Expt 6

LAB REPORT

FAMILIARIZATION WITH ALTERNATING CURRENT (AC) WAVES Course- EECE- 164 Expt No- 6 OBJECTIVE. To study ac (sinusoidal) wave forms and correlate them with practically measurable effective values as well as developing an understanding on a simple ac circuit in the process of performing the experiment.

THEORY. Any periodic variation of current or voltage where the current (or voltage), when measured along any particular direction, goes positive as well as negative, is defined to be an AC quantity. Sinusoidal AC wave shapes are the ones where the variation (current or voltage) is a sine function of time. Vm

T Fig 1. An ac (sinusoidal) voltage waveform For the wave form in Fig.1, Time period = T Frequency, f = 1/ T v = V sin 2πft = V sin( 2π / T )t Effective value: Effective (rms) values of sinusoidal waveforms are given as: V=

T V 1 2 v dt = m ∫ T0 2

(For sinusoidal wave)

T

I 1 2 I= i dt = m ∫ T0 2

(For sinusoidal wave)

These values are directly measured in ac voltmeter / ammeters and can be used in power calculation as: P = I 2R = V 2 / R

1

Phase difference: v/i t θ T Fig 2. Two sinusoidal waves with phase difference Phase difference between two ac sinusoidal waveforms is the difference in electrical angle between two identical points of the two waves. In fig. 2, the voltage and current equations are given as: v = Vm Sin(2π / T )t i = I m Sin(2π / Tt − θ ) Impedance: Relation between the voltage across and the current through any component of an ac circuit is given by impedance. For the voltage and current waveforms in Fig. 2, the corresponding impedance Z is given as: Z = Vm / I m ∠θ = Vrms / I rms ∠θ

APPARATUS. Oscilloscope Function generation Decade resistor Capacitor bank AC voltmeter AC ammeter SPST Breadboard

PROCEDURE. + +

10 VP-P 1 KHz

Osc Ch#1

_

1μF

Capacitor 10 VP-P 1 KHz

Osc Ch#1

_

Fig – 1

Fig – 2 2

Osc Ch#2

1. I connected the output of the function generator directly to channel 1 of the oscilloscope as shown in fig 1. I set the amplitude of the wave at 10V and the frequency at 1 kHz and selected sinusoidal wave shape. 2. I sketched the waveshape observed on the oscilloscope as shown bellow and determine the time period of the wave and calculate the frequency.

Function Generator Frequency = 1 KHz

T = 5 x time/div = 5 x 0.2 ms = 1 ms f = 1/T = 1/1ms = 1 KHz T 3. I changed the frequency to 500 Hz and observed the display of the wave. I sketched the wave shape observed on the oscilloscope as shown bellow and determine the time period of the wave and calculate the frequency. Function Generator Frequency = 500 Hz

T = 4 x time/div = 4 x 0.5 ms = 2 ms f = 1/T = 1/2ms = 500 Hz T 4. Again, I changed the frequency to 2 KHz and observed the display of the wave. I sketched the wave shape observed on the oscilloscope as shown bellow and determine the time period of the wave and calculate the frequency.

Function Generator Frequency = 2 KHz

T = 5 x time/div = 5 x 0.1 ms = 0.5 ms f = 1/T = 1/0.5ms = 2 KHz T

3

5. Now, I measure the input voltage with an ac voltmeter and the input current with an ac ammeter and found the following readings: Input voltage = 3.17 volt ac Input current = 21.7 mA The ratio between the voltage and the current gives the magnitude of the impedance, Z. 6. Now, I constructed the circuit as shown in Fig. 2 and observed the wave shapes of oscilloscope channels 1 and 2 simultaneously. I found the frequency of both the waves and amplitude from the display and determined the phase difference between the two waves. The phase difference is given by, 360 X ∆T T , where ‘ ∆T ’ is the time delay between the two waves. I also observed which of the two waves lead and noted that the voltage in channel 2 is the voltage across a resistance and hence this is in phase with the current flowing in the circuit.

Phase Difference = = = 32.40 T

Report: 1. I compared both the frequency of the wave determined from the oscilloscope. I found out the value of the frequency at both the channels. 1 1 = = 2 KHz T 5Χ0.1ms 1 1 = = 2 KHz Frequency at Channel#2 : T 5Χ0.1ms The value of the frequency of this wave is equal to the frequency of the wave which was measured at step 4 of procedure. Frequency at Channel#1 :

2.

I calculated the rms value of the voltage and current from the oscilloscope.

Amplitude at Channel#1 : 1.6 X 2 volt = 3.2 volt Amplitude at Channel#2 : 2.2 X 2 volt = 4.4 volt We find that the voltage measured in channel 1 is equal to the voltage measured at step 5 of procedure. 3.17 volt ≅ 3.2 volt 3. The time period is more when the frequency of the wave is decreased and the time period is less when the frequency of the wave is increased. 4

4. I calculated the magnitude and phase angle of the impedance from the readings taken in step 5 and 6 of above procedure. V∠θ 3.17∠0 0 volt Impedance, Z = = 146.08 Ω ∠ –-32.40 = 0 I∠θ 21.7∠32.4 mA Voltage is leading current by 32.40

PRECAUTION. 1. Power supply must be switched on after ensuring that all the connections have been done accurately & has been checked by teacher. 2.

Each reading must be taken with care.

3.

Precautions must be taken with bare circuits when in energized condition.

4. We should take care so that the current flow does not exceed the current limit specified in the rheostat and capacitor. 5.

Oscilloscope must be calibrated before starting the test.

5