Passive Components in AC Circuits

Table of Contents

Electrical and electronic circuits consist of connecting together many different components to form a complete and closed circuit. The three main passive components used in any circuit are the: Resistor, the Capacitor and the Inductor. All three of these passive components have one thing in common, they limit the flow of electrical current through a circuit but in very different ways.

Electrical current can flow through a circuit in either of two ways. If it flows in one steady direction only it is classed as direct current, (DC). If the electrical current alternates in both directions back and forth it is classed as alternating current, (AC). Although they present an impedance within a circuit, passive components in AC circuits behave very differently to those in DC circuits.

Passive components consume electrical energy and therefore can not increase or amplify the power of any electrical signals applied to them, simply because they are passive and as such will always have a gain of less than one. Passive components used in electrical and electronic circuits can be connected in an infinite number of ways as shown below, with the operation of these circuits depending on the interaction between their different electrical properties.

Passive Components in AC Circuits

passive components in ac circuits

Where: R is resistance, C is capacitance and L is inductance.

Resistors whether used in DC or AC circuits will always have the same value of resistance no matter what the supply frequency. This is because resistors are classed to be pure having parasitic properties such as infinite capacitance C = ∞ and zero inductance L = 0. Also for a resistive circuit the voltage and current are always in-phase so the power consumed at any instant can be found by multiplying the voltage by the current at that instant.

Capacitors and inductors on the other hand, have a different type of AC resistance known as reactance, (XL and XC). Reactance also impedes the flow of current, but the amount of reactance is not a fixed quantity for one inductor or capacitor in the same way that a resistor has a fixed value of resistance. The reactance value of an inductor or a capacitor depends upon the frequency of the supply current as well as on the DC value of the component itself.

The following is a list of passive components commonly used in AC circuits along with their corresponding equations which can be used to find their value or circuit current. Note that a theoretically perfect (pure) capacitor or inductor does not have any resistance. However in the real world they will always have some resistive value no matter how small.

Purely Resistive Circuit

Resistor – Resistors regulate, impede or set the flow of current through a particular path or impose a voltage reduction in an electrical circuit as a result of this current flow. Resistors have a form of impedance which is simply termed resistance, ( R ) with the resistive value of a resistor being measured in Ohms, Ω. Resistors can be of either a fixed value or a variable value (potentiometers).

purely resistive circuit resistor circuit equations

Purely Capacitive Circuit

Capacitor – The capacitor is a component which has the ability or “capacity” to store energy in the form of an electrical charge like a small battery. The capacitance value of a capacitor is measured in Farads, F. At DC a capacitor has infinite (open-circuit) impedance, ( XC ) while at very high frequencies a capacitor has zero impedance (short-circuit).

purely capacitive circuit capacitor circuit equations

Purely Inductive Circuit

Inductor – An inductor is a coil of wire that induces a magnetic field within itself or within a central core as a direct result of current passing through the coil. The inductance value of an inductor is measured in Henries, H. At DC an inductor has zero impedance (short-circuit), while at high frequencies an inductor has infinite (open-circuit) impedance, ( XL ).

purely inductive circuit inductor circuit equations

Series AC Circuits

Passive components in AC circuits can be connected together in series combinations to form RC, RL and LC circuits as shown.

Series RC Circuit

series rc circuit series rc circuit equations

Series RL Circuit

series rl circuit series rl circuit equations

Series LC Circuit

series lc circuit series lc circuit equations

Parallel AC Circuits

Passive components in AC circuits can also be connected together in parallel combinations to form RC, RL and LC circuits as shown.

Parallel RC Circuit

parallel rc circuit parallel rc circuit equations

Parallel RL Circuit

parallel rl circuit parallel rl circuit equations

Parallel LC Circuit

parallel lc circuit parallel lc circuit equations

Passive RLC Circuits

All three passive components in AC circuits can also be connected together in both series RLC and parallel RLC combinations as shown below.

Series RLC Circuit

passive components in ac circuit series rlc circuit equations

Parallel RLC Circuit

parallel rlc circuit parallel rlc circuit equations

We have seen above that passive components in AC circuits behave very differently than when connected in a DC circuit due to the influence of frequency, ( ƒ ). In a purely resistive circuit, the current is in-phase with the voltage. In a purely capacitive circuit the current in the capacitor leads the voltage by 90o and in a purely inductive circuit the current lags the voltage by 90o.

The opposition to current flow through a passive component in an AC circuit is called: resistanceR for a resistor, capacitive reactanceXC for a capacitor and inductive reactanceXL for an inductor. The combination of resistance and reactance is called Impedance.

In a series circuit, the phasor sum of the voltages across the circuits components is equal to the supply voltage, VS. In a parallel circuit, the phasor sum of the currents flowing in each branch and therefore through each of the circuits components is equal to the supply current, IS.

For both parallel and series connected RLC circuits, when the supply current is “in-phase” with the supply voltage the circuit resonance occurs as XL = XC. A Series Resonance Circuit is known as an Acceptor Circuit. A Parallel Resonance Circuit is known as a Rejecter Circuit.


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