EXAMINATION PAPER:  ACADEMIC SESSION 2019/2020

Campus                                             Medway                      

Faculty                                             Engineering & Science

Level                                                   5

Exam Session                                  April/May 2020

MODULE CODE                            ELEC1034

MODULE TITLE                         ELECTRICAL CIRCUITS

Type of Examination                     Online Exam

 

Original duration of examination  2 hours            

List of appendices                          Formula Sheet

 

To be submitted by 29^th April 2020 at 5pm BST

 

 

 

Instructions to Candidates

 

Answer FOUR questions out of the following SIX questions.  

All questions carry equal marks.

To maximise your marks, make sure you show the relevant method and formulae where appropriate.

 

Students will be required to achieve an overall grade of 40% to achieve a pass.

             

Q1.

(a) Kirchhoff’s current law (KCL) and Kirchhoff’s voltage law (KVL) are the two fundamental laws in electrical circuits.

(i) In Figure Q1(a), if   V₁=3V, V₂=9V, V₅=5V, determine the voltages V₃, V₄, V₆  and V₇ by applying Kirchhoff’s Voltage Law (KVL).

[9 marks]

 

Figure Q1(a)

 

(ii)        In Figure Q1(a), if  i₃=2A, i₅=−2A, i₆=1A, i₇=5A, determine the currents i₁, i₂, i₄, by using KCL.

 [9 marks]

 

(b) Determine the Thevenin Equivalent circuit for the circuit in Figure Q1(b) that contains a current source and two resistors. Draw the appropriate circuit diagram for each stage.

[7 marks]

       

ANSWER(Purchase full paper to get all the solutions)

1ai)

KVL

Loop 1

                                            Equation 1

Given V₁=3V, V₂=9V, V₅=5V,

 

 

Loop 2

                                        

                                                     Equation 2

Loop 3

                                        

                                                    Equation 3

Loop 4

                                                    Equation 4

 

 

From Equation 3

 

 

 

From equation 2

 

 

 

 

 

 

1aii)

Given i₃=2A, i₅=−2A, i₆=1A, i₇=5A,

Node 1:

 

 

 

Node 2:

 

 

 

Node 3:

 

 

 

 

1b)

 

 

 

Q2.

1. The superposition theorem is one of the powerful theorems in the field of electrical engineering and has a widespread application. 

 

1. 1. State the principle of superposition theorem.            [2 marks]

 

1. 2. Determine current i_x in the circuit of Figure Q2(a) using the principle of   superposition

[8 marks]

 

 

 

 

 

 

 

1. In Wheatstone bridge shown in Figure Q2(b), if R₁=680?, R₂=3.3k?, R₄=8.2k?. To what value must R₃ be set in order to balance the bridge? 

 

   

1. With the aid of diagrams describe and compare the two different ways of connecting a 3-phase system.

[5 marks]

 

2. Describe the advantages and disadvantages of 3-phase connections. 

 

Q3.

(a) An RC low-pass filter is shown in Figure Q3(a), in which R=500Ω, C=0.2µF, determine:

1. Its time constant          [3 marks]
2. 3dB frequency in Hz   [3 marks]
3. The phase shift of output voltage v_out if v_in=10sin(2π×20000t) [4 marks]

 

(b)    An induction motor is a type of AC electric motor.

1. Briefly explain the working principles of the induction motor.      [5 marks]
2. With the use of a diagram, describe the various losses in the operation of an induction motor. 

[4 marks]

(c)       Give expressions for the sine wave voltage signals having:

1. 0.8V peak-to-peak and 1000 rads^-1 frequency.     [2 marks]
2. 10V peak amplitude and 10 kHz frequency.          [2 marks]
3. 50mV peak amplitude and 5ms period.      [2 marks]

[Total 25 marks]

Q4.

1. Discuss the importance of power factor.             [3 marks]
2. A 50kW load operates from a 60Hz frequency and 10kV         line with a power factor of

rms

60% lagging. It is desired to achieve a 90% lagging power factor for the system.

1. 1. Explain the process of the power factor correction and draw the power triangle for the power factor improvement.

[6 marks]

 

1. 2. Calculate the apparent power for the system with a power factor of 60% and

                     90%.                                                                                                         [4 marks]

 

1. 3. Calculate the capacitance that must be placed in parallel with the load to achieve a 90% lagging power factor.

[12 marks] [Total 25 marks]

Q5.

(a) In the circuit shown in figure Q5(a) the switch has been closed for a long time (all transients have decayed) and the capacitor is charged up. At time t=0⁺ the switch is OPENED and the capacitor discharges.

1. What is the voltage on the capacitor at time t=0⁺.            [5 marks]
2. Calculate the time constant of the discharge circuit.        [3 marks]
3. Write an expression for the voltage on the Capacitor for t>0.     [4 marks]
4. What is the voltage on the capacitor after 0.25 ms.         [2 marks]
5. How long is it until the capacitor voltage has decayed to 0.5V?            [5 marks]

 

 

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