To study R-L parallel circuit. Also draw the phasor diagram

Experiment Number: 07

Aim of The Experiment: –

To study R-L parallel circuit. Also draw the phasor diagram.

Apparatus Required: –

Sl. No.NameSpecificationQuantity
1Single-phase auto transformer5KVA, (0-270)V01 Nos.
2Voltmeter(0-250)V, MI01 Nos.
3Ammeter(0-5)A, MI01 Nos.
4Ammeter(0-2)A, MI02 Nos.
5Rheostat(0-80)Ω, 5A01 Nos.
6Inductor01 Nos.
7Connecting WiresPVC Insulated CopperAs per required
Table 7.1

Circuit Diagram: –

Theory: –

In R-L parallel AC circuit a resistor of resistance R ohm, and Inductor of inductance L henry are connected i parallel of each other. These two elements are connected across single phase ac supply of rms V volts as shown in above fig.

As the circuit shown is parallel circuit the voltage across each element will remain the same but the flow of current will differ in resistor (R) and inductor (L) depends upon the respective capacity.

As shown in phasor diagram IR will be in the same phase with the applied voltage V and VL will lag with voltage by 900.

the resulting can be obtained from phasor diagram.

\[I_Z\ \ =\ \sqrt{(I_R^2+I_L^2\ )}\]

thus, the power factor is

\[\cos\phi =\dfrac{I_R}{I_Z} \] \[=\dfrac{I_R}{\sqrt{{I_R^2+I_L^2}}}\]
\[=\dfrac{\dfrac{V}{R}}{\sqrt{\left\{(\dfrac{V}{R})^2+(\dfrac{V}{X_L} )^2\right\}}}\]
\[=\dfrac{\dfrac{V}{R}}{\dfrac{V}{\sqrt{\dfrac{1}{R^2} +\dfrac{1}{X_L^2}}}}\]
\[=\dfrac{X_L}{\sqrt{(R^2+X_L^2\ )}}\]

let, R will be the value of resistance and L will be the value of inductance. The value of Impedance (Z) and admittance of the circuit will be as:

\[Z=\dfrac{1}{Y}\] \[=\dfrac{1}{\sqrt{(G^2+B_L^2\ )}}\] \[=\dfrac{1}{\sqrt{\{\dfrac{1}{R^2}\ +\dfrac{1}{X_L^2\ }\}}}\] \[=\dfrac{RX_L}{\sqrt{(R^2+X_L^2\ )}}\]

where G is conductance in siemens, XL is inductive reactance in ohm, BL is inductive susceptance.

from the phasor an admittance triangle can be drawn:

power factor is

\[Cos\phi=\dfrac{G}{Y}\] \[=\dfrac{\dfrac{1}{R}}{\sqrt{(G^2+B_L^2\ )}}\] \[=\dfrac{\dfrac{1}{R}}{\sqrt{(\dfrac{1}{R^2} +\dfrac{1}{X_L^2})}}\] \[=\dfrac{X_L}{\sqrt{(R^2+X_L^2\ )}}\]

Procedures: –

  1. Connect all the instruments as per circuit diagram given above.
  2. Before switch on the main power supply make sure that single-phase auto transformer knob is at zero position.
  3. Now slowly increase the supply voltage to the circuit after giving supply to the single-phase auto-transformer.
  4. Take all the corresponding readings of the connected instruments in the circuit as per observation table.
  5. Now calculate IZ, power factor Cosɸ and % error as per given formula.

Precaution: –

  1. Don’t switch on power supply without concerning teacher.
  2. Single phase auto-transformer must be kept at minimum potential point before switch on the experiment.

Observation Table: –

Sl. No.V (in volts.)I (in Amp.)IR (in Amp.)IL (in Amp.)IZ (in Amp.)Cosɸ= (IR/IZ)% Error
[{(I-IZ )/I}*100]
1
2
3
4
5
6
7
8
Table No. 7.2

Conclusion:

To be written by student.

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For Your Reference: –

Studying an R-L parallel circuit involves understanding the behavior of the circuit components and the overall impedance of the circuit.

R-L Parallel Circuit:

In an R-L parallel circuit, a resistor (R) and an inductor (L) are connected in parallel with each other.

Characteristics:

Impedance (Z): The total impedance of an R-L parallel circuit is determined by the parallel combination of the impedance of the resistor (R) and the impedance of the inductor (XL).

\[\color{red}{ Z = \frac{R \cdot X_L}{R + X_L}}\]

Resonance: Similar to the series circuit, a parallel R-L circuit also exhibits resonance, but the behavior is slightly different. At resonance, the total impedance is minimized.

Phasor Diagram:

In the phasor diagram for an R-L parallel circuit, we represent the voltage across the resistor (VR), the voltage across the inductor (VL), and the total voltage (V). The phasor diagram helps visualize the phase relationships between these voltages.

Phasor Diagram Components:
  1. Voltage across the Resistor (VR): It is in phase with the current flowing through the circuit.
  2. Voltage across the Inductor (VL): It lags the current by 90 degrees due to the inductive nature of the circuit.
  3. Total Voltage (V): It is the vector sum of VR and VL.
Phasor Diagram Construction:
  1. Draw a horizontal line to represent the reference axis for voltage (usually the x-axis).
  2. Draw VR along the reference axis (since it’s in phase with the current).
  3. Draw VL perpendicular to VR, lagging it by 90 degrees.
  4. The vector sum of VR and VL gives the total voltage V, which may not necessarily align perfectly with either VR or VL due to their phase difference.
Example Phasor Diagram: