Basics of Circuits

1. Unit - 1
AC Fundamentals

2. Difference between Direct Current and Alternating
Current
Direct Current Circuit
Alternating Current Circuit
2

3. 3

4. Frequency
The number of cycles that occur in one second.
Is commonly measured in cycles per second (cycles/sec) and, in normal usage, is
expressed in units of Hertz (Hz).
Time Period
The inverse of Frequency and usually expressed in milliseconds
The time taken in seconds to complete one cycle of an alternating
quantity. It is represented by T.
Terminologies
4

5. Amplitude
The amplitude of a sine wave is the value of that sine wave at its peak.
The effective voltage of the AC power system is 0.707 times the peak voltage
Instantaneous Value
The value of an alternating quantity at any instant
Terminologies
Phase
-is the fractional part of time period or cycle through which the
quantity has advanced from the selected zero position of reference
5

6. 6

7. Problems
7

8. Values of Alternating Voltage and Current
Average value:
It is the average of the instantaneous value for a particular time period.
0.636 Vm , 0.636 Im
Peak Value
-is the maximum value attained by an alternating quantity.
8

9. Values of Alternating Voltage and Current
Root Mean Square (RMS) or Effective Value
is that steady current (dc) which when flowing through a given resistance for
a given time produces the same amount of heat as produced by the
alternating current through the same resistance for the same time
m
m
rms I
I
I 707
.
0
2

 m
m
rms V
V
V 707
.
0
2


9

10. AC Circuit Containing Pure Inductance Only
dt
di
L
v  dt
t
L
V
di m

sin


 dt
t
L
V
i m

sin
)
2
sin(
)
cos
(








 t
L
V
t
L
V
i m
m
i is maximum when is unity,
)
2
sin(

 
t
)
2
sin(

 
 t
I
i m
Therefore:
L
V
I m
m


Hence:
L
v = Vm sinωt
VL
I
900
10

11. Phase Angle for Inductive Circuit:
In a pure inductance, current lags the voltage by 900
v i
v = Vm sinωt
)
2
sin(

 
 t
I
i m
11

12. AC Circuit Containing Pure Capacitance
v = Vm sinωt
t
CV
Cv
q m 
sin


)
sin
(
)
(
t
CV
dt
d
dt
q
d
i m 


t
CV
i m 
 cos

)
2
sin(


 
 t
CV
i m
i is maximum when is unity,
)
2
sin(

 
t
)
2
sin(

 
 t
I
i m
Therefore:
m
m CV
I 

Hence:
C
VC
I
900
12

13. In a pure capacitance, current leads the voltage by 900
Phase Angle for Capacitive Circuit:
v i
v = Vm sinωt
)
2
sin(

 
 t
I
i m
13

14. Practice problems:
14

15. 15
Practice problems:
3. An alternating current of frequency 60 Hz has a maximum value of 120 A.
a) Write down the equation for its instantaneous value.
b) Find the instantaneous value after 1/360 second and
c) Find the time taken to reach 96 A for the first time.