# A. Study of phase difference between voltage and current in series RC and LR circuit B. Study of resonant frequency in parallel LC circuit

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Introduction

## Title: A. Study of phase difference between voltage and current in series RC and LR circuit

## B. Study of resonant frequency in parallel LC circuit

Part A:

Objective:

1. To display the waveforms of voltage and currents in series RC and LR circuits by a CRO.

2. To determine the phase differences between voltage and current in the circuits.

Apparatus:

CRO (dual trace) | 1 |

Low voltage power supply | 1 |

1100-turn inductance coil | 1 |

Resistance substation box | 1 |

Capacitance substitution box | 1 |

Double C-coil with clip | 1 |

Connecting wires | n |

Procedure and Results:

- RC circuit

After connecting the RC circuit, turning on the low voltage a.c.power supply and setting it to 2V and 50Hz, the traces shown on the CRO was observed and sketched.

Capacitance = 1μF, Resistance = 2.2kΩ:

It clearly showed that there was phase difference between the voltage and the current. The current lead the voltage by about π/4 rad -π/2 rad.

Then the steps were repeated with the other resistor of different resistance (R).

Capacitance = 1μF, Resistance = 100Ω:

→ The phase difference between the voltage and the current was about π/2 rad.

Capacitance = 1μF, Resistance = 100kΩ:

→ The phase difference between the voltage and the current was about 0 rad. (in phase)

- RL circuit

Middle

The voltage leads the current by π/2 rad.

1100-turn coil with resistance100kΩ:

→ The phase difference between the voltage and the current was about 0 rad. (in phase)

Disscusion:

- The channel 1 of the CRO should be connected across both the capacitor and the resistor but not the capacitor only. Because if the cannel 1 of the CRO is connected across the capacitor only, it just shows the trace of VC but not applied voltage, and the trace will not change whether changing the resistance of the resistor.

- The channel 2 of the CRO could give the current through the capacitor beause the current across the resistor is in phase with that of voltage. By measuring the voltage across the resistor, the current across the capacitor can be determined.

- The phase differences between the voltage and the current for both RC and LR circuits in steps 5 and 11 were not equal to 90°. It was because the applied voltage V was the sum of VR and VC, and there is always a phase differenceδbetween the applied voltage V and the current I. But since tan δ= VC/VR,

Conclusion

Similarly, refer to equation (1) , when the capacitance remains constant, which mean the smaller the inductance is, the higher the resonant frequency is. From the experimental results in step 10, since inductance will decease when core is removed, the data was found to follow the equation and showed the expected results.

Sources of error and improvement:

- The instruments are not accurate and precise enough. For example, the capacitors may not have the same capacitance as it showed. So it made the trend not accurate. So the capacitance of capacitors should be tested first if it is available. Also , if graphs could be plotted to observe the relationships, the equation could be proved clearer.

- Since the capacitance substitution box and inductor were not pure and may have some resistance, so some of the voltage may be dissipated by them. And it made the voltages vary in different times. So purer capacitors and inductors should be used.

Conclusion:

The resonant frequency was found from the results with different capacitance and inductance and it was determined that the inductance and capacitance are the factors affecting the frequency of oscillations in the parallel LC circuit.

S.7 Physics TAS Experiment Chan Man Lok 7C (16) P.

This student written piece of work is one of many that can be found in our AS and A Level Electrical & Thermal Physics section.

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