Characteristic Characteristic of Sinusoidal Voltage or Current
I. Objective 1. To determine determine and understa understand nd the waveform waveform of alternati alternating ng voltage voltage or current. 2. To have have an idea idea about about frequenc frequency, y, cycle, cycle, and and period. period. 3. To examine the characteristics characteristics of a sinusoidal sinusoidal voltage, its maximum or peak value, the average and the root mean square or effective value. 4. To verify verify the validity validity of mathema mathematica ticall formulas formulas presented presented by comparing the theoretical value and experimental value obtain through oscilloscope.
II. II. Theo Theory ry Alternating current and voltages continually changes its magnitude and direction in a magnitude and direction in manner, which depends upon the type of power supply. Thus, we could obtain square wave, triangular wave and in fact, any other shape for the voltage that we please. Theory shows and practice has proven however, that there is one type of waveform which is suited for running running electric machinery. machinery. This is known as a sine wave. It has been found that this kind of wave permits us to obtain the highest efficiency from transformers, transformers, motors and generators and also results in quietest operation. Another interesting property property is that a sine wave of voltage will always produce a sine wave of current. This would not be the case if a triangular or a square wave were used. Since sinusoidal voltage or current oscillates and the value of which recur at equal intervals of time then it is considered periodic. In this respect, each complete succession succession of values in a period of T (time) is called a cycle. While the number of cycles completed in one second is known as frequency (f) expressed in hertz (hz). Most commercial power line frequencies are now standardized at 60 hz. (60 cycles/second).
Graph dito
Effective or RMS (root-mean-square) value
III.
Instruments and Components 1 variac or multi-tapped step-down transformer 1 oscilloscope 1 AC voltmeter (0-250V) 1 DC voltmeter (0-30V) Connecting wires
IV. Procedures A. Effective Value of Voltage 1. Using your variac or multi-tapped step-down transformer, AC voltmeter and oscilloscope connects the circuits shown in figure 1.1
Fig. 1.1
2. Turn-on the power supply and set the variac transformer to four different voltages level not exceeding 60 volts for trials 1, 2, 3, and 4 respectively. The oscilloscope should display a sinusoidal waveform. 3. Measure the voltage output of the variac transformer with the use of an AC voltmeter and record this value as E on table 1-1. The voltmeter reading indicates the effective or rms value in volts.
4. Measure the peak and peak-to-peak values of the sine wave displayed in the oscilloscope and record the values as E p-p on table 1-1. Note: Ep-p = 2Em. 5. Calculate the effective value of voltage E’ and the percentage difference between E and E’. E’ = 0.707E m. Table 1-1 No. of trials
E (volts) 5V 15.3 V 25.3 V 35 V
1 2 3 4
Em (volts) 7.6 V 22.8 V 36.4 V 51.2 V
Ep-p (volts) 15.6 V 46.0 V 73.6 V 103.2 V
E1 5.37 15.8 25.7 35.6
V V V V
% difference 7.4% 3.27% 1.58% 1.7%
6. Measure the time or period in seconds covered by one-complete cycle as shown on the horizontal axis of the oscilloscope. Record the data on table 1-2, calculate the frequency and the percentage difference Table 1-2 No. of trials 1 2 3 4
T (secs) 16.64 16.72 16.64 16.64
ms ms ms ms
f 1 = (hz)
f (hz)
60.10 hz 59.8 hz 60.10 hz 60.10 hz
60 60 60 60
% difference
hz hz hz hz
0.17% 0.33% 0.17% 0.17%
7. Return the voltage to zero and turn off the power supply. B. Average Value Measurement 1. Using your variac / transformer and AC voltmeter connect the circuit shown in fig. 1-2.
Fig. 1-2 2. Turn on the power supply and set the variac to four different voltage level not exceeding 20 volts for trials 1, 2, 3 and 4 respectively. 3. Replace AC voltmeter by a DC voltmeter (0-30V)
4. Observe and record the voltmeter reading for each trial on table 13. No. of trials 1 2 3 4
Eac 4 8 12 16
Edc 0.6 V ≈ 0 V 0.3 V≈ 0 V 0.5 V≈ 0 V 0.3 V≈ 0 V
5. Return the voltage to zero and turn off the power supply.
V.Questions and Problems 1. How long does it take the voltage to go from zero to maximum on a 60 hz power line?
T= 16.67 mSec.
2. An incandescent lamp rate at 100 watts gives a certain amount of light when placed across the 120 V ac power line. Would the amount of light increase, decrease or remain the same when the lamp is placed across a 120 V dc power line? Explain your answer.
The light will decrease when the lamp is placed across a 120 V dc power line because the dc power line would have lesser amount of current than the ac or in other words we could get the same light output if we double the needed wattage of the bulb.
3. What is the effective value of an AC sine wave current having a peakto-peak value of 8 amperes?
Irms = 0.707 Vrms 2.828 Amps.
4. Explain what is meant by the terms effective voltage and effective current?
This are the values that would have equal effects as the DC could do.
5. In a sinusoidal voltage / current
a. At what angle or angles are the voltage / current increasing at its fastest rate? b. At what angle or angles are the voltage / current momentarily constant?
6. Prove that for a sinusoidal wave of one cycle, the average value is zero.
For the positive half cycle, we have its average value equal to Vave =0.636 Vm And, for the negative half cycle we will have, Vave = -0.636 Vm
Adding this two half cycles to produce a single cycle will give us a zero average value.
VI. Discussion: We are instructed to perform experiment 1 - Characteristic of Sinusoidal Voltage or Current. We firstly constructed the indicated set up for then experiment. We then garnered all the unknown values using the oscilloscope and a multi tester. The oscilloscope did almost the providing of important details. We computed for the percentage difference of the voltage output measured against the computed value and throughout we got values lesser than 10 % which gave us an idea that the values we have is reliable. Subsequently, we do the same thing for the frequency and as what we got on the first set up; we also got values lower than 10%. In a student’s point of view, this experiment took a while considering that there is enough materials and apparatus that will be used by the student. The application of these experiment is highly recommended for us to understand the real of sinusoidal waves.
VII. Conclusion: After we performed the experiment determine the waveform of alternating voltage or current. We also understand what it will look like using an oscilloscope.
We also compare our computed frequency, cycle, and period against the measured one. Using an oscilloscope we examined the characteristics of a sinusoidal voltage, its maximum or peak value, the average and the root mean square or effective value. Subsequently, we proved those mathematical formulas concerned in a sinusoidal wave by comparing the theoretical value and experimental value obtain through oscilloscope. We can now say that in understanding Sinusoidal voltage or current the use of the theories and the mathematical formulas are indeed very helpful.
