As energy storage elements and dynamic elements, inductance and capacitance are widely used in engineering technology, such as filtering and resonance in electronic circuits, compensation and power transmission in power systems, etc.

The characteristics of inductance and capacitance in DC circuits are very simple. Simply put, ignoring resistance, inductance is equivalent to short circuit in DC circuits, while capacitance is equivalent to open circuit in DC circuits.

Of course, in actual inductance coils and capacitors, there will be more or less loss, that is, there will be resistance. For example, the resistance of motor coils ranges from a few ohms to tens of ohms, while the resistance of capacitors is relatively small.

In general, inductance and capacitance are relatively rarely used in DC circuits. For example, inductance coils can be used for excitation of electromagnets, and capacitors can be used for DC isolation or energy storage. They are more often used in AC circuits.So, how do inductance and capacitance perform in AC circuits?

1. Sinusoidal AC circuit

The so-called AC circuit refers to a circuit in which the voltage and current in the circuit change periodically over time, as shown in Figure 1-2 below. The AC circuits mentioned above all refer to sinusoidal AC circuits. The voltage and current of a sinusoidal AC circuit change sinusoidally over time. The "sinusoidal law" here can be a sine function or a cosine function, because the sine function and the cosine function have the same change law, and the only difference between them is the phase angle difference. In addition, the sinusoidal AC circuit is also the circuit we come into contact with in our daily life and work.

Combined with the voltage and current waveforms, when the voltage and current waveforms are in the positive half cycle, it indicates that their actual direction is consistent with the reference direction; when the waveform is in the negative half cycle, it indicates that the actual direction of the voltage and current is opposite to the reference direction

However, inductors and capacitors are special. Their voltages and currents do not change synchronously, but have a phase difference. The so-called phase difference can be understood as the difference in the changing trend of voltage and current. For example, in an inductor component, when the current value at the timing zero point is zero and increases with time, the voltage value at the timing zero point is the maximum value and decreases with time
The voltage and current of a capacitor also have a phase difference. But unlike inductance, in capacitor elements, when the current value at the timing zero point is zero and increases with time, the voltage value at the timing zero point is the minimum value (negative value) and increases with time.

The reason why there is a phase difference between the voltage and current of the capacitor is the same as that of the inductor, because its voltage and current are not in direct proportion, but the voltage and current of the capacitor are in integral relationship, so the voltage and current relationship of the inductor and capacitor are also different. In order to make everyone see this difference intuitively, we take the series-parallel circuit of inductor and capacitor as an example.

2. Voltage-current relationship when inductor and capacitor are connected in series

The inductor and capacitor are connected in series, so they flow through the same current. But they will not cause their respective voltage-current relationship to change due to series connection
That is, in the LC series sinusoidal AC circuit, at any moment, the inductor voltage and capacitor voltage are in opposite directions

3. Voltage-current relationship when inductor and capacitor are connected in parallel

The inductor and capacitor are connected in parallel, so they bear the same voltage. Similarly, they will not change their voltage-current relationship due to parallel connection.

Based on the same voltage, the current of the inductor and the current of the capacitor are in anti-phase relationship,
and when the inductor current and the capacitor current are equal in magnitude and opposite in direction, the parallel combination of the inductor and the capacitor is equivalent to an open circuit to the outside, because the sum of their currents is zero, and there is no current to the outside. For ease of understanding, you can assign values and examples by yourself, and I will not elaborate on it here. It is like taking two dry batteries with equal voltages and connecting them end to end in parallel, and there is no current to the outside.

In summary, when the inductor and the capacitor are connected in series, the currents of the two are equal and the voltages are reversed. If the voltages are equal in magnitude, their series combination is equivalent to a short circuit, which is also called the series resonance of the inductor and the capacitor; when the inductor and the capacitor are connected in parallel, the voltages of the two are equal and the currents are reversed. If the currents are equal in magnitude, their parallel combination is equivalent to an open circuit, which is also called the parallel resonance of the inductor and the capacitor.