Passive Components in AC Circuits
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 cannot increase or amplify the power of any
electrical signals applied to them, because they are passive and as such
will always have a gain of less than one. Resistors have a form of
impedance which is termed
resistance, (
R ).
Resistors whether used in DC or AC circuits will always have the same
value of resistance from DC to very high AC frequencies.
Capacitors and inductors on the other hand, have a different type of AC resistance known as
reactance, (
XL , 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. The resistive value of a resistor is
measured in Ohms,
Ω. Resistors can be of a fixed value or variable.
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 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 ).
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 RL Circuit
Series LC Circuit
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 RL Circuit
Parallel LC Circuit
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
Parallel RLC Circuit
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 90
o and in a purely inductive circuit the current lags the voltage by 90
o.
The opposition to current flow through a passive component in an AC circuit is called:
resistance,
R for a resistor,
capacitive reactance,
XC for a capacitor and
inductive reactance,
XL 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
Rejector Circuit.
