AC Components and Circuits
AC RL Circuits
Section 3-3 Parallel RL Circuit Analysis
Currents in Parallel RL Circuits
Currents in parallel RL circuits
Phasor diagram for parallel RL circuits.
The total current of a series RL circuit is:
- IT = Total current
- IR = Resistor current
- IL = Inductor current
In most practical situations, however, the resistor and inductor currents are not known. So the application of the equation for total current is preceded by determining IR and IL:
If XL is not directly know, you also have to calculate XL = 2pfL.
The phase angle for a parallel RL circuit is usually determined from the resistive and reactive currents.
Currents in a parallel RL circuit.
The phasor diagram shows that there is no phase shift for the resistor current (IR) and there is a phase of -90º for the inductor current. The phase shift for the total circuit is thus somewhere between 0 and -90º.
The phase shift for a parallel RL circuit is:
q = Phase angle*
IL = Inductor current
IR = Resistor current
Given: VT, f, R, and L
Determine: IT and q
1. Calculate XL
XL = 2pfl
2. Calculate IL
3. Calculate IR
At this point, you know IL and IR
4. Calculate IT
5. Calculate q
Steps 4 and 5 are the values to be determined.
Impedance in Parallel RL Circuits
The impedance of a parallel RL circuit is:
- Z = Circuit impedance
- VT= Total voltage
- IT = Total current
Analyzing Parallel RL Circuits
| A typical analysis of a parallel RL circuit begins with known values for: |
- Total rms voltage applied to the circuit (VT)
- Applied frequency (f)
- Value of the resistor (R)
- Value of the inductor (L)
The objective, then, is to determine all other relevant circuit values:
) Resistor current (IR) Inductor current (IL) Total current (IT) Impedance (Z) Phase angle (q)
- Voltage across the resistor (VR)
- Voltage across the inductor (VL)
- Inductive reactance (XL
1. Determine VR and VL from VT
2. Calculate XL from f and L
3. Calculate IR by applying Ohm's law to VR and R
4. Calculate IL by applying Ohm's Law to VL and XL
5. Calculate IT from IR and IL
6. Calculate Z by applying Ohm's law to VT and IT
7. Calculate q from IL and IR
Endless Examples & Exercises
|Work these problems until you are confident you have mastered the procedures. |
- All angles are expressed in degrees.
- Round answers to the nearest tenth.