Voltage and Current Source

Mesh Network and Analysis

Kirchhoff Current and Voltage Law

Superposition Theorem

Thevenin Theorem

Norton Theorem

Maximum Power Transfer Theorem

Reciprocity Theorem

Compensation Theorem

Tellegen Theorem

Voltage Divider

Star - Delta Transformation

RL Circuit

RL Series Circuit

RL Parallel Circuit

RLC Circuit

Series RLC Circuit

Parallel RLC Circuit

Resonance in Series RLC Circuit

In **RL parallel circuit** resistor andinductor are connected in parallel with each other and this combination is supplied by a voltage source, V_{in}. The output voltage of circuit is V_{out}. Since the resistor and inductor are connected in parallel, the input voltage is equal to output voltage but the currents 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:

I_{T} = the total current flowing from voltage source in amperes.

I_{R} = the current flowing in the resistor branch in amperes.

I_{L} = the current flowing in the inductor branch in amperes.

θ = angle between I_{R} and I_{T}.

So the total current I_{T} : I_{T}^{2} = I_{R}^{2} + I_{L}^{2}

In complex form the electric currents are written as:

I_{R} = V_{in} / R

I_{L} = V_{in} / jωL (where 1/j = - j)

Or, I_{L} = - j V_{in} / ωL

Therefore total current I_{T} = V_{in} / R - j V_{in} / ωL

## Impedance of Parallel RL Circuit

Let

Z = total impedance of the circuit in ohms.

R= resistance of circuit in ohms.

L = inductance of circuit in Henry.

X_{L} = inductive reactance in ohms.

Since resistance and inductance are connected in parallel, the 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 X_{L} )

### 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 X_{L}: X_{L} = 2πfL

Step 2. We know that in parallel circuit, the voltage across inductor and resistor remains the same so: V_{R} = V_{L} = V

Step 3. Use Ohm's law to find the current flowing through inductor and resistor

I_{R} = V / R and IL = V / XL

Step 4. Now calculate the total current: : I_{T}^{2} = I_{R}^{2} + I_{L}^{2}

Step 5. Determine the phase angles for resistor and inductor and for parallel circuit, its always θ_{R} = 0° and θ_{L} = - 90°

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:

Z = V / I_{T}

Step 7. Now calculate the total phase angle for the circuit which is given by : θ_{T} = - tan ^{ - 1}(I_{L}/ I_{R}) . The total phase angle of a parallel RL circuit always lies between 0° to -90°. It is 0° for pure resistive circuit and -90° for pure inductive circuit.

**Please give us your valuable comment/suggestion. This will help us to improve this page.**