4.8 Self-assessment test 103Z,Z2/(Z, + Z2)= [(12.81 • 11.4)/24.2]/_(51.34 + 52.13 - 51.7)
= 6.03/_51.77 ~ lI
= 6.03(cos 51.77 + j sin 51.77) = (3.73 + j4.73) tq
The impedance of the capacitive branch is
z~ - (5 -j2) n
The impedance of the complete circuit,
Zeq- 23 -+- 2122/(21 -Jr 22) -- (5 q- 3.73) q-j(-2 -t- 4.73)11
SO
Zeq = (8.73 + j2.73) = x/(8.732 + 2.732)/_tan-l(2.73/8.73) = 9.15/17.36~2 The current drawn from the supply is
V//Zeq- (100,/9.15)/_0- 17.36- 10.92/_-17.36~ A
The total power consumed is
P = VI cos ~b = 100 • 10.92 cos 17.36 = 1042 W
3 The reactive power in the capacitive reactance is
Q = I2Xc = 10.922 • 2 = 238 Var
4 The equivalent reactance of the whole circuit is positive, indicating an
effective inductive reactance so that the overall power factor is lagging and
its value is given by cos ~b = cos 17.36 = 0.9544.4.8 SELF-ASSESSMENT TEST
1 Define an alternating quantity.
2 Give the unit of frequency.
3 Write down the relationship between frequency (f) and periodic time (T).
4 What is the peak value of the alternating quantity represented by
25 sin ox?
5 What is the frequency of the alternating quantity represented by
50 cos 314 t?
6 If v = V sin 2Eft and i = I cos 27rft state the phase difference between v
and i.
7 What is the rms value of a sinusoidal voltage whose maximum value is
141 V?