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# Single Phase Circuits Investigation

Extracts from this document...

Introduction

Electrical and Electronic Principles

Assignment Two

Single Phase Circuits

Gary Short

### Contents

Part One – Laboratory Exercise                                Pages 3 & 4

Part Two – Practical Calculations                                Page 5

1. Page 5
2. Page 5
3. Page 6
4. Page 6
5. Page 7

Part Three – Theoretical Calculations                                Page 8

3.1,      a)                                                        Page 8

1. Page 8
2. Page 8
3. Page 9

Part Four – Conclusions                                        Page 9

Appendix

Diagram 1                                                        Page 10

Diagram 2                                                        Page 10

Diagram 3                                                        Page 11

Diagram 4                                                        Page 11

Introduction

The assignment investigates voltages, phase angles and power in AC reactive circuits using phasor diagrams, impedance triangles and calculations.

Part One – Laboratory Exercise

Circuit A

Value of components in the circuit

R = 470 Ω

L = 100 mH

Using a multimeter the following voltages were measured:

VR = 1.43v

VL = 2.17v

VS = 2.89v

The circuit was then connected to an oscilloscope so that one channel displays VR and the other VL.  The readings taken are shown in diagram 1, they show that the Phase shift is approximately 90°.  They also show the VL

Middle

The phasor diagram for Circuit A verifies that VL is leading VR.

The phasor diagram for Circuit B verifies that VC is lagging VR.

You are unable to get an exact scale for the diagrams as a ruler was used.  VL is slightly out as there is resistance on the inductor, this means angle φ would not be exactly 90°.

2.2) – Using ohms law calculate the current in each circuit.

Circuit A                                                Circuit B

R = 470Ω                                                R = 470Ω

VR = 1.43v                                                VR = 2.38v

I =  =  = 3.04 mA                                I =  =  = 5.06 mA

2.3) – Calculate XL, XC and Z for each circuit by two methods.

Circuit A

1. XL =  =  = 714Ω

b)        XL = 2.π.f.l   = 2xπx1000x100x10 = 628Ω

Circuit B

1. XC =  =  = 154Ω
1. XC =  =  = 159Ω

Results Table and comparisons

 Circuit A Result Comparison a)XL 714Ω The results of calculation b)

Conclusion

b)XC

159Ω

Difference

5Ω

2.4) Draw impedance triangles for both circuits and use them to determine the phase angle (Φ) of each circuit.

Circuit A

Z = 784Ω                                                        Scale: 1cm = 100Ω

XL = 628Ω

R = 470Ω

Φ = TAN-1

Φ = TAN-1

Φ = 53°

Circuit B

Z = 496Ω                                                        Scale: 1cm = 100Ω

XC = 159Ω

R = 470Ω

Φ = TAN-1

Φ = TAN-1

Φ = -33°

2.5) Using the phase angle to calculate the power factor of the circuit, then calculate the power in the circuit.

Circuit A

Power factor = cos (Φ)

Power factor = cos (53)

Power factor = 0.60

Power = VS x I x power factor

Power = 2.89 x 3.04 x 0.60

Power = 5.27 watts

Circuit B

Power factor = cos (Φ)

Power factor = cos (-33)

Power factor = 0.83

Power = VS x I x power factor

Power = 2.54 x 5.06 x 0.83

Power = 10.7 watts

Part Three – Theoretical Calculation

1. A coil has a resistance of 12Ω and inductance of 15.9mH, connected across a 240v 50Hz supply
1. Calculate the reactance of the inductance:

XL = 2.π.f.l

XL = 2 x π x 50 x 15.9x10

XL = 4.995 Ω

XL = 5 Ω

1. Calculate the impedance of the coil:

Page         12126.doc

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