Passive components in series resonant circuits

Electrical and electronic circuits involve connecting many different components together to form a complete closed circuit. The three main passive components used in any circuit are resistors, capacitors, and inductors, all of which have one thing in common: they limit the current passing through the circuit, but in very different ways.

Current can flow through a circuit in either of two ways. If it flows only in one stable direction, it is classified as direct current (DC). If the current flows back and forth in two directions, it is classified as alternating current (AC). Although they exhibit impedance in circuits, the behavior of passive components in AC circuits is very different from that in DC circuits.

Passive components consume electrical energy and therefore cannot increase or amplify the power of any electrical signal applied to them, simply because they are passive and therefore their gain is always less than one. Passive components used in electrical and electronic circuits can be connected in countless ways as shown below, and the operation of these circuits depends on the interaction between their different electrical characteristics.

Passive components in AC series resonance (also known as variable frequency resonance) circuits

Among them, R is a resistor, C is a capacitor, and L is an inductor.  

Regardless of the power frequency, resistors used in DC or AC circuits always have the same resistance value. This is because resistors are classified as pure resistors with parasitic characteristics, such as infinite capacitance C=∞ and zero inductance L=0. Similarly, for resistive circuits, voltage and current are always in phase, so the power consumed at any moment can be calculated by multiplying the voltage by the current at that moment.  

On the other hand, capacitors and inductors have different types of AC resistance, known as reactance (XL and XC). Reactance also impedes the flow of current, but for an inductor or capacitor, the amount of reactance is not fixed, just like a resistor has a fixed resistance value. The reactance value of an inductor or capacitor depends on the frequency of the power supply current and the DC value of the component itself.  

The following is a list of commonly used passive components and their corresponding equations in AC series resonant circuits, which can be used to find their values or circuit currents. Please note that theoretically perfect (pure) capacitors or inductors have no resistance. However, in the real world, regardless of their size, they will always have a certain resistance value.

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By hvhipot