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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.

Equation

The total current of a series RL circuit is:

 IT = Ö IR2 + IL2

Where:

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:

 IR = VT R
and
 IL = VT XL

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.

Equation

The phase shift for a parallel RL circuit is:

 q = tan-1 IL IR

Where:

q = Phase angle*

IL = Inductor current

IR = Resistor current

Procedure

 Given: VT, f, R, and L Determine: IT and q

1. Calculate XL

XL = 2pfl

2. Calculate IL

 IL = VT XL

3. Calculate IR

 IR = VT R

At this point, you know IL and IR

4. Calculate IT

 IT = Ö IR2 + IL2

5. Calculate q

 q = tan-1 IL IR

Steps 4 and 5 are the values to be determined.

Examples

Impedance in Parallel RL Circuits

Equation

The impedance of a parallel RL circuit is:

 Z = VT IT

Where:

Z = Circuit impedance
VT= Total voltage
IT = Total current

Examples

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: Voltage across the resistor (VR) Voltage across the inductor (VL) Inductive reactance (XL) Resistor current (IR) Inductor current (IL) Total current (IT) Impedance (Z) Phase angle (q)
 General Procedure 1. Determine VR and VL from  VT2. Calculate XL from f and L3. Calculate IR by applying Ohm's law to VR and R4. Calculate IL by applying Ohm's Law to VL  and XL5. Calculate IT from IR and IL6. Calculate Z by applying Ohm's law to VT and  IT 7. Calculate q from IL and IR

Examples

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.