universiti malaysia perlis dmt 112 circuit theory i...
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UNIVERSITI MALAYSIA PERLIS
Peperiksaan Semester Pertama
Sidang Akademik 2014/2015
Oktober 2014
DMT 112 – Circuit Theory I
[Teori Litar I]
Please make sure that this question paper has THIRTEEN (13) printed pages including
this front page before you start the examination. [Sila pastikan kertas soalan ini mengandungi TIGA BELAS (13) muka surat yang bercetak termasuk muka
hadapan sebelum anda memulakan peperiksaan ini.]
This question paper has SIX (6) questions. Answer any FIVE (5) questions only. Each
question contributes 20 marks. [Kertas soalan ini mengandungi ENAM (6) soalan. Jawab mana-mana LIMA (5) soalan sahaja. Markah
bagi tiap-tiap soalan adalah 20 markah.]
Appendix for formula is given. [Lampiran untuk formula diberi.]
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Question 1 [Soalan 1]
(a) (i) Voltage, current and resistance are essential element of an electrical
circuit. Using your own words, relate the relationship for voltage, current
and resistance based on Ohm’s Law. [Voltan, arus dan rintangan adalah elemen penting dalam litar elektrik. Menggunakan
perkataan anda sendiri, kaitkan hubungan untuk voltan, arus dan rintangan berdasarkan
Hukum Ohm.]
(2 Marks/ Markah)
(ii) Figure 1(a) show a graph of current versus voltage for three resistance
values. Based on the graph, determine the resistances of R1, R2 and R3. [Rajah 1(a) menunjukkan graf arus melawan voltan bagi tiga nilai rintangan.
Berdasarkan graf tersebut, tentukan rintangan bagi R1, R2 dan R3.]
(6 Marks/ Markah)
Figure 1(a) [Rajah 1(a)]
.…3/-
6
5
4
3
2
1
1 2 3 4 5 6
I (mA)
V (V)
R1
R2
R3
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(b) Illustrate each of the following term by using a suitable circuit diagram: [Gambarkan setiap istilah berikut dengan menggunakan gambarajah litar yang sesuai:]
(4 Marks/ Markah)
(i) Branch. [Cabang.]
(ii) Node. [Nod.]
(iii) Loop. [Gelung.]
(iv) Mesh. [Jejaring.]
(c) Simplified the circuit in Figure 1(b) by using the concept of source
transformation and calculate the voltage, Vo. [Permudahkan litar dalam Rajah 1(b) dengan menggunakan konsep jelmaan punca dan kirakan
voltan, Vo.]
(8 Marks/ Markah)
10 Ω
40 Ω
12 Ω 20 Ω
50 V 8 A 40 V
Vo
Figure 1(b) [Rajah 1(b)]
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Question 2 [Soalan 2]
(a) (i) State Kirchhoff’s laws on voltage and currents. [Nyatakan hukum Kirchhoff bagi voltan dan arus.]
(4 Marks/ Markah)
(ii) Based on Figure 2(a), calculate voltage, Va using Kirchhoff’s current and
voltage law. [Berdasarkan Rajah 2(a), kirakan voltan, Va menggunakan hukum Kirchhoff arus dan
voltan.]
(6 Marks/ Markah)
1 Ω
3 Ω
6 Ω
5 V3 AVa
Figure 2(a) [Rajah 2(a)]
.…5/-
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(b) Based on the circuit in Figure 2(b), calculate; [Berdasarkan litar dalam Rajah 2(b), kirakan;]
(i) the equivalent resistance, Req. [rintangan setara, Req.]
(3 Marks/ Markah)
(ii) the total current, IT. [jumlah arus, IT.]
(2 Marks/ Markah)
(iii) the power absorbed by the voltage source. [kuasa terserap oleh sumber voltan.]
(2 Marks/ Markah)
(iv) current, I1 using current divider rule. [arus, I1 menggunakan aturan pembahagi arus.]
