PE304 – Tutorial #2 – Basic Electrical Theory - Curtin University

PE304 – Tutorial #2 Soln
James Darbyshire & Professor Chem Nayar
Faculty of Engineering and Computing
Department of Electrical and Computer Engineering
Curtin University of Technology
PE304 – Tutorial #2 – Basic Electrical Theory
Question 1: Using rms values to represent their magnitudes, the voltage across and the current
into a load are as follows in phasor form.
V = V
I = I
Show that the instantaneous power p(t) = v(t).i(t) can be written as;
p(t) = P + P cos(2t) + Q sin(2t)
where average power P = VI cos and reactive power Q = VI sin
Answer:
Question 2: The real or average power is expressed as:
P = Re[S] = VI cos
This is the product of the voltage and the current that is in phase with the voltage. The current
can be expressed in terms of a in phase component i p(t) and out of phase component i q(t).
i p (t) = 2I p cos(t) = ( 2I cos)cos(t)
i q (t) = 2I q sin(t) = ( 2I sin)sin(t)
If the voltage across a load is V = 120V and the current is I = 1A lagging at 30˚. Plot the
following as a function of t;
a) v, i and p(t)

Tutorial #2 Solution 2 of 2
b) i p(t) as defined above and p 1(t) = v.i p
c) i q(t) as defined above and p 2(t) = v.i q
d) Calculate the average power P
e) Calculate the peak power of p 2 and Q.
f) Calculate the load power factor (PF). Is this load inductive or capacitive? Does the
load draw positive vars?
Answer:
a)
b)
c)
d/e/f)
James Darbyshire & Professor Chem Nayar

Tutorial #2 Solution 3 of 3
Question 3: A sinusoidal voltage v = 2V sin t is applied to a single phase load. The current
drawn by the load corresponds to figure 1. The zero crossing of the current waveform lags the
voltage waveform by 30˚. Calculate the average power drawn by the load. The displacement
power factor (DPF), the total harmonic distortion, and the power factor.
Where V = 120V, A = 10A.
Figure 1
Answer:
The expansion of the Fourier series for the above waveform is given by:
The ratio of the fundamental component to the rms is given by:
James Darbyshire & Professor Chem Nayar

Tutorial #2 Solution 4 of 4
Question 4: A three phase inductive load is supplied in steady state by a balanced three phase
voltage source with a phase voltage of 120Vrms. The load draws a total of 10kW at a power
factor of 0.85 (lagging). Calculate the rms values of the phase currents and the magnitude of the
per-phase load impedance. Draw a phasor diagram showing all three voltages and currents.
Answer:
James Darbyshire & Professor Chem Nayar