Supercapacitors are one of the common electronic components. When purchasing supercapacitors, how do we choose the appropriate capacitance to meet practical needs and save costs? To accurately know the capacitance of a capacitor, one needs to learn how to calculate its capacitance. So, how should we calculate it? Below, we will use two examples to understand the capacitance calculation method of electrolytic capacitors:
1. How to calculate the capacitance of an isolated charged sphere (R=r0) in vacuum? If the charge of an isolated charge Q=q and its potential U=q/(4 πε 0r0) relative to infinity, then its capacitance C=Q/U=4 πε 0r0. From the calculation results, it can be seen that the capacitance is only related to the size, shape, and spatial environment of the charged body, and is independent of the amount charged.
2. Calculation method for capacitance of parallel plate supercapacitors. The so-called parallel plate capacitor refers to an electronic component composed of two relatively parallel metal plates separated by a dielectric with a relative dielectric constant of ε r and a thickness of d. If the charge stored in a parallel plate capacitor Q=q, then the charges on the positive and negative plates are+q and - q, respectively, and the potential difference between the two plates is u. Parallel plate capacitors can be seen as two isolated charged body capacitors connected in series. If the potential of the positive electrode plate relative to infinity is U+=u+, then the potential of the negative electrode plate is U -=u+- u. The electrical capacities of the positive and negative plates are+q/u+, - q/(u+- u), respectively. The combined capacity of the two in series is 1/C=1/(+q/u+)+1/- q/(u+- u)=u/q, that is, C=q/u.
From the derivation of physics, it can be concluded that u=4 π dq/(ε r ε 0S), so C=ε r ε 0S/4 π dq. Similarly, the capacitance of a supercapacitor is only related to its structural size, and does not depend on its charged capacity. When purchasing a supercapacitor, it is best to choose a capacitor with the appropriate amount of capacitance. By using the above method to calculate the electrical capacity yourself, it can save costs and not affect practical applications, eliminating extravagance and waste.