Module 2
A.C. Circuits
The flow of electricity can be done in two ways like AC (alternating current) and DC (direct
current). Electricity can be defined as the flow of electrons throughout a conductor such as a
wire. The main disparity among AC & DC mainly lies within the direction where the electrons
supplies. In direct current, the flow of electrons will be in a single direction & in the alternating
current; the flow of electrons will change their directions like going forward & then going
backward.
• In Alternating current, movement of electric charge periodically reverses its direction.
• Whereas in DC, flow of electric charge is only in one direction.
Why we use A.C. in homes
• AC voltage is capable of converting voltage levels just with use of transformers.
– To transmit AC over a long distance, voltage is stepped up to 400 KV at
generating stations and stepped down at a low level , 400/230 V for household
and commercial utilization.
– AC motors are simple in construction, more efficient and robust as compared to
DC motors.
,Sinusoidal Alternating Quantity:
Alternating quantity that varies according to sin of angle .
The instantaneous value of a sine-wave voltage for any angle of rotation is expressed in the
formula:
V= Vm sin
is the angle
Vm = the maximum voltage value
V = the instantaneous value of voltage at angle
Terms to know
1. Cycle: When an Alternating qty goes through complete set of positive and negative
values or goes through 360 electrical degrees.
2. Alternation: One half cycle
3. Time Period: Time taken to complete one cycle by AC.
4. Frequency: No of cycle made per second.
5. Amplitude: Maximum value attained by an alternating quantity in one cycle and also
called Peak Value / Max. Value
, Peak and RMS Values
The magnitude of alternating quatity can be expressed in three ways:
1 Peak Value
2 Average Value
3 Effective or rms value
Peak Value:
The maximum value attained by an alternating quantity during oone cycle is called peak value.
This is also called maximum value or amplitude. The peak of an alternating voltage or current is
represented by Vm and Im
Average Value:
The average value of a periodic waveform whether it is a sine wave, square wave or triangular
waveform is defined as: “the quotient of the area under the waveform with respect to time”.
In other words, the averaging of all the instantaneous values along time axis with time being one
full period, (T).
For symmetrical waves like sinusoidal current or voltage waveform, the positive half cycle will
be exactly equal to negative half cycle. Therefore, the average value over a complete cycle will
be zero. The work is done by both, positive and negative cycle and hence the average value is
determined without considering the signs.So, the only positive half cycle is considered to
determine the average value of alternating quantities of sinusoidal waves.
Divide the positive half cycle into (n) number of equal parts as shown in the above figure
Let i1, i2, i3…….. in be the mid ordinates
The Average value of current Iav = mean of the mid ordinates
, Derivation for average value of sinusoidal current:
Let us consider a sinusoidal current i = ImSinωt as shown in the figure below. We will calculate
its average value for one time period ωt = π from the definition of average value of alternating
current.
𝜋
Area of alternation = 0
𝑖 𝑑(𝑤𝑡)
𝜋
= 0
Im 𝑠𝑖𝑛 𝑤𝑡 𝑑(𝑤𝑡)
𝜋
= Im 0
𝑠𝑖𝑛 𝑤𝑡 𝑑(𝑤𝑡)
Π
= Im −cos 𝑤𝑡 0
= Im −(−1 − 1)
= 2Im
Base = π
Therefore, Average value of sinusoidal current = 2𝐼𝑚 𝜋
A.C. Circuits
The flow of electricity can be done in two ways like AC (alternating current) and DC (direct
current). Electricity can be defined as the flow of electrons throughout a conductor such as a
wire. The main disparity among AC & DC mainly lies within the direction where the electrons
supplies. In direct current, the flow of electrons will be in a single direction & in the alternating
current; the flow of electrons will change their directions like going forward & then going
backward.
• In Alternating current, movement of electric charge periodically reverses its direction.
• Whereas in DC, flow of electric charge is only in one direction.
Why we use A.C. in homes
• AC voltage is capable of converting voltage levels just with use of transformers.
– To transmit AC over a long distance, voltage is stepped up to 400 KV at
generating stations and stepped down at a low level , 400/230 V for household
and commercial utilization.
– AC motors are simple in construction, more efficient and robust as compared to
DC motors.
,Sinusoidal Alternating Quantity:
Alternating quantity that varies according to sin of angle .
The instantaneous value of a sine-wave voltage for any angle of rotation is expressed in the
formula:
V= Vm sin
is the angle
Vm = the maximum voltage value
V = the instantaneous value of voltage at angle
Terms to know
1. Cycle: When an Alternating qty goes through complete set of positive and negative
values or goes through 360 electrical degrees.
2. Alternation: One half cycle
3. Time Period: Time taken to complete one cycle by AC.
4. Frequency: No of cycle made per second.
5. Amplitude: Maximum value attained by an alternating quantity in one cycle and also
called Peak Value / Max. Value
, Peak and RMS Values
The magnitude of alternating quatity can be expressed in three ways:
1 Peak Value
2 Average Value
3 Effective or rms value
Peak Value:
The maximum value attained by an alternating quantity during oone cycle is called peak value.
This is also called maximum value or amplitude. The peak of an alternating voltage or current is
represented by Vm and Im
Average Value:
The average value of a periodic waveform whether it is a sine wave, square wave or triangular
waveform is defined as: “the quotient of the area under the waveform with respect to time”.
In other words, the averaging of all the instantaneous values along time axis with time being one
full period, (T).
For symmetrical waves like sinusoidal current or voltage waveform, the positive half cycle will
be exactly equal to negative half cycle. Therefore, the average value over a complete cycle will
be zero. The work is done by both, positive and negative cycle and hence the average value is
determined without considering the signs.So, the only positive half cycle is considered to
determine the average value of alternating quantities of sinusoidal waves.
Divide the positive half cycle into (n) number of equal parts as shown in the above figure
Let i1, i2, i3…….. in be the mid ordinates
The Average value of current Iav = mean of the mid ordinates
, Derivation for average value of sinusoidal current:
Let us consider a sinusoidal current i = ImSinωt as shown in the figure below. We will calculate
its average value for one time period ωt = π from the definition of average value of alternating
current.
𝜋
Area of alternation = 0
𝑖 𝑑(𝑤𝑡)
𝜋
= 0
Im 𝑠𝑖𝑛 𝑤𝑡 𝑑(𝑤𝑡)
𝜋
= Im 0
𝑠𝑖𝑛 𝑤𝑡 𝑑(𝑤𝑡)
Π
= Im −cos 𝑤𝑡 0
= Im −(−1 − 1)
= 2Im
Base = π
Therefore, Average value of sinusoidal current = 2𝐼𝑚 𝜋
