unit 24 r-l-c series circuits -...

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.


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.


Phase relationships of current and voltage.


R-L-C series circuit schematic.


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


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)


Total Impedance

• The impedance of the circuit is the vector

sum of resistance, inductive reactance,

and capacitive reactance.

• Z = √ R2 + (XL – XC)2


Addition of impedance vectors.


Impedance triangle.


Current

• The total current flow is the applied voltage divided by the impedance.

• I = E / Z


Resistive Volt Drop

• The resistive volt drop is equal to the

current times the resistance.

• ER = I x R


Watts

• The true power can be computed using

any of the pure resistive values.

• P = ER x I (Ohm’s law)


Inductance and Inductive Reactance

• L = XL / (2f)

• XL = 2fL

Inductor Volt Drop

• EL = I x XL

Inductive VARs

• VARsL = EL x I


Capacitance & Capacitive Reactance

• C = 1 / 2fXC and XC = 1/ 2fC

Capacitor Volt Drop

• EC = I x XC

Capacitive VARs

• VARsC = EC x I


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


Addition of power vectors.


Power Factor

• PF = Watts / VA

Angle Theta

• Cosine θ = PF


Example circuit #1 values.


Example circuit #2 given values.


Example circuit #3 given values.


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.


Example resonant circuit at 1000 Hz.


Resonant properties.


Current increases sharply at resonance.


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°.


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:

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.


Review:

7. Resonance occurs when inductive

reactance and capacitive reactance

become equal.

unit 24 r-l-c series circuits -...

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