# Why doesn't capacitor voltage and inductor current allow sudden changes?

08/09/2021 Seektronics

We all know that capacitor voltages cannot change abruptly and inductor currents cannot change abruptly, what is the theoretical basis for this?

Take an example of an RC first-order low-pass filter.

Vin charges capacitor C1 through the R1 resistor, the potential of Vin is added to the two metal pole plates of capacitor C. The positive and negative charges are gathered towards the two-pole plates of the capacitor respectively under the effect of the potential difference and an electric field is formed, which is the charging process of the capacitor.

Charging of capacitors

The charge number, which measures the charge of a capacitor, is Q，Q = CV and C is a constant, so the charge number is proportional to the voltage.

C = Q/V, the capacity represents the ability of the capacitor to store charge and the differential expression is：

Current is the amount of change in the number of charges per unit of time：

Combining the two equations (1) and (2) yields：

It follows from the formula that： the amount of change in current and voltage across a capacitor is proportional, or the amount of change in voltage across a capacitor is proportional to the current.

It is assumed that the voltage of the capacitor can change abruptly, i.e. an infinite current is required. In practice there is no infinite current, i.e. the voltage cannot change abruptly.

Let's look at why inductor currents cannot change abruptly？

The sum of the fluxes in each turn of an inductor coil is called the chain Ψ and measures how much of the inductor coil is magnetized.

The magnetic chain is proportional to the current, the higher the current, the more the inductor coil is charged with the magnetic chain, i.e. Ψ = L*I, for a given inductor coil, L is a constant.

L = Ψ/I, the inductance represents the electromagnetic conversion capacity of the inductor coil and the differential expression is：

According to the principle of electromagnetic induction, a change in the magnetic chain produces an induced voltage, the greater the change in the chain the higher the induced voltage, i.e：

Combining the two equations (1) and (2) yields：

It can be seen from the formula: the rate of change of inductor voltage and current are proportional, or the rate of change of current and inductor voltage are proportional.

The assumption that the inductor current can change abruptly, i.e. that an infinite voltage is required, also does not exist in practice, i.e. the inductor current cannot change abruptly.