AC Components and Circuits AC RL Circuits
Section 33 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: I_{T} = Ö  I_{R}^{2} + I_{L}^{2}  Where:  I_{T} = Total current
 I_{R} = Resistor current
 I_{L} = 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 I_{R} and I_{L}: If X_{L} is not directly know, you also have to calculate X_{L} = 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 (I_{R}) 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: Where: 
q = Phase angle* 
I_{L} = Inductor current 
I_{R} = Resistor current  Procedure Given: V_{T}, f, R, and L Determine: I_{T} and q   1. Calculate X_{L} X_{L} = 2pfl 2. Calculate I_{L} 3. Calculate I_{R} At this point, you know I_{L} and I_{R} 4. Calculate I_{T} I_{T} = Ö  I_{R}^{2} + I_{L}^{2}  5. Calculate q 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: Where:  Z = Circuit impedance
 V_{T}= Total voltage
 I_{T} = 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 (V_{T})
 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 (V_{R})
 Voltage across the inductor (V_{L})
 Inductive reactance (X_{L})
 Resistor current (I_{R})
 Inductor current (I_{L})
 Total current (I_{T})
 Impedance (Z)
 Phase angle (q)
  General Procedure 1. Determine V_{R} and VL from V_{T} 2. Calculate X_{L } from f and L 3. Calculate I_{R} by applying Ohm's law to V_{R} and R 4. Calculate I_{L} by applying Ohm's Law to V_{L} and X_{L} 5. Calculate I_{T} from I_{R} and I_{L} 6. Calculate Z by applying Ohm's law to V_{T} and I_{T} 7. Calculate q from I_{L} and I_{R}  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.
 
