In an R-L-C series circuit (resistor-inductor-capacitor series circuit), the components are connected in sequence with each other, meaning the current flows through them one after the other. Here are some important relations and characteristics of an R-L-C series circuit:
Impedance (Z): Impedance is the effective opposition to the flow of alternating current (AC) in the circuit. It is a complex quantity that takes into account the resistance (R), inductive reactance (XL), and capacitive reactance (XC) of the circuit. The impedance can be calculated using the following formula:
=
2
+
(
−
)
2
Z=
R
2
+(X
L
−X
C
)
2
where
X
L
is the inductive reactance (
2
2πfL) and
X
C
is the capacitive reactance
(
1
2
)
(
2πfC
1
),
f is the frequency of the AC signal,
L is the inductance, and
C is the capacitance.
Phase Angle (
ϕ): The phase angle represents the phase difference between the current (
I) and the voltage (
V) in the circuit. It is given by:
tan
=
−
tanϕ=
R
X
L
−X
C
Resonance Frequency (
res
f
res
): Resonance frequency is the frequency at which the inductive reactance (
X
L
) is equal to the capacitive reactance (
X
C
), resulting in the minimum impedance. At resonance, the impedance becomes equal to the resistance (
R). The resonance frequency can be calculated using:
res
=
1
2
f
res
=
2π
LC
1
Quality Factor (
Q): The quality factor indicates the selectivity or sharpness of the circuit's resonance. It is the ratio of the reactance to the resistance at resonance:
=
=
1
Q=
R
X
L
=
R
1
C
L
Current Amplitude (
max
I
max
): The maximum current amplitude in the circuit occurs at resonance and is given by:
max
=
=
I
max
=
Z
V
=
R
V
Power Factor (
PF
PF): The power factor is the ratio of the real power (power dissipated in the resistor) to the apparent power (product of voltage and current magnitude):
PF
=
Real Power
Apparent Power
=
PF=
Apparent Power
Real Power
=
Z
R
These relations and characteristics are essential for analyzing and understanding the behavior of R-L-C series circuits under AC conditions. They help engineers and researchers design circuits, optimize their performance, and troubleshoot issues related to impedance, phase relationships, and resonance.