= 10 x10^-6 = 10 uF

C=e0*A/d

10 x 10^-6=8.85 x10^-12*0.3/d

So d= 2.655 x 10^-7 m

E=0.5CV^2=0.5*10^-5*20*20= 2 x 10^-3 J

Efield=V/d=20/2.655 x10^-7= 75329566.85 V/m

Energy density=E/Ad= 25109.86 J/m^3

2.)C=kCold= 30 uF

E=3Eold= 6 x 10^-3 J

Q=3*Qold=600 microcouloumbs

Efield=V/d= 75329566.85 V/m

Energy density= 3*Energy density old= 75329.58 J/m^3

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