1

ELEC 2134
Midsession test, S1 2016
Total Marks: 30
Time: 1 hour
Q1Consider the voltage and current of an AC circuit given by v( t ) 340 cos(100 t 45 )  
and i( t ) 2 sin(100 t 55 )   .
Determine-
(i) (4 marks) the time by which i(t) is advanced or delayed with respect to v(t).
(ii) (1 mark) the power factor

Q2 (a) (6 marks) Using nodal analysis, compute the voltage Vo (phasor) in the circuit of
Figure 1.

Figure 1
(b) (2 marks) Figure 2 shows a wye (Y) network. Using wye-delta transform find the
impedances of an equivalent delta network.
Useful formulas: b c a b b c c a
Y Y
a b c a
Z Z Z Z Z Z Z Z
Z , Z
Z Z Z Z
 
 
 
 


Figure 2
2

(c) (2 marks) At  = 100 rad/s, the equivalent admittance Y for the circuit in Figure 3 is
(0.1+j0.2) Siemens. Find the values of R and C.

Figure 3



Q3 (a) (3 marks) What load impedance should be connected to terminal AB to achieve
maximum power transfer in the circuit of Figure 4?

Figure 4

(b) (2 marks) If P is the average power, Q is reactive power and θ is the phase difference
between voltage and current in an AC circuit, show that Q Ptan .

3

Q4 (a) (3 marks) Find the trigonometric Fourier series of the function f(t) shown in Figure 5,
up to the first harmonic only (i.e. up to n = 1), and sketch the amplitude spectrum up to the
first harmonic.
f(t)
t1 2 3
1
-1
-1-2-3 4-4

Figure 5
(b) (2 marks) The signal in part (a) is input to the circuit shown in Figure 6, i.e. )()( tftvi  ,
and it is desired to know the amplitude of the output waveform )(tvo at harmonic
frequencies, i.e.  = n, where n ≥ 0 is an integer. Explain why it is reasonable to use
phasor analysis to do this.

Figure 6
(c) (5 marks) Using the Fourier transform convolution property )()()(  XHY  , where
)(X and )(Y are the Fourier transforms of the input and output of a linear circuit
respectively, show that for the circuit in Figure 7, the output voltage )()( tuetv tout
 if
)()( ttvin  , where u(t) is the unit step function. Hint: Analyse the circuit in the frequency
domain to derive
)(
)(
)(



in
out
V
V
H  .
1W
1H
vin(t)
+
-
vout(t)
+
-

Figure 7