(3 Marks/ Markah)
30 Ω 30 Ω
25 Ω
40 Ω
30 Ω
60 Ω
10 Ω
20 Ω
50 Ω
20 V
ITI1
Figure 2(b) [Rajah 2(b)]
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Question 3 [Soalan 3]
(a) (i) The objective of node analysis is to find unknown node voltage. List down
the steps for node analysis. [Objektif analisis nod adalah untuk mencari voltan nod yang tidak diketahui. Senaraikan
langkah-langkah untuk analisis nod.]
(4 Marks/ Markah)
(ii) Calculate current, i1 using node analysis method based on the circuit in
Figure 3(a). [Kirakan arus, i1 menggunakan analisis nod berdasarkan litar dalam Rajah 3(a).]
(7 Marks/ Markah)
10 A 10 Ω
10 Ω
10 Ω8 V
12 A10 Ω
V1 V2
i1
Figure 3(a) [Rajah 3(a)]
.…7/-
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(b) Refering to Figure 3(b), calculate current, Ix using mesh analysis. [Merujuk kepada Rajah 3(b), kirakan arus, Ix menggunakan analisis jejaring.]
(9 Marks/ Markah)
20 A 40 Ω
10 Ω
20 V
4Ix
Ix
Figure 3(b) [Rajah 3(b)]
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Question 4 [Soalan 4]
(a) (i) Based on the basic structure of a capacitor in Figure 4(a), explain how a
capacitor storing charges. [Berdasarkan struktur asas sebuah pemuat dalam Rajah 4(a) terangkan bagaimana
pemuat menyimpan cas.]
(4 Marks/ Markah)
R
A
B
Figure 4(a) [Rajah 4(a)]
(ii) Obtain the energy stored in each capacitor under dc conditions as in
Figure 4(b). [Dapatkan tenaga yang tersimpan dalam setiap pemuat di bawah keadaan dc seperti
dalam Rajah 4(b).]
(8 Marks/ Markah)
4 mF
4 kΩ
6 kΩ
10 kΩ
8 mF
8 kΩ12 mA
Figure 4(b) [Rajah 4(b)]
.…9/-
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(b) Based on Figure 4(c), calculate the equivalent inductance. [Berdasarkan Rajah 4(c), kirakan kearuhan setara.]
(4 Marks/ Markah)
L1
20 mH
L5
6 mH
L4
12 mH
L2
4 mH
L3
8 mH
Figure 4(c) [Rajah 4(c)]
(c) Given the arrangement of capacitors in Figure 4(d), calculate the equivalent
capacitance. [Diberi susunan pemuat-pemuat dalam Rajah 4(d), kirakan kemuatan setara.]
(4 Marks/ Markah)
C1
12 µF
C2
1.2 µF
C3
1.8 µF
C6
2.2 µF
C4
3 µF
C5
4.5 µF
Figure 4(d) [Rajah 4(d)]
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Question 5 [Soalan 5]
(a) State the definition of Thevenin’s equivalent circuit. [Nyatakan definisi litar setara Thevenin.]
(2 Marks/ Markah)
(b) Based on Figure 5, calculate; [Berdasarkan Rajah 5, kirakan;]
(i) Thevenin’s voltage, VTH. [voltan Thevenin, VTH.]
(6 Marks/ Markah)
(ii) Thevenin’s equivalent resistance, RTH. [rintangan setara Thevenin, RTH.]
(4 Marks/ Markah)
(iii) value of RL when maximum power is transferred. [nilai RL apabila kuasa maksimum dipindahkan.]
(2 Marks/ Markah)
(iv) the maximum power transfer, Pmax. [pemindahan kuasa maksimum, Pmax.]
(2 Marks/ Markah)
(v) sketch the equivalents Thevenin’s and Norton’s network. [lakarkan rangkaian setara Thevenin dan Norton.]
