- RL Parallel Circuit Definition: An RL parallel circuit is a setup where a resistor and an inductor are connected in parallel and share the same voltage source.
- Voltage Equality: In an RL parallel circuit, the input voltage equals the output voltage, though currents in the resistor and inductor differ.
- Impedance Calculation: The total impedance in a parallel RL circuit involves combining the resistance and inductive reactance.
- Current Calculation: Ohm’s law is used to find the currents in the resistor and inductor branches, then summing them for total current.
- Phase Angle Range: The total phase angle in a parallel RL circuit lies between 0° (pure resistive) and -90° (pure inductive).
In an RL parallel circuit, the resistor and inductor are connected in parallel and supplied by a voltage source (Vin). The output voltage (Vout) equals the input voltage because of the parallel connection, but the currents in the resistor and inductor differ.
The parallel RL circuit is not typically used as a voltage filter because the output voltage is equal to the input voltage. Therefore, it is less common than the series RL circuit for filtering applications.
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,
In complex form, the currents are expressed as:
Impedance of Parallel RL Circuit
Let, Z = total impedance of the circuit in ohms.
R = resistance of circuit in ohms.
L = inductor of circuit in Henry.
XL = inductive reactance in ohms.
Because the resistance and inductor are connected in parallel, the total impedance (Z) of the circuit is calculated 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 are known 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,
Step 2. We know that in parallel circuit, the voltage across inductor and resistor remains the same so,
Step 3. Use Ohm’s law to find the current flowing through inductor and resistor,
Step 4. Now calculate the total current,
Step 5. Determine the phase angles for resistor and inductor and for parallel circuit, its always
Step 6. Since we have already calculated the total current flowing in the circuit and voltage V is also known to us, by using Ohm’s law; we can easily calculate the total impedance:
Step 7. Now calculate the total phase angle for the circuit which is given by,
The total phase angle of a parallel RL circuit always lies between 0o to -90o. It is 0o for pure resistive circuit and -90o for pure inductive circuit.
