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This is an examination paper for the beng (hons) electrical and electronic engineering course at the faculty of science and engineering, department of engineering and technology, manchester metropolitan university. The paper contains five questions covering various topics in electrical and electronic engineering such as circuit time constants, delta connected balanced 3-phase load, single-phase transformer, q-factor in resonant circuits, and electric field strength.
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Exam ination for th e BEng (H O NS) ELECTR ICA LAND ELECTR O NIC ENGINEER ING (FULL-TIME/ SANDWICH ) YEA R O NE
Tuesday 21 May 2002
9 .30 am to 11.30 am
Instructions to Candidates
A nsw er any FO UR questions.
Break dow n of m ark s for each question is sh ow n in square parenth eses.
In th e circuit of Figure Q 1, w h ich initially h as no current, th e sw itch is closed at tim e t = 0. Calculate:- (a) th e circuit tim e constant w h en th e sw itch is closed. [2] (b ) th e current i 2 w h en th e sw itch h as b e e n closed for 1 second. [2] (c) th e current i 2 4 m s after th e sw itch w as closed. [4] (d) th e voltages vL, and vR 2 4 m s after th e sw itch w as closed. [4] (e) th e tim e tak en for th e supply current, is to reach 500m A [5]
Th e sw itch is k ept closed for 1 second and th en opened. Calculate:- (f) th e circuit tim e constant w h en th e sw itch is open [2] (g) th e current, i 2 , im m ediately after opening th e sw itch [2] (h ) th e voltage vR 1 and its direction im m ediately after opening th e sw itch. [4]
You m ay assum e th at th e equations relating th e grow th and decay of current in a series connected resistor and inductor are:
w h ere th e sym b ols h ave th eir usualm eanings
Figure Q 1
i = I (1o − e ) i = I (^) oe
− Rt − L
Rt and L
t=
G (^) 600mH
i
=30V vL
vR
R (^2) = 90 Ω 2
is
i 1
vR
Vs
(a) Th e approxim ate equivalent circuit for a single ph ase transform er referred to th e prim ary side is sh ow n in Figure Q 3. Explain th e function of th e equivalent circuit param eters R1eq, X1eq, Ro, and Xo [8]
(b ) Th e follow ing test results are for a 2.5 k VA , 240/110 V transform er. Both tests w ere carried out on th e 240 V w inding.
O pen circuit test : 240 V, 1.0 A , 45 W Sh ort circuit test : 5.5 V, 8.0 A , 38 W
Calculate; (i) th e equivalent circuit param eters referred to th e 240 V side.
[8] (ii) th e fullload current in th e 240 V w inding;
[3] (iii) th e percentage regulation w h en th e transform er is supplying a 2.5 k VA , 0.85 pf lagging load at rated voltage
[6]
Figure Q 3
Io
I 1 R1eq
X1eq
(Referred to primary side)
Xo
Im
Ro
Iw
(a) D e fine th e term Q -factor w h ich m ay be applied to all resonant circuits. [4] (b ) Sh ow th at, for a series resonant circuit, th e Q - factor m ay be expressed as:-
(c) Th e series LCR circuit sh ow n in Figure Q 4 is supplied from a 5 V, variab le frequency supply.
Calculate:- (i) th e resonant frequency fo; [4] (ii) th e current at th e resonant frequency; [2] (iii) th e Q -factor of th e circuit. [3] (iv) th e voltage across th e inductor at th e resonant frequency [3] (v) th e b andw idth [3]
Figure Q 4
ω (^0)
1 Ω 0.5 mH^ 0.1 μF
(a) D e fine Electric Field Strength (E) and state clearly th e units in w h ich it is m easured. [5] (b ) Figure Q 6 sh ow s tw o point ch arges A and B, situated in air.
(i) D e term ine th e m agnitude and d irection of th e Electric Field Strength (E) at th e point P. (You m ay assum e th at εo = 8. 85 × 10 -12^ F/m ) [6] (ii) Find th e value of th e ch arge at B w h ich w ould reduce th e field strength at P to zero [6]
Figure Q 6
(c) A capacitor consists of tw o m etalplates, each of area 800 cm 2 separated by a distance of 1.5m m. Th e space b e tw een th e plates is filled by a 1.2 m m th ick sh eet of m ica (εr = 5) and a 0.3 m m th ick sh eet of paper (εr = 2). Calculate th e capacitance of th e capacitor [8]
