# How the capacitance of this very small capacitor too large?

You can see that this is a very small capacitor and rated $$100\mu F$$.

It has metal sheets of area $$1.1cm^2$$ each. And there was a thin paper for insulation. Its thickness would be aproximately $$0.5×10^{-4} m$$.

I actually don't know the value of Dielectric constant but insulation the is same paper as used in most capacitors. But i can assume it to be around 2 to 4.

Now calculating capacitance C:

$$C = {\epsilon ×A}/d$$ $$= 4×9×10^{-12} ×{1.1×10^{-4}}/{0.5×10^{-4}}$$ $$= 7.92×10^{-11}F$$

$$8×10^{-11}F$$ (approx.)

We know that this value is off from the actuall value by $$10^7/8$$.

Why my value is so less as compared to actual value? What things are left cause i added everything from equation. But i think it has to do something with metal casing of capacitor and the fact that its metal sheets are rolled instead of being flat.

You can see that this is a very small capacitor and rated 100μF.

It's not really so small. 100 uF surface-mount capacitors are available in smaller packages than that. As small as 2.0 x 1.25 x 1.45 mm, for example, but with fairly low voltage rating at that size. Or 3.2 x 1.6 x 1.9 mm with the same 10 V rating as the one you have.

I actually don't know the value of Dielectric constant but insulation the is same paper as used in most capacitors. But i can assume it to be around 2 to 4.

This is an electrolytic capacitor. The most common (and lowest cost) type is called an "aluminum electrolytic" capacitor. The dielectric constant is in the range of 8 to 10, not 2 to 4. (source).

Its thickness would be aproximately 0.5×10−4m.

The thickness of the paper isn't critical. The paper is impregnated with an electrolyte that acts as a conductor. The capacitive effect happens across a thin layer of aluminum oxide that is produced by oxidizing the surface of the anode foil. The thickness of this layer can be quite low, on the order of 1.5 nm per volt (referring to the withstand voltage or the maximum voltage the capacitor must be able to be charged to without breakdown).

The capacitance is further enhanced by etching the foil to roughen it, increasing its surface area and increasing the capacitance by up to about 100 times (same source).

• Thanks! It was very helpful to me. I didn't knew about electrolytic capacitors Dec 20, 2021 at 15:15