# Dielectric material between two plates

I wonder if the capacitance is the same if we have two plates with a dielectric material between. I mean, is it the same when the dielectric material only touches one of the plates, compared with when it touches both plates?

• okay. So in this case $C_1>C_3>C_2$? If we assume the are separated. And what about if we have same capacitor as $C_1$ but instead of full dielectric material we have half of it, and it touches both sides. Is it then $\frac{fd}{2}$? Thanks! Oct 28 '21 at 13:02
• @MathLover, What is $C_3$? If the dielectric occupies half of the space, then $fd = d/2$ and hence $f = 1/2$, I didn't understand your question. Oct 28 '21 at 13:09
• $C_3$ is the capacitor in the left in your picture. My main question is when is the capacitans as big as possible? I see in your picture that $C_1$ is the biggest and $C_2$ the smallest. But, how about other cases? Oct 28 '21 at 13:54
• The picture on the left and right are equivalent. You can split the entire capacitance (left) into two capacitors $C_1$ and $C_2$, which are in series as shown on the picture in the right. The naming $C_1$ and $C_2$ are arbitrary, and $fd$ just represents a fraction f of the value $d$ (which represents the separation between the two plates of the capacitor). Maximising the capacitance is naturally when $fd = d$; that is, the dielectric occupies the entire space. You can prove it mathematically by setting $\frac{dC_{eq}}{df}$ to zero, where $C_{eq}$ is the equivalent capacitance of the system. Oct 28 '21 at 14:04