Electrolytic capacitors such as the kind you described are made by taking two long, thin sheets of aluminum, separated with paper saturated with an electrolyte, and rolled up into a cylinder. Each foil sheet is one terminal.
Now, the more surface area the aluminum sheets have, the more capacitance you get (and the larger the capacitor’s physical size).
To make a high-value, small capacitor, you have to minimize aluminum foil thickness and paper insulator thickness.
Now, when the paper insulator is very thin, it won’t take much voltage to break it down and short out the capacitor.
That’s why they have a voltage rating. The same capacitance, but higher working voltage of course has a thicker paper insulator (and because the aluminum plates are spaced further apart by the thicker paper, the capacitance per unit size is lower.
So you need more aluminum area and thicker paper for a higher voltage capacitor, therefore it will be larger.
Product details of 100uF 16V/25V/50V Capacitor:
- Mounting: THT
- Capacitance: 100uF
- Voltage-Rated: 16V/25V/50V
- Tolerance: ±20%
- Features: Standard General Purpose
- Maximum Temperature: 85°C
1 x 100uF 16V/25V/50V Electrolytic Capacitor.