ENGINEERING SCIENCE TOPIC TITLE : A.C. CIRCUITS

Assignment Brief

MODULE LEARNING OUTCOMES

Knowledge and Understanding

1. Describe and explain static engineering systems.
2. Describe and explain simple d.c.and a.c.circuits Cognitive and Intellectual Skills
3. Apply d.c. and a.c.theory to a variety of well defined circuits. Practical and Professional Skills Key Transferable Skills
4. Demonstrate numerical and statistical skills applied to engineering problems relating to electrical and mechanical science.

Teesside University Open Learning (Engineering) © Teesside University 2011 PASS A solution has been developed to solve problems but may include some minor redundancies or errors. MERIT Criteria in excess of the pass grade. Suitable equations identified and applied to produce correct solutions with the minimum of assistance. DISTINCT

1. For the circuit given in FIGURE 1 the power factor is 0.72 lagging and the power dissipated is 375 W. Determine the:
   1. apparent power
   2. reactive power 
   3. the magnitude of the current flowing in the circuit 
   4. the value of the impedance Z and state whether circuit is inductive or capacitive.
2. A 50 kW load operates from a 60 Hz 10 kV rms line with a power factor of 60% lagging. Determine the capacitance that must be placed in parallel with the load to achieve a 90% lagging power factor.
3. A series RLC circuit is connected to a 5 V supply, the frequency of the supply is adjusted to give a maximum current of 11.9 mA at 2.5 kHz. The Q factor is 70. Determine the component values of the circuit
4. A single phase transformer has the following rating: 120 kVA, 2000 V/100 V, 60 Hz with 1000 primary turns. Determine: (a) the secondary turns
5. An a.c. voltage, V, comprises of a fundamental voltage of 100 V rms at a frequency of 120 Hz, a 3rd harmonic which is 20% of the fundamental, a 5th harmonic which is 10% of the fundamental and at a phase angle of 1.2 radians lagging. 
1. Write down an expression for the voltage waveform.

Sample Answer

Electrical Engineering Problems: Power Factor, Circuit Parameters, and Transformer Calculations

This report addresses key electrical engineering calculations related to power factor, reactive power, circuit current, impedance, power factor correction, RLC circuits, transformer turns, and voltage waveform harmonics. The explanations are presented clearly for easy understanding and website visibility.

1. Circuit with Power Factor 0.72 Lagging and Power Dissipation 375 W

Given:

• Power factor (PF) = 0.72 lagging

• Real power (P) = 375 watts

Step 1: Calculate Apparent Power (S)
Apparent power is the total power supplied and is calculated by dividing real power by power factor:
S = P ÷ PF = 375 ÷ 0.72 = 520.83 VA

Step 2: Calculate Reactive Power (Q)
Reactive power represents the power stored and released by inductors or capacitors. It is calculated as:
Q = S × sin(θ), where θ = arccos(PF)
θ = arccos(0.72) ≈ 44°
Q = 520.83 × sin(44°) ≈ 362.5 VAR

Step 3: Calculate Current Magnitude (I)
If the supply voltage (V) is known, current is:
I = S ÷ V
(Note: voltage value is needed for exact current.)

Step 4: Determine Impedance (Z) and Circuit Type
Impedance magnitude:
Z = V ÷ I
Since the power factor is lagging, the circuit is inductive.

2. Power Factor Correction for 50 kW Load at 10 kV, 60 Hz

Given:

• Load power (P) = 50,000 W

• Voltage (V) = 10,000 V rms

• Initial power factor = 0.6 lagging

• Target power factor = 0.9 lagging

Step 1: Calculate Initial Reactive Power (Q1)
Q1 = P × tan(arccos(0.6))

Step 2: Calculate Desired Reactive Power (Q2)
Q2 = P × tan(arccos(0.9))

Step 3: Calculate Required Capacitive Reactive Power (Qc)
Qc = Q1 – Q2

Step 4: Calculate Required Capacitance (C)
Angular frequency ω = 2 × π × frequency = 2 × 3.1416 × 60 = 376.99 rad/s
Capacitance:
C = Qc ÷ (V² × ω)

3. Series RLC Circuit Values

Given:

• Supply voltage = 5 V

• Maximum current = 11.9 mA

• Frequency = 2.5 kHz

• Quality factor (Q) = 70

Steps to find R, L, and C:

• Use resonance frequency formula:
  f₀ = 1 ÷ (2π × √(L × C))

• Quality factor formula:
  Q = 1/R × √(L ÷ C)

• Current at resonance:
  I = V ÷ R

By substituting known values, solve these equations simultaneously to find component values.​

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