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Revision tutorial p.1

1. In the following circuit, v(t) = 250 cos (100t + 20o) V, i(t) = 10 cos (100t + 40o) A.
(a)
Sketch v(t) and i(t) together. Show clearly the phase angles and amplitudes. Does v(t) lead i(t) ?

(b)
If Z is two elements in series, find the two elements and the values.


i(t)
(c) Sketch impedance Z and phasors V, I in a complex plane. (23)


Z
v(t)
(a) Sketch v(t) and i(t) together. i(t) = 10 cos (100t + 40o) A.
Show clearly the phase angles and amplitudes.
10A
v(t) = 250 cos (100t + 20o) V
amplitude 250V


-40o

i(t) leads v(t) by 20o As i(t) peak (10A) is at left side of v(t) peak (250V)
phase angle
-250V
-20o
( if at right side, then i lags v )
p.2

Using Euler equation

(b) If Z is two elements in series,
find the two elements and the values.

oo
Find Z first, use complex method \Z = 25 [cos(-20 ) + jsin(-20 )] ohm = 23.5-j8.55 ohm
Transform v(t) into V phasor
Hence Z is C in series with R
v(t) = 250 cos (100t + 20o) V 1j
\Z = R += R -
jC(2*pi*f) (2*pi*f)C

V = 250 20o V 1
=-j jj =-1
j
Frequency NOT included in phasor since
Equate real and j part
All current and voltage will have SAME frequency
\R = 23.5 ohm
o
V 25020 V
\Z == 1
1040 A \8.55 =
Io
(2*pi*f)C
250V oo
=(20 -40 )
1
10A \C == 1.17mF
o 100(8.55)
= 25 -20 ohm
Hence Z is 1.17mF in series with 23.5 ohm

p.3

o
( similarly if Z = 25 20 ohm XL : reactance of L
XC : reactance of C
then Z is 23.5 ohm in series with 8.55 ohm L )
by complex method Transform L into j w L Transform C into 1 / j w C
For example
If L = 10mH

C = 1mF


Then XL = j w L = j (100) 10mH = j ohm
Then XC = 1 / j w C = 1 / j (100) 1mF = -j10 ohm
Sketch impedance Z and phasors V, I in a complex plane
or phasor diagram


I = 1040oA

40o V = 25020o V 20o 20o

Z = 25-20o W

p4

2. An industrial load A is connected in parallel to a 200 Vrms, 50Hz power supply. Load A is composed of 6W in series with j8 W. (a) Find the complex current flowing in load A IA. Find also the average power P, reactive power Q, apparent power S, and power factor PF supplied by the power supply. (b) If a load B is connected in parallel to load A to make the total power factor = 1, find the element and value of load B. (c) When PF = 1, find the current delivered by the 200V supply (IS , in rms) and the current in load B (IB , in rms). (d)
Hence plot IS, IB , and IA in a phasor diagram. [40]


I
IB

C
6W
IA2000o Vrms 50Hz


j8W
Load B Load A

Find the complex current flowing in load A IA
For load A

V


\IA =
Z
2000o Vrms

=
6 + j8 ohm 2000o Vrms
=

22 -1
6 + 8 tan 8
6 2000o Vrms
=
1053.1oohm
= 20-53.1o Arms


p.5

Find also the average power P, reactive power Q,
apparent power S, and power factor PF

of load A supplied by the power supply.

Load A is R in series with L, same I, use P = I2R , I in rms
I