A 10uF parallel plate capacitor is connected to a 12V battery. Once the capacitor is fully charged, the battery is disconnected without any loss of charge on the plates.
a) 12V
b) 6V
the voltage is inversely proportional to the capacitance which increases with the increase in the surface of the plate… the charge is kept constant)
c) 24V
done the work of separating the plates…the increased dielectric supports the constant field (Gauss’s law)…so the dielectric volume has doubled the voltage
a) 12V is correct.
b) V=(Q*d)/(E_o*A) where A is the surface of the plates. The area of a circle is 4*pi*r^2.
So if you double the radius of the plates, 4*pi*(2r)^2=16*pi*r^2 which is 4A.
Plug it back into V and you get 1/4V because it’s inversely related.
12(1/4)=3V.
c) 24V is also correct.