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(ELEC102)test2_pastj.pdf
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(7)

(a)
(a) Explain very briefly why voltage in a capacitor and current in an inductor is continuous with time. (7)
1 Energy must be continuous with time.
Hence EC and EL must be continuous with time (unchanged after switching)
+
VC
iC EC = 2 CV (t)2 C
-
iL + VL EL = 2 Li (t)2 L (7)
-

Hence VC and iL must be continuous with time.

2 Another short proof
dV (t) di (t)
iC = CC VL = LL
dt dt
If dt is 0, infinite iC or VL is required, which is not possible. Hence dVC/dt and diL/dt must be finite, or VC and iL must be continuous with time .
(19)

(b) The switch has been closed for a long time. At t = 0 second, the switch is 4A

4.

4Vopened. (i) If X = 1mH, find i(0) , i(), time constant ( = L/R) , i(t) and
v(t) for t t 0 . Given that i(t) = i() +[i(0) -i()] exp(-t/) .

v(t) = v() +[v(0) -v()] exp(-t/) . (19)
(b)
t = 0

2A
4V
t < 0 2A 4V
4V
4. 2A
t 0 2A 4V 1mH 2V
4. 2A



2A
4V
i(0) = 2 A (5) i( ) = 4A (4) L 1mH
== = 1ms (3)
R1.
t
i ( t ) = i ( ) + [ i (0) . i ( )] * e .
. t /1ms
= 4 A + [2 A . 4 A ]* e
(3)
. t /1ms
= 4 A . 2 Ae
. t /1ms

v (t ) = i(t ) *1.= 4 V . 2 Ve (4)
(15)

If I(t) = 2sin(100*t + 5o ) A , find V(t). Does I(t) lead V((t) (15)
V(t) =10V sin(t +)



V(t) oo
=10V sin(100t + 5 . 36 ) (5) =10V sin(100t . 31o )
I(t) leads V(t) (2)
2 2

T == = 20ms (4)
100



t 2ms
o oo
= * 360 = * 360 = 36 (4)


T 20ms
(10)

(28)

o .6

(a) If i(t) = 8sin(2kt + 30 )mA, Z = 2x10 F, find Z in . and find Vo(t).
v(t)

i(t)


Vo(t)

11

(a) Z == =.j250.
(3)

jCj*2krad / s *2F
Vo(t) = 8mA *250.sin(2kt + 30o . 90o ) (7) = 2V sin(2kt . 60o )


(18)

(b) If i(t) = 2cos(2kt -30o)A , v(t) =
10cos(2kt + 30o)V , and Z is R in parallel
with X. Find Y ( = 1/Z ) in . -1 . Find also

v = 10 30 V 10V

the element and value of X. Draw also the

(4)
30phasor diagram of v(t) and v(t).
-30
2A i = 2 -30 A

(b) o
I 2. 30 Ao .1
Y == = 0.2. 60 .
V 10+ 30oV

= 0.2cos(.60o ) + 0.2jsin(.60o )
= 0.1S . j0.1732S
11
=+ (10)
R jX X 1
X =L . L == . 2.89mH (4)
0.1732*2k

(10)

If X = 2j., find i using superposition.
Find also the Thevenin impedance at terminals ab and hence
find the Thevenin voltage at ab . (24)

i

. 2j.
a

b

20oA
2.

20oV

(a) i1 ba . 2j.


2V


2.

2V 1A

i1 == (5)
2.+ 2j. 1+ j

i2 b 2j. a . 2j.


2A

2. 2A

i2 = 2A * =
(5)
2.+ 2j. 1+ j

(14)

i = i1+ i2 = 3A (2)
1+ j

(b) ba
. 2j.

2.

Zth = 2. (4)



Zth = 2.

3A
Vth
2j.

1+ j
a
3A

Vth = *(2 + 2j).= 6V (8)
1+ j
33
= (1. j)1+ j 2
2A



2 . 4j 2V 2j. 1+ j . 2j.
2V

2A
0V


(19)

A load D with 1100VAR (C) is connected in parallel to load B. Find the power factor of the combined load. Find also t