# Study of Series R-L-C Circuit

Aim:- Study of Series R-L-C Circuit to;

1.     Calculate the values of unknown parameters of R-L-C circuit.

2.     Determine the power factor of the circuit.

3.     To draw a phasor diagram of the circuit based on practical data and find out the applied voltage and power factor from the phasor diagram.

Apparatus Required:-

 S. No. Name of Equipment Type Range Quantity 1. Ammeter MC 0-5A 1 3. Voltmeter MC 0-300V 3 4. Inductive Coil Variable 5A, 250V 1 5. Rheostat Single tube 500ohms, 5A 1 6. Capacitor - - 1 7. Single Phase variac - 230V, 10A 1

Theory:- In the present circuit, resistance R, inductor L and copulation C are connected in series across a voltage Source V. Thus the current in all the elements is same, whereas voltage across each element would be different. The resultant applied voltage V is the phasor sum of all the voltages across these elements. In such a series circuit, following basic relations can be derived:

Voltage across the resistance, VR = IR

Voltage across the inductance, VL = IXL

Voltage across the capacitance, VC = IXc

Power drawn by the circuit, P =VI

Power factor of the circuit, = P/VI

Where,

XL = Inductive reactance  =   =  2

XC Capacitive reactance =  =

The power factor of such a circuit is lagging the power Factor of this dreat will be leading Hence, by measuring the voltage across various elements, applied voltage: current flowing in the circuit and the power consumed by the circuit, all the parameters of the circuit can bá»‹ calkulated.

Circuit Diagram:-

PROCEDURE:

1.     Connect the circuit as per the circuit diagram shown in fig.

2.     Adjust the setting of variac, so that applied voltage to the R-L-C series circuit is zero.

3.     Switch-ON the main supply.

4.     Apply a low voltage to R-L-C series circuit and record the readings of ammeter, wattmeter and voltage across resistor, inductor, capacitor and across the terminals C and E of the variac. Voltages should be measured by a single voltmeter to increase the accuracy of measurement.

5.     Repeat step 4 for increased voltage applied to the circuit. It is sufficient to record 3 or 4 set of readings.

6.     Switch-off the main supply.

7.     Draw the phasor diagram, corresponding to one set of reading, preferable at higher voltage, and verify the calculated value of power factor.

Observation Table:-

 S. No. V (V) I(mA) VR(V) VL(V) VC(V) 1. 230.5 0.4 51.7 103.3 320.2

Calculation:-

 S. No. R= XL= XC = Z = P.F. = 1. 129.25 258.25 800.5 576.25 0.231

Precaucation:-

1.     Make the connections properly.

2.     Note the readings of voltmeters and ammeters properly.

3.     Remove insulations from the connecting wire so as the current will flow properly