Unit 25R-L-C Parallel Circuits

Unit 25 R-L-C Parallel Circuits

Objectives:

• Discuss parallel circuits that contain resistance (R), inductance (L), and capacitance (C).

• Compute the values of an R-L-C parallel circuit.

• Compute all circuit values.

Unit 25 R-L-C Parallel Circuits

Objectives:

• Discuss the operation of a parallel resonant circuit.

• Compute the power factor correction for an AC motor.

Unit 25 R-L-C Parallel Circuits

• In the R-L-C parallel circuit, the voltage is the same across all the component branches. However, the currents through the branches will have a phase shift based on the various component properties.

• Inductive current lags the voltage.• Capacitive current leads the voltage.• Resistive current is in phase with the

voltage.

Unit 25 R-L-C Parallel Circuits

Phase relationships of current and voltage.

Unit 25 R-L-C Parallel Circuits

R-L-C parallel circuit schematic.

Unit 25 R-L-C Parallel Circuits

Circuit Values• Z = total impedance of the circuit

• IT = total circuit current

• IR = resistor current flow

• P = true power (watts)• L = inductance of the inductor

• IL = inductor current flow

• VARsL = reactive power of the inductor

Unit 25 R-L-C Parallel Circuits

Circuit Values

• C = capacitance of the capacitor (farads)

• IC = capacitor current flow

• VARsC = reactive power of the capacitor

• VA = volt-amperes (apparent power)

• PF = power factor

• angle θ = degrees of phase shift (theta)

Unit 25 R-L-C Parallel Circuits

Impedance

Z = 1 / √(1/R)2 + (1/XL – 1/XC)2

Z = R x X / √(R2 + X2)

Inductance and Inductive Reactance

L = XL / 2πF and XL = 2πFL

Capacitance and Capacitive Reactance

C = 1 / 2πFXC and XC = 1 / 2πFC

Unit 25 R-L-C Parallel Circuits

Resistive Current

IR = E / R

Inductive Current

IL = E / XL

Capacitive Current

IC = E / XC

Unit 25 R-L-C Parallel Circuits

Vector diagram of currents.

Unit 25 R-L-C Parallel Circuits

Reducing vector currents.

Unit 25 R-L-C Parallel Circuits

True Power

P = E x IR

Reactive Power

VARsTotal = √(VARsL – VARsC)2

Apparent Power

VA = E x IT

VA = √P2 + (VARsL – VARsC)2

Unit 25 R-L-C Parallel Circuits

Power Factor

PF = Watts / VA

Angle Theta

Cosine θ = PF

Unit 25 R-L-C Parallel Circuits

Example circuit #1 values.

Unit 25 R-L-C Parallel Circuits

Example circuit #2 given values.

Unit 25 R-L-C Parallel Circuits

Parallel Resonance

Parallel resonant circuits are often called tank circuits. The special properties of this circuit can be used to heat treat sections of metal pipe and welds.

Unit 25 R-L-C Parallel Circuits

Example resonant circuit at 1200 Hz.

Unit 25 R-L-C Parallel Circuits

Tank circuit with circulating current.

Unit 25 R-L-C Parallel Circuits

Induction heating system.

Unit 25 R-L-C Parallel Circuits

Frequency controls heat penetration depth.

Unit 25 R-L-C Parallel Circuits

Power Factor Correction

Power factor correction can be done at either the load or the service. In each situation a capacitor or capacitor bank is connected in parallel.

Unit 25 R-L-C Parallel Circuits

Determining motor power factor.

Unit 25 R-L-C Parallel Circuits

Equivalent motor circuit.

Unit 25 R-L-C Parallel Circuits

Capacitor used to correct motor PF.

Unit 25 R-L-C Parallel Circuits

Review:

1. The voltage applied to all legs of an R-L-C parallel circuit is the same.

2. The current flow in the resistive leg will be in phase with the voltage.

3. The current flow in the inductive leg will lag the voltage by 90°.

4. The current flow in the capacitive leg will lead the voltage by 90°.

Unit 25 R-L-C Parallel Circuits

Review:

5. Angle theta for the circuit is determined by the amounts of inductance and capacitance.

6. An L-C resonant circuit is often referred to as a tank circuit.

7. When an L-C parallel circuit reaches resonance, the line current drops and the total impedance increases.

Unit 25 R-L-C Parallel Circuits

Review:

8. When an L-C parallel circuit becomes resonant, the total circuit current is determined by the amount of pure resistance in the circuit.

9. Total circuit current and total impedance in a resonant tank circuit are proportional to the Q of the circuit.

Unit 25 R-L-C Parallel Circuits

Review:

10.Motor power factor can be corrected by connecting capacitance in parallel with the motor. The same amount of capacitive VARs must be connected as inductive VARs.