MILITARY INSTITUTE OF SCIENCE & TECHNOLOGY

Department of Electrical Electronic and communication Engineering COURSE

EXPT. NO.-01

FAMILIARIZATION WITH ALTERNATING CURRENT (AC) WAVES

OBJECTIVE:
To study ac (sinusoidal) wave forms and correlate them with practically measurable effective
values. An understanding on a simple ac circuit is also expected to be developed in the
experiment.

INTRODUCTION:
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.
v

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:
T
1 V

∫
V = = (For sinusoidal wave)
2m

T v dt 0 2
T
I
1
∫
I = = (For sinusoidal wave)
2m

0
2
T i dt
These values are directly measured in ac voltmeter / ammeters and can be used in power
calculation as:
22
PIRV/R
==

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 V Sin T t m
= (2π / )
i = I Sin(2π /Tt −θ ) m

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 / Irms∠θ

EQUIPMENT LIST:
1. Oscilloscope
2. Function generation
3. Decade resistor
4. Capacitor bank
5. AC voltmeter
6. AC ammeter
7. SPST
8. Breadboard

CIRCUIT DIAGRAM:
1μF

+
10Vp-p 1 KHz
10Vp-p
_ Osc.
1 KHz Osc. Ch-1 Fig 2
Fig 1
100Ω Osc. Ch-2
Ch-1 PROCEDURE:

1. Connect the output of the function generator directly to channel 1 of the oscilloscope as
shown in fig 1. Set the amplitude of the wave at 10V and the frequency at 1 kHz.
Select sinusoidal wave shape.
2. Sketch the wave shape observed on the oscilloscope. Determine the time period of the
wave and calculate the frequency.
3. Measure the voltage with an ac voltmeter.
4. Change the frequency to 500Hz and note what happens to the display of the wave. Repeat
when the frequency is increased to 2 KHz.
5. Construct the circuit as shown in Fig. 2. Measure the input voltage with an ac voltmeter
 and the input current with an ac ammeter. The ration between the voltage and the
current gives the magnitude of the impedance, Z.
6. Observe the wave shapes of oscilloscope channels 1 and 2 simultaneously. Find the
frequency of both the waves and amplitude from the display. Determine the phase
difference between the two waves. The phase difference is give by 360ft, where 't' is
the time delay between the two waves. Also observe which of the two waves lead.
Note 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.

REPORT:
1. Compare the frequency of the wave determined from the oscilloscope with the mentioned
value on the function generator in step 2 of the procedure.
2. Calculate the rms value of the voltage observed in step 2 of the procedure and compare
with that measured in step 3.
3. How does the time period vary when the frequency of the wave is changed in step 4? 4.
Calculate the magnitude of the impedance from the readings taken in step 5. 5. Find the
magnitude and the phase angle of the impedance from the readings taken in step 5 and 6.