PROCEDURE USING LABORATORY CIRCUITS



PROCEDURE USING LABORATORY CIRCUITS

PART 1

INVESTIGATION OF THE RLC SERIES CIRCUIT

l) Using a function generator FG, an oscilloscope CRO, one digital voltmeter of frequency range up to l0kHz on a.c. volt scales and the RLC circuit components. Design and draw a suitable circuit.

2) Write an appropriate formula that may be used to calculate the resonant frequency for the f the given L and C values.

3) Write the self-inductance value of the investigated coil (copy this value from the label placed on the coil).

4) Rearrange the resonant frequency formula in order to calculate the capacitance C for resonant frequency assumed at ……….. Hz.

5) To select the resistance R value, you have to realize that the series RLC circuit at resonance has a minimum impedance value equal to its pure resistance. This resistance limits the total current that is drawn from the supply. Too low a value of resistance may overload the supply and cause its failure. Yet a lower value of resistance gives a higher quality factor in the series circuit. Therefore to choose the resistance you have to make a certain compromise in order to suit the above requirements. Now, write a suitable formula to calculate the quality factor.

6) Convert the formula to calculate the resistance when the quality factor Q is assumed as ……….

7) Round off the calculated resistance value to the nearest 1000 Q, and set this

value up on'a decade resistance box. Using a decade capacitance box, set up the

required value of capacitance.

8) Using all the selected equipment, connect the circuit.

9) Adjust the function generator voltage to 6 V r.m.s., then select the appropriate frequencies as indicated in the table below. When selecting the frequencies, keep the power supply voltage at the same level. Use a digital voltmeter with flying leads to measure the function generator voltage.

10) Use the same digital voltmeter to obtain the voltage readings on each of the

circuit elements. Record the readings in the Table 1.

TABLE 1

|f |kHz | | | | |

|Hz |V |V |V |V |A |

| | | | | | |

14) Add suitable scales to the graph provided, and then plot the readings.

15) Give the expression used to calculate the current corresponding to the half-power points, and then calculate its value.

16) Draw a horizontal line corresponding to the calculated half-power current

and find out the cut-off frequencies. Tabulate the readings.

|f1 |f2 |

|Hz |Hz |

| | |

17) Using the cut-off frequencies obtained, calculate the bandwidth.

18) Using the resonant frequency and the cut-off frequencies, calculate the quality factor Q of the circuit.

19) The quality factor Q could have a similar value to that assumed previously for the calculation of the resistor R. Now, for the rise of voltage measured across the capacitor and inductor at resonance, calculate the Q factors and compare the results with those obtained before.

20) Applying Ohm's law, calculate the effective resistance of the series circuit being at resonance.

21) Using the obtained effective resistance, calculate once again the Q factor to check

its value (use the inductance).

22) Applying the capacitance value, calculate the Q factor

as well.

23) Referring to the obtained effective resistance of the entire series circuit, determine the effective resistance of the inductor L while it is carrying

the alternating current Io at resonance.

|[pic] |[pic] |

|[pic] |[pic] |

| | |

24) Compare the calculated value of the inductor effective resistance with that obtained for the d.c. current measurement (use ohmmeter). Comment briefly on the difference, if one is evident.

25) Draw a phasor diagram at the frequency of ……… kHz in the space provided. Add suitable scales on the axes. Assume the current at the horizontal position.

|[pic] |deg | |

|[pic] |rad | |

26) Measure the phase angle from the diagram and record its value.

|A |Inductive | |

|B |Capacitive | |

27) Place a tick in the appropriate square to indicate the network character.

28) Using the voltage readings, check the phase angle by means of calculation.

PROCEDURE USING LABORATORY CIRCUITS

PART 2

INVESTIGATION OF THE GLC PARALLEL CIRCUIT

1) Design an draw a laboratory circuit consisting of a parallel LC branch connected in series with a resistor R and supplied from a function generator FG. The circuit should also contain an oscilloscope CRO facilitating the search for an exact resonant frequency by voltage and current comparison. To measure the oscillator output voltage, use a digital voltmeter. To find the total circuit current, use a digital ammeter.

2) Two functions of resistor R are: to limit a maximum circuit current; and to provide an oscilloscope channel with a voltage proportional to and in phase with the circuit current. Determine the resistance R value that is set on a decade resistance box to limit the current to 3 mA when the oscillator voltage is adjusted to 6 V r.m.s.

3) Using a decade capacitance box set to l uF, an air-cored inductor of …… mH

(used in previous experiments) and all the indicated equipment, set up the circuit.

4) Write a suitable formula that can be used to determine a parallel resonant frequency.

5) Calculate the resonant frequency from this formula.

6) Switch on the function generator FG and set its output voltage to 6 V r.m.s.

Select the oscillator frequencies as indicated in the table below, then obtain current measurements at each frequency setting. Keep the oscillator voltage constant at each setting of frequency. Record the current readings.

TABLE 3

f |kHz | | | | | | | | | | | | | |I |mA | | | | | | | | | | | | | |f |kHz | | | | | | | | | | | | | |I |mA | | | | | | | | | | | | | |

7) Set the oscilloscope to the X-Y mode. Set the frequency so as to obtain an

oblique straight line on the screen to determine the exact resonant frequency.

Read the frequency on the oscillator scale, and record its value in the empty

space of the table. Measure and record the current at resonance.

8) Plot the current against frequency to obtain the frequency-response characteristic of the network.

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Fig.1

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L=

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f

Hz

Ieff

mA

fop=

fop=

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