Physics ALTERNATING CURRENT

TRANSFORMER

A transformer is an electrical device that works on the principle of mutual induction to convert a given AC voltage into a larger voltage (step-up transformer) or a lower voltage (step-down transformer).

`text(Principle :)`

If two coils are inductively coupled (mutual inductance) and the current or magnetic flux linked with one is continuously changing with time, then an induced EMF is produced in the second coil. Therefore, if the current fed into the primary is an Alternating Current, then the time varying magnetic flux and the resulting induced voltage in the secondary will also be alternating and with the identical angular frequency.

`text(Schematic Design :)`

A schematic diagram for a transformer is shown here.

The transformer consists of a rectangular soft iron core made up of laminated sheets, well insulated from one another with two sets of coils on either side, the primary and the secondary. The soft-iron core causes the two sets of coils to be magnetically linked (i.e. there is 'coupling'and hence mutual inductance) such that when an alternating current is passed through the primary coil it induces a magnetic flux in the secondary.

Let the input voltage supplied by `AC` source is

`E = E_0Sin(omega t)`

Now, this creates an induced emf `E_p` across the primary coil due to EMI. Similarly, an induced emf `E_s` , appears across the secondary. If `N_p` is the number of turns in the primary and `N_s` , in the secondary coils, then,

`E_s/E_p = N_s/N_p`

The term `N_s/N_p =k` is called the transformation ratio and depending on it's value (i.e. `> 1 or < 1)` the transformer has a step-up or a step-down function. In a step-up transformer, the primary coil is made of a few turns of copper wire whereas the secondary coil consists of large number of turns of copper wire. In a step-down transformer, the primary coil consists of large number of turns of insulated copper wire whereas the secondary coil consists of few turns of fine insulated copper wire.

Efficiency of a Transformer

The efficiency `eta` of a transformer is defined as the ratio of the output power (output across the load resistor `R_L`, ) to the input power. Therefore,

`eta = text(Output power)/text(Input power)` `= (i_sE_s)/(i_pE_p)`

Where `i_s` and `i_p` are the currents through the secondary and the primary respectively.

Energy Losses in a Transformer

Efficiency of a practical transformer is never 100%. The following are the losses in a transformer.

(1) Leakage of magnetic flux occurs which leads to energy losses.

(2) Energy is lost in the form of heat due to joule heating in primary and in secondary coil of conducting copper wires.

(3) Owing to repeated magnetization and demagnetization of iron core, energy is lost. This loss is known as hysteresis loss.

(4) Energy is also lost due to the production of eddy currents in the iron core. This type of loss can be minimized by using laminated cores.

Note: For an ideal Transformer no losses ie Power input = Power output

Uses of Transformer

(1) Electrical power is transmitted at high voltage and low current so that power loss in the form of heat is minimized. For this step up transformer is used at power generation end.

(2) It is used in voltage regulators and stabilizers.

(3) A step-up transformer is used for production of X-rays.

(4) A step-down transformer is used in induction furnaces , mobile charger ,etc.

AC Generator

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.