Unit 24 R-L-C Series Circuits
Unit 24
R-L-C Series Circuits
Phase relationships of current and voltage.
Unit 24 R-L-C Series Circuits
Unit 24 R-L-C Series Circuits
Objectives:
• Discuss series circuits that contain
resistance (R), inductance (L), and
capacitance (C).
• Discuss the impedance of an R-L-C series
circuit.
• Review all R-L-C series circuit values.
• Discuss series resonant circuits.
Unit 24 R-L-C Series Circuits
In a series circuit, there is only one
pathway for current. Therefore, the total
current is flowing through each component.
However, the individual component
voltages will have varying phase
relationships. Each component will also
have an ohm value found by dividing the
component volt drop by the circuit current.
The component power values resolve with
vector addition.
R-L-C series circuit schematic.
Unit 24 R-L-C Series Circuits
Circuit Values
• Z = total impedance of the circuit
• IT = total circuit current
• ER = voltage drop across the resistor
• P = true power (watts)
• L = inductance of the inductor
• EL = voltage drop across the inductor
Unit 24 R-L-C Series Circuits
Unit 24 R-L-C Series Circuits
Circuit Values
• VARsL = reactive power of the inductor
• C = capacitance of the capacitor (farads)
• EC = volt drop across the capacitor
• VARsC = reactive power of the capacitor
• VA = volt-amperes (apparent power)
• PF = power factor
• angle θ = degrees of phase shift (theta)
Unit 24 R-L-C Series Circuits
Total Impedance
• The impedance of the circuit is the vector
sum of resistance, inductive reactance,
and capacitive reactance.
• Z = √ R2 + (XL – XC)2
Unit 24 R-L-C Series Circuits
Impedance triangle.
Unit 24 R-L-C Series Circuits
Current
• The total current flow is the applied
voltage divided by the impedance.
• I=E/Z
Unit 24 R-L-C Series Circuits
Resistive Volt Drop
• The resistive volt drop is equal to the
current times the resistance.
• ER = I x R
Addition of impedance vectors.
Unit 24 R-L-C Series Circuits
Watts
• The true power can be computed using
any of the pure resistive values.
• P = ER x I (Ohm’s law)
Unit 24 R-L-C Series Circuits
Apparent Power
• VA = ET x I
Apparent power can also be found using
vector addition of true power and reactive
power.
• VA = √P2 + (VARsL – VARsC)2
Unit 24 R-L-C Series Circuits
Unit 24 R-L-C Series Circuits
Inductance and Inductive Reactance
• L = XL / (2f)
• XL = 2fL
Inductor Volt Drop
• EL = I x XL
Inductive VARs
• VARsL = EL x I
Unit 24 R-L-C Series Circuits
Capacitance & Capacitive Reactance
• C = 1 / 2fXC and XC = 1/ 2fC
Addition of power vectors.
Unit 24 R-L-C Series Circuits
Power Factor
• PF = Watts / VA
Capacitor Volt Drop
• EC = I x XC
Capacitive VARs
• VARsC = EC x I
Angle Theta
• Cosine θ = PF
Unit 24 R-L-C Series Circuits
Example circuit #1 values.
Unit 24 R-L-C Series Circuits
Series Resonance
When an inductor and capacitor are
connected in series, there will be one
frequency at which the inductive
reactance and capacitive reactance will
become equal. This is the resonant
frequency. The current will only be limited
by pure resistance.
Unit 24 R-L-C Series Circuits
Unit 24 R-L-C Series Circuits
Example circuit #2 given values.
Example resonant circuit at 1000 Hz.
Unit 24 R-L-C Series Circuits
Unit 24 R-L-C Series Circuits
Example circuit #3 given values.
Resonant properties.
Unit 24 R-L-C Series Circuits
Unit 24 R-L-C Series Circuits
Review:
Current increases sharply at resonance.
5. In an R-L-C circuit, inductive and
capacitive values are 180° out of phase
with each other. Adding them results in
the elimination of the smaller value and a
reduction of the larger value.
6. L-C resonant circuits increase the
current and voltage drop at the resonant
frequency.
Unit 24 R-L-C Series Circuits
Unit 24 R-L-C Series Circuits
Review:
1. The voltage dropped across the resistor
in an R-L-C series circuit will be in phase
with the current.
2. The voltage dropped across the inductor
in an R-L-C series circuit will lead the
current by 90°.
Unit 24 R-L-C Series Circuits
Review:
3. The voltage dropped across the
capacitor in an R-L-C series circuit will
lag the current by 90°.
4. Vector addition can be used in an R-L-C
series circuit to find circuit values of
voltage, impedance, and apparent
power.
Review:
7. Resonance occurs when inductive
reactance and capacitive reactance
become equal.