RL Parallel Circuit

parallel rl circuit

In RL parallel circuit resistor andinductor are connected in parallel with each other and this combination is supplied by a voltage source, Vin. The output voltage of circuit is Vout. Since the resistor and inductor are connected in parallel, the input voltage is equal to output voltage but the current flowing in resistor and inductor are different. The parallel RL circuit is not used as filter for voltages because in this circuit the output voltage is equal to input voltage and for this reason it is not commonly used as compared to series RL circuit.

Let us say:
IT = the total current flowing from voltage source in amperes.
IR = the current flowing in the resistor branch in amperes.
IL = the current flowing in the inductor branch in amperes.
θ = angle between IR and IT.
So the total current IT : IT2 = IR2 + IL2

Vector Diagram of RL Parallel Circuit

Vector Diagram of RL Parallel Circuit

In complex form the electric currents are written as:
IR = Vin / R
IL = Vin / jωL (where 1/j = - j)
Or, IL = - j Vin / ωL
Therefore total current IT = Vin / R - j Vin / ωL

Impedance of Parallel RL Circuit

rl parallel circuit

RL Parallel Circuit

Z = total impedance of the circuit in ohms.
R= resistance of circuit in ohms.
L = inductance of circuit in Henry.
XL = inductive reactance in ohms.
Since resistance and inductance are connected in parallel so total impedance of the circuit is given by

In order to remove "j" from the denominator multiply and divide numerator and denominator by ( R - j XL )

Analysis of a Parallel RL Circuit

In parallel RL circuit, the values of resistance, inductance, frequency and supply voltage is known but for finding the other parameters of RL parallel circuit follow these steps:
Step 1. Since the value of frequency is already known we can easily find the value of inductive reactance XL: XL = 2πfL

Step 2. We know that in parallel circuit the voltage across inductor and resistor remains the same so: VR = VL = V

Step 3. Use Ohm's law to find the current flowing through inductor and resistor
IR = V / R and IL = V / XL

Step 4. Now calculate the total current: : IT2 = IR2 + IL2

Step 5. Determine the phase angles for resistor and inductor and for parallel circuit its always θR = 0° and θL = - 90°

Step 6. Since we have already calculated total current flowing in the circuit and voltage V is also known to us. So by using Ohm's law we can easily calculate the total impedance:
Z = V / IT

Step 7. Now calculate the total phase angle for the circuit which is given by : θT = - tan - 1(IL/ IR) . The total phase angle of a parallel RL circuit is always lies between 0° to -90°. It is 0° for pure resistive circuit and -90° for pure inductive circuit.

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