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Applied Electricity PHY 222 2.0
Tutorial Number 01
1. Express in rectangular and polar notations the phasors for the following
quantities.
a.) i = 10 sin ωt
b.) i = 5 sin (ωt +π/3)
c.) v = 40 sin (ωt +π/6)
d.) v = 60 sin (ωt +π/4)
Draw the phasor diagram representing the above voltage currents.
2. Express each of the following phasors in polar notations.
a.) 10 + j5
b.) 3 – j8
c.) 4+ j3
d.) 20 – j10
3. A voltage , v = 150 sin(314t + 30) volts, is maintained across a coil having a
resistance of 20Ω and an inductance of 0.1 H. derive expression for the r.m.s
values of the voltage and current phasors in
a.) Rectangular notation, b.) Polar notation. Draw the phasor diagram.
4. Define the r.m.s value, peak value and average value of an alternating current.
Explain why r.m.s value is more generally employed in a.c measurements than
either average or the peak value.
5. A coil of 200 turns is rotated at 3000r/min in a magnetic field having a uniform
density of 0.1T, the axis of rotation at right angles to the direction of the flux. The
mean area per turn is 40cm2. Calculate
 The frequency,
 the period,
 the maximum value of the generated e.m.f..
 The value of the generated e.m.f. when the coil has rotated through 30.
from the position of zero e.m.f.
6. A single phase motor take 8.3 A at a power factor of 0.866 lagging when
connected to 230V, 50Hz supply. Two similar capacitors are connected in
parallel with each other to form a capacitance bank. This capacitance bank is
now connected in parallel with the motor to raise the power factor to 0.95.
Determine the capacitance of each capacitor.
7. Show by a phasor diagram that the sum of three phase balanced current is zero
and hence no current with flow in the neutral connection of balanced star
connected system.
8. A balanced star-connected load of (8 + j6)Ω per phase is connected to a threephase, 230V supply. Find the line current, Power factor, active, reactive and total
power.
9. A balanced three-phase delta connected load of 160kW takes a line current of
100A with a line voltage of 11,000V 50Hz. Find the circuit constant of the load
for phase.
10. A load of 20kW (balanced) with 0.7 pf lagging is fed from a 400V, three phase
supply as shown in figure below. Three equal capacitors are connected in delta
across the load to improve the overall pf to 0.85 lagging. Find the resultant
current drawn from the supply and the capacitance of each capacitor.
A
C
B
C
C
20kW
0.7 pf
Lagging
C
11. A delta connected unbalanced loads is arranged as shown in figure below and is
connected to balanced supply voltage of 415V. The phase sequence is RYB.
Calculate the phase and line currents.
R
Y
B
12. A three phase load draws a current of 10A at a lagging pf of 0.65 from a 600V,
50Hz source. The line current reduces to 7.2A when a capacitor bank is
connected across in ; a) Star-connected , and b) delta connected. Find the kVAR
rating of the bank in each case.
13. Briefly describe the electrical power generation and distribution using a block
diagram.
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