(4 Marks/ Markah)
1 A 6 Ω
14 Ω
3 A 5 Ω RL
a
b
14 V
Figure 5 [Rajah 5]
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Question 6 [Soalan 6]
(a) A source free RL circuit is shown in Figure 6(a). The switch has been closed for
a long time and is opened at t = 0. Calculate; [Suatu litar bebas sumber RL ditunjukkan dalam Rajah 6(a). Suis telah ditutup untuk masa yang
lama dan dibuka pada t = 0. Kirakan;]
(i) the initial value of current, iL(0). [nilai arus awalan, iL(0).]
(2 Marks/ Markah)
(ii) the time constant, τ of the circuit for t > 0. [pemalar masa, τ bagi litar untuk t > 0.]
(3 Marks/ Markah)
(iii) numerical expression for iL(t) for t ≥ 0. [persamaan berangka bagi iL(t) untuk t ≥ 0.]
(1 Mark/ Markah)
(iv) current io(t) for t ≥ 0 using current divider rule. [arus io(t) untuk t ≥ 0 menggunakan aturan pembahagi arus.]
(2 Marks/ Markah)
(v) voltage Vo(t) for t ≥ 0. [voltage Vo(t) untuk t ≥ 0.]
(2 Marks/ Markah)
20 A 0.1 Ω 2 H
20 Ω
10 Ω 40 Ω
t = 0
iLio
Vo
Figure 6(a) [Rajah 6(a)]
.…12/-
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(b) The switch in Figure 6(b) has been in position a for a long time. At time t = 0, the
switch is moved to position b. Calculate; [Suis dalam Rajah 6(b) berada pada kedudukan a untuk jangkamasa yang lama. Pada masa t = 0,
suis telah dipindahkan ke kedudukan b. Kirakan;]
(i) the initial value of vc(0). [nilai awal untuk vc(0).]
(3 Marks/Markah)
(ii) the time constant, when t > 0. [pemalar masa, apabila t > 0.]
(2 Marks/Markah)
(iii) the value of vc(t) at t = 2s and t = 6s. [nilai vc(t) pada t = 2s dan t = 6s.]
(3 Marks/Markah)
(iv) the initial energy stored in the capacitor. [nilai awal tenaga yang tersimpan di dalam pemuat.]
(2 Marks/Markah)
3 kΩ
5 kΩ 0.5 mF
4 kΩ
24V 30V
a b
VC
Figure 6(b) [Rajah 6(b)]
-ooOoo-
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Appendix [Lampiran ]
𝑞 = 𝐶𝑉
𝐶 = 𝑒𝐴
𝑑
𝑖(𝑡) = 𝐶𝑑𝑣
𝑑𝑡
𝑣(𝑡) = 𝐿𝑑𝑖(𝑡)
𝑑𝑡
𝑣 =1
𝐶∫ 𝑖 𝑑𝑡 + 𝑣(𝑡0)
𝑡
𝑡0
𝑖(𝑡) = 1
𝐿∫ 𝑣(𝑡)𝑑𝑡 + 𝑖(𝑡0)
𝑡
𝑡0
𝑊 = 1
2𝐶𝑉2
𝑊 = 1
2𝐿𝑖2
𝜏 = 𝐿
𝑅
𝜏 = 𝑅𝐶
𝑖(𝑡) = 𝐼𝑜𝑒−𝑡/𝜏
𝑖(𝑡) =𝑉0
𝑅𝑒−𝑡/𝜏
𝑣𝑅(𝑡) = 𝐼𝑜𝑅𝑒−𝑡/𝜏
𝑣(𝑡) = 𝑉0𝑒−𝑡/𝜏
𝑝(𝑡) = 𝐼𝑜2𝑅𝑒−2𝑡/𝜏
𝑝(𝑡) =𝑉𝑜
2
𝑅𝑒−2𝑡/𝜏
𝑖𝐿(𝑡) = 𝑖(∞) + [𝑖(0) − 𝑖(∞)]𝑒−𝑡/𝜏
𝑣(𝑡) = 𝑣(∞) + [𝑣(0) − 𝑣(∞)]𝑒−𝑡/𝜏