The term 'AC' is short for 'Alternating Current' and refers to a current which alternates (in direction) with a fixed periodicity. The most common type of Alternating Current is the 'sinusoidally varying' type (or simply a sin function of time), where the instantaneous current is given by the relation,
`i(t) = i_0 sin(omegat +phi)`
where the term `i_0` is defined as the 'peak' current and represents the maximum magnitude of electrical current, whereas the term `omega` is defined as the angular frequency given by `omega = 2 pi f` , where `f` is the frequency in Hz. The term `phi` refers to the 'in initial phase' as in any sinusoidal function.
Now, an Alternating Current (AC) is produced by a an AC Source or AC Generator which works on the principle of electro-magnetic induction
`text(Principle)`
A coil is placed inside a strong magnetic field and mounted on an axle about which it is made to rotate, (driven by a mechanical system). As it rotates, the magnetic flux through it alternates and a resultant induced current is produced which alternates with a frequency which is equal to the frequency for the rotation of the coil.
`text(Schematic Design)`
The Armature coil which is a rectangular coil of N turns wound over a soft-iron core (to increase the magnetization) is mounted on an axle along the symmetry axis of the coil that can be coupled to a rotating wheel/turbine etc. A strong uniform magnetic field produced by a permanent magnet or electromagnet cuts through the rotating Armature coil as shown in the figure. Notice that the axis of rotation for the Armature coil is perpendicular to the magnetic field lines.
The Armature coil is also connected to two slip rings `C_1` and `C_2` which in turn are in contact with two carbon brushes `B_1` and `B_2` such that there is permanent electrical contact without hampering the rotation of the coil . The brushes are connected to two terminals P and Q which function as the output terminals for the Generator and the external circuit is connected across P and Q.
The armature coil is driven at a constant angular speed `omega` such that at given instant, the angle between the coil's area vector `vecA `and the magnetic field `vecB` is `theta = (omega t +phi)`, therefore the magnetic flux, `phi_B=vecB.vecA` is given by the relation.
`phi_B = NBACos(omega t+ phi)` . Hence, by application of Faraday's law, the induced EMF (developed across the terminals P and Q),
`E = - (dphi_B)/(dt) =NBA omega sin(omega t+phi)` which can be expressed as,
`E = E_0 sin (omega t +phi)` , where the term `E_0` is define as the
'peak' voltage given by `E_0 = NBA omega = NBA xx 2 pi f`.
It is important to note here that the peak voltage `E_0` depends on not only the intensity of the magnetic field B, the geometry of the Armature coil (N and A) but also on the angular frequency `omega` (or frequency f) of rotation.
Household power supplied in India and most of Asia/Europe is AC with an alternating frequency of 50 Hz.
The term 'AC' is short for 'Alternating Current' and refers to a current which alternates (in direction) with a fixed periodicity. The most common type of Alternating Current is the 'sinusoidally varying' type (or simply a sin function of time), where the instantaneous current is given by the relation,
`i(t) = i_0 sin(omegat +phi)`
where the term `i_0` is defined as the 'peak' current and represents the maximum magnitude of electrical current, whereas the term `omega` is defined as the angular frequency given by `omega = 2 pi f` , where `f` is the frequency in Hz. The term `phi` refers to the 'in initial phase' as in any sinusoidal function.
Now, an Alternating Current (AC) is produced by a an AC Source or AC Generator which works on the principle of electro-magnetic induction
`text(Principle)`
A coil is placed inside a strong magnetic field and mounted on an axle about which it is made to rotate, (driven by a mechanical system). As it rotates, the magnetic flux through it alternates and a resultant induced current is produced which alternates with a frequency which is equal to the frequency for the rotation of the coil.
`text(Schematic Design)`
The Armature coil which is a rectangular coil of N turns wound over a soft-iron core (to increase the magnetization) is mounted on an axle along the symmetry axis of the coil that can be coupled to a rotating wheel/turbine etc. A strong uniform magnetic field produced by a permanent magnet or electromagnet cuts through the rotating Armature coil as shown in the figure. Notice that the axis of rotation for the Armature coil is perpendicular to the magnetic field lines.
The Armature coil is also connected to two slip rings `C_1` and `C_2` which in turn are in contact with two carbon brushes `B_1` and `B_2` such that there is permanent electrical contact without hampering the rotation of the coil . The brushes are connected to two terminals P and Q which function as the output terminals for the Generator and the external circuit is connected across P and Q.
The armature coil is driven at a constant angular speed `omega` such that at given instant, the angle between the coil's area vector `vecA `and the magnetic field `vecB` is `theta = (omega t +phi)`, therefore the magnetic flux, `phi_B=vecB.vecA` is given by the relation.
`phi_B = NBACos(omega t+ phi)` . Hence, by application of Faraday's law, the induced EMF (developed across the terminals P and Q),
`E = - (dphi_B)/(dt) =NBA omega sin(omega t+phi)` which can be expressed as,
`E = E_0 sin (omega t +phi)` , where the term `E_0` is define as the
'peak' voltage given by `E_0 = NBA omega = NBA xx 2 pi f`.
It is important to note here that the peak voltage `E_0` depends on not only the intensity of the magnetic field B, the geometry of the Armature coil (N and A) but also on the angular frequency `omega` (or frequency f) of rotation.
Household power supplied in India and most of Asia/Europe is AC with an alternating frequency of 50 Hz.