ELECTRICAL AND ELECTRONIC PRINCIPLES-CIRCUIT THEORY

MODULE TITLE : ELECTRICAL AND ELECTRONIC PRINCIPLES

TOPIC TITLE : CIRCUIT THEORY

TUTOR MARKED ASSIGNMENT 1 (v3.1)

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Student declaration:

I declare that all the work submitted is my own work and that no part of it has been copied from

any other source without full acknowledgement and complies with the University's guiding

principles as stated in the Regulations Relating To Academic Misconduct*.

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*http://www.tees.ac.uk/docs/index.cfm?folder=Student%20Regulations&name=Academic%20Regulations

EEP - 1 - TMA (v3.1)

© Teesside University 2014

Published by Teesside University Open Learning (Engineering)

School of Science & Engineering

Teesside University

Tees Valley, UK

TS1 3BA

+44 (0)1642 342740

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IMPORTANT

Before you start please read the following instructions carefully.

1. This assignment forms part of the formal assessment for this module. If

you fail to reach the required standard for the assignment then you will be

allowed to resubmit but a resubmission will only be eligible for a Pass

grade, not a Merit or Distinction.

You should therefore not submit the assignment until you are reasonably

sure that you have completed it successfully. Seek your tutor's advice if

unsure.

Answer each of the five questions as completely as you are able in the time you have available

2. Ensure that you indicate the number of the question you are answering.

3. Make a copy of your answers before submitting the assignment.

4. Complete all details on the front page of this TMA and return it with

the completed assignment including supporting calculations where

appropriate. The preferred submission is via your TUOL(E) Blackboard

account:

https://eat.tees.ac.uk

5. Your tutor’s comments on the assignment will be posted on Blackboard.

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Assessment Criteria

This assignment relates to the application of circuit theory to solve problems

involving a.c.networks and tuned circuits. The assignment forms Element 1 of

the module’s assessment criteria that covers in part Learning Outcomes 1 and 4

as indicated below.

MODULE LEARNING OUTCOMES

Knowledge and Understanding 1. Demonstrate detailed knowledge of circuit theory relating to simple

electrical/electronic circuits,

Cognitive and Intellectual Skills 2. Apply circuit theory techniques to the solution of a.c. circuit problems,

including analysis of complex waves and Laplace transforms for the transient

analysis of networks.

Practical and Professional Skills 3. Calculate the parameters of a.c. equivalent circuits, including the solution of

two port networks.

Key Transferable Skills 4. Apply numerical skills to a variety of electrical and electronic engineering

problems relating to circuit theory and analysis.

PASS MERIT

Criteria in excess of the pass

grade.

DISTINCTION

Criteria in excess of the

merit grade.

Learning outcomes are

satisfied as evidenced by

substantially correct circuit

analysis.

The transfer of competence

gained in one situation to

related but unfamiliar

circumstances.

The ability to integrate

knowledge from two or

more topic areas to solve a

significantly more complex

problem.

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© Teesside University 2014 Teesside University Open Learning (Engineering)

You are encouraged to use the spreadsheet accompanying the assignment

on Blackboard to solve complex simultaneous equations.

1. FIGURE 1 shows a 50 Ω load being fed from two voltage sources via

their associated reactances. Determine the current i flowing in the load by:

(a) applying Thévenin’s theorem

(b) applying the superposition theorem

(c) by transforming the two voltage sources and their associated

reactances into current sources (and thus form a pair of Norton

generators).

j4 Ω j6 Ω

i

v 50 Ω v 1 @ 0.7 p.f. lag 2

v1 =

v2 =

2 ×415cos(100πt )

2 ×415sin (100πt )

volts

volts

FIG. 1

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V 1

120 0° V

V 2

120 90° V

V 3

20 45° V

Z 1 2 Ω

Z 2 –j5 Ω

Z 3 4 Ω

Z 4 –j5 Ω

Z 5 j4 Ω

2. Determine, using the values given in TABLE A, the current I in the

circuit of FIGURE 2 by:

(a) mesh analysis

(b) nodal analysis.

V 3

Z I Z Z

1 2 3

V 1

Z 4

Z 5

V 2

FIG. 2 TABLE A

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3. For the balanced three-phase loads shown in FIGURE 3, ZY = (15 + j15) Ω and Z∆ = (45 + j45) Ω. Determine:

(a) the equivalent single ∆-connected load,

(b) the equivalent single Y-connected load obtained from the

∆-Y transformation of (a) above,

(c) the equivalent single Y-connected load obtained by transforming

the ∆ sub-load of FIGURE 3 to a Y and with the star-points of

the two Y-sub-circuits connected together,

(d) the total power consumed in case (a) above if the line voltage of

the three-phase supply is 415 V at 50 Hz.

415 V

ZY

ZY ZY

Z∆ Z∆

Z∆

FIG. 3

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4. FIGURE 4(a) shows two inductances connected in parallel across an

a.c. supply.

(a) Apply Kirchhoff’s voltage law to loop abef and to loop abcdef of

the circuit.

(b) Hence or otherwise obtain the current ratio I1

in terms of the I2

circuit inductances.

(c) See if you can show that L1 and L2 can be replaced by the

equivalent inductor, Leq, of FIGURE 4(b) where

(d) A 1 nF capacitor is placed across the two inductors

(FIGURE 4 (c)). If L1 = L2 = L and k = 0.5, determine the required

value of L if the minimum current I flows from the supply when it is

at a frequency of 1 MHz.

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a I b c I

I1 I2

V L1 M L2 V

Leq

f e d

(a) (b)

I

I1 I2

V L1 M L2

(c)

FIG. 4

© Teesside University 2014 Teesside University Open Learning (Engineering)

5. A 415V to 11 kV transformer has a rating of 200 kVA. The

winding resistance and leakage reactance when referred to the primary

are 0.014 Ω and 0.057 Ω respectively.

(a) Determine the % regulation of the transformer at 0.8 power factor lagging.

(b) In designing a particular 415V to 11 kV, 200 kVA transformer,

the primary winding resistance is to be 10 mΩ. Find the maximum

winding resistance of the secondary winding if the transformer is

to have 2% regulation at unity power factor.