Practical - 15 :- Study of LCR meter

1. Objective

This experiment aims to familiarize the student with the properties of an inductor. Upon completion, you will be able to:

• Measure the DC resistance and inductance of a coil.

• Determine the inductive reactance () and impedance (Z) of the coil at various frequencies.

• Calculate the power factor and the phase angle (φ) for the circuit.

• Analyze the relationship between frequency, inductive reactance, and impedance.

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2. Apparatus Required

• Function Generator

• Digital LCR Meter

• Digital Multimeter (DMM)

• AC Milliammeter (0-300mA range)

• Inductor Coil (Choke)

• Connecting Wires

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3. Theory

An inductor is a passive electrical component that stores energy in a magnetic field when electric current flows through it. A practical inductor or coil consists of a wire winding and thus possesses both inductance (L) and some inherent DC resistance (R).

• Inductive Reactance (XL​): This is the opposition offered by the inductor to the flow of alternating current. It is directly proportional to the frequency (f) of the AC signal and the inductance (L) of the coil. It is measured in Ohms (Ω)

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• Impedance (Z): In an AC circuit, the impedance is the total opposition to current flow. For a real inductor (modeled as a series RL circuit), it is the vector sum of its internal resistance (R) and its inductive reactance (XL​). It is also measured in Ohms (Ω).    

From Ohm's Law for AC circuits, impedance can also be found by:

• Power Factor (cos φ): This is the ratio of the circuit's resistance to its impedance. It represents the phase difference between the voltage and current.  

  
  

  The phase angle φ can be found by ϕ=arccos(ZR​).

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4. Circuit Diagram  

The circuit consists of a function generator (AC source) connected in series with an AC ammeter and the inductor coil. A voltmeter is connected in parallel across the coil to measure the applied voltage.

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5. Procedure

1. Measure DC Resistance: Set the Digital Multimeter (DMM) to measure resistance. Measure and record the internal DC resistance (R) of the inductor coil.

2. Measure Inductance: Set the Digital LCR meter to measure inductance. Measure and record the inductance (L) of the same coil.

3. Construct the Circuit: Assemble the circuit as shown in the diagram above. Ensure all connections are secure.

4. Set Initial Parameters: Turn on the function generator and set it to produce a sine wave with an output voltage of 6 V (rms) and a frequency of 100 Hz.

5. Record Current: Note and record the AC current () flowing through the circuit as shown by the AC milliammeter.

6. Vary the Frequency: Keeping the output voltage constant at 6 V (rms), increase the frequency in steps as outlined in the observation table (e.g., 120 Hz, 1 kHz, etc.). At each frequency step, measure and record the corresponding AC current.

7. Calculations: After recording all measurements, turn off the power supply. Use the recorded data to calculate the impedance (Z), inductive reactance (), inductance (L), and power factor for each frequency setting.

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6. Observation and Calculation Table

A. Direct Measurements

• DC Resistance of the coil (R) = ____________

• Inductance of the coil (L) from LCR Meter = ____________ mH

B. AC Circuit Measurements & Calculations

• Applied Voltage () = 6 V

Sl. No.	Frequency ()	Measured Current ()	Impedance ()	Inductive Reactance ()	Calculated Inductance ()	Power Factor ()	Phase Angle ()
	(Hz)	(A)	()	()	(H)		(degrees)
1	100 Hz
2	120 Hz
3	500 Hz
4	1 kHz
5	2 kHz

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7. Results and Conclusion

1. The inductance of the coil as measured by the LCR meter is _________ H.

2. The average inductance calculated from the AC measurements is _________ H.

3. As the frequency of the AC signal increases, the inductive reactance () of the coil ____________ (increases/decreases).

4. As the frequency increases, the total impedance (Z) of the coil ____________ (increases/decreases).

5. Compare the value of inductance from the LCR meter with the average value calculated from the experiment. Discuss any significant differences found.

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8. Precautions

• Ensure the AC ammeter and voltmeter are set to the appropriate AC ranges.

• Make sure all connections are tight and correct before switching on the power supply.

• When taking readings from analog meters, avoid parallax error by viewing the needle from directly above.

• Do not leave the circuit powered on for an unnecessarily long time.