Department of Engineering Science and Physics
ENS 136
Assignment 3: Alternating voltage and current, frequency, time
period, two-phase voltage supply, and the behavior of
capacitors and inductors under AC signals.
Electric power is supplied as a 60-Hz AC voltage, which is a sinusoidal signal
(sine or cosine waveform). Fig. 1 shows AC voltage waveform for 110 volts line
voltage. Since AC voltage is constantly changing with time, it is normally
expressed with its effective value (technically, root-mean-square or RMS value).
RMS value is obtained by dividing maximum voltage of the sinusoidal waveform
by square root of 2.
Figure 1.
Fall 2010
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Syed A. Rizvi
Department of Engineering Science and Physics
ENS 136
Time period, T measured in seconds, of a periodic signal is the time needed to
complete on cycle of the signal. In the case of the sine waveform shown in Fig. 1
the time period is the time needed to go from 0 to positive maximum to 0 to
negative maximum and to 0 again. This set of transitions forms one period of the
sine wave. The frequency of the signal is the number of periods in one second.
Mathematically,
Frequency, f = 1/T
The frequency is expressed in terms of cycles per second or Hertz. Sometimes
frequency of the signal is also expressed in terms radians per second. This form
of frequency is called angular frequency and is represented by the symbol .
Frequency f and the angular frequency  are related by expression
f = 2
Build the circuit shown in Fig. 2.
Figure 2.
Note V1 is a signal source (not the power source). Furthermore, XSC is an
oscilloscope, which is a measuring device that can display the waveform of a
signal. Change the setting of the multi-meter (XMM) to AC for measuring AC
voltage. In this mode it will measure the RMS value of the AC signal.
From the oscilloscope display measure the time period T
T = _____________
Fall 2010
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Syed A. Rizvi
Department of Engineering Science and Physics
ENS 136
Now calculate the frequency f = 1/T = ______________
Is it the same as frequency of the AC source voltage?
Now measure the peak voltage from the oscilloscope display (any positive peak)
Vpeak = _____________
Calculate the RMS voltage as Vrms = Vpeak / srt(2)
Is the calculated Vrms the same as the one measure by the multimeter?
Now build the circuit shown in Fig. 3. This circuit represents two-phase 110 volts
power supply. Note that in the circuit shown in Fig. 3 V1 and V2 are power
sources (not the signal sources). Also, V2 has a phase difference of 180 o with
respect to V1.
Fall 2010
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Syed A. Rizvi
Department of Engineering Science and Physics
ENS 136
Figure 3.
Now measure the voltage between the +tive terminal of V1 and the ground (call it
V1), the voltage between the +tive terminal of V2 and the ground (call it V2), and
the voltage between the +tive terminal of V1 and the +tive terminal of V2 (call it
V12). Record your measurement below:
V1 = ___________
V2 = ___________
V12 = ___________
Now from the oscilloscope measure the peak voltages for sources V1 and V2 (call
them V1peak and V2peak, respectively) as well as the maximum difference between
V1 and V2 (call it V12peak).
V1peak = ____________
V2peak = ____________
V12peak = ____________
Now compute RMS voltages as follows:
V1rms = V1peak / srt(2) = ____________
V2rms = V2peak / srt(2) = ____________
V12rms = V12peak / srt(2) = ____________
Are these values the same as the measured values?
Now change the phase of the AC source V2 to “0.” How does it impact the values
of V1, V2, and V12? Please explain.
Fall 2010
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Syed A. Rizvi
Department of Engineering Science and Physics
ENS 136
Build the circuit in Fig. 4 (XFG is a function generator). Select sinusoidal signal
from the signal generator with 10 volts peak-to-peak amplitude. Measure the
peak-to-peak output voltage (across the capacitor) and the current for each of the
input frequencies shown in table 1.
Figure 4.
Plot the data in Table 1 in terms of frequency vs VCPP as well as IC. Explain the
behavior of the capacitor with the change in frequency.
Fall 2010
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Syed A. Rizvi
Department of Engineering Science and Physics
ENS 136
Table 1
Frequency
VCPP
IC
0.001 Hz
20 Hz
50 Hz
100 Hz
200 Hz
300 Hz
400 Hz
500 Hz
600 Hz
700 Hz
800 Hz
900 Hz
1 KHz
2 KHz
4 KHz
6 KHz
8 KHz
10 KHz
15 KHz
20 KHz
Fall 2010
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Syed A. Rizvi
Department of Engineering Science and Physics
ENS 136
Build the circuit in Fig. 5. Select sinusoidal signal from the signal generator with
10 volts peak-to-peak amplitude. Measure the peak-to-peak output voltage
(across the inductor) and the current for each of the input frequencies shown in
table 2.
Figure 5.
Plot the data in Table 2 in terms of frequency vs VLPP as well as IL. Explain the
behavior of the inductor with the change in frequency.
Fall 2010
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Syed A. Rizvi
Department of Engineering Science and Physics
ENS 136
Table 2
Frequency
VLPP
IL
0.001 Hz
20 Hz
50 Hz
100 Hz
200 Hz
300 Hz
400 Hz
500 Hz
600 Hz
700 Hz
800 Hz
900 Hz
1 KHz
2 KHz
4 KHz
6 KHz
8 KHz
10 KHz
15 KHz
20 KHz
Fall 2010
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Syed A. Rizvi