JEE Main & Advanced Physics Electro Magnetic Induction Transformer

It is a device which raises or lowers the voltage in ac circuits through mutual induction.

It consists of two coils wound on the same core. The alternating current passing through the primary creates a continuously changing flux through the core. This changing flux induces an alternating emf in the secondary.

(1) Transformer works on ac only and never on dc.

(2) It can increase or decrease either voltage or current but not both simultaneously.

(3) Transformer does not change the frequency of input ac.

(4) There is no electrical connection between the winding but they are linked magnetically.

(5) Effective resistance between primary and secondary winding is infinite.

(6) The flux per turn of each coil must be same i.e. \[{{\varphi }_{S}}={{\varphi }_{P}}\]; \[-\frac{d{{\varphi }_{S}}}{dt}=-\frac{d{{\varphi }_{P}}}{dt}\].

(7) If \[{{N}_{P}}=\] number of turns in primary, \[{{N}_{S}}=\] number of turns in secondary, \[{{V}_{P}}=\] applied (input) voltage to primary, \[{{V}_{S}}=\] Voltage across secondary (load voltage or output), \[{{e}_{P}}=\] induced emf in primary ;  \[{{e}_{S}}=\]induced emf in secondary, \[\phi =\] flux linked with primary as well as secondary, current in primary;  \[{{i}_{S}}=\]current in secondary (or load current)

As in an ideal transformer there is no loss of power i.e.\[{{P}_{out}}={{P}_{in}}\]so  \[{{V}_{S}}{{i}_{S}}={{V}_{P}}{{i}_{P}}\]  and  \[{{V}_{P}}\approx {{e}_{P}}\], \[{{V}_{S}}\approx {{e}_{S}}\]. Hence \[\frac{{{e}_{S}}}{{{e}_{P}}}=\frac{{{N}_{S}}}{{{N}_{P}}}=\frac{{{V}_{S}}}{{{V}_{P}}}=\frac{{{i}_{P}}}{{{i}_{S}}}=k\]; k = Transformation ratio (or turn ratio)  

Types of transformer

(8) Efficiency of transformer \[(\eta )\]: Efficiency is defined as the ratio of output power and input power

i.e.  \[\eta \,%=\frac{{{P}_{out}}}{{{P}_{in}}}\times 100=\frac{{{V}_{S}}{{i}_{S}}}{{{V}_{P}}{{i}_{P}}}\times 100\]

For an ideal transformer \[{{P}_{\text{out}}}={{P}_{\text{in}}}\] so \[\eta =100%\] (But efficiency of practical transformer lies between \[70%-90%\])

For practical transformer \[{{P}_{in}}={{P}_{out}}+{{P}_{losses}}\]

so   \[\eta \,=\frac{{{P}_{out}}}{{{P}_{in}}}\times 100=\frac{{{P}_{out}}}{({{P}_{out}}+{{P}_{L}})}\times 100=\frac{({{P}_{in}}-{{P}_{L}})}{{{P}_{in}}}\times 100\]

(9) Losses in transformer : In transformers some power is always lost due to, heating effect, flux leakage eddy currents, hysteresis and humming.

(i) \[Cu\] loss \[({{i}^{2}}R)\] : When current flows through the transformer windings some power is wasted in the form of heat \[(H={{i}^{2}}Rt).\]To minimize this loss windings are made of thick Cu wires (To reduce resistance)

(ii) Eddy current loss : Some electrical power is wasted in the form of heat due to eddy currents, induced in core, to minimize this loss transformers core are laminated and silicon is added to the core material as it increases the resistivity. The material of the core is then called silicon-iron (steel).

(iii) Hystersis loss : The alternating current flowing through the coils magnetises and demagnetises the iron core again and again. Therefore, during each cycle of magnetisation, some energy is lost due to hysteresis. However, the loss of energy can be minimised by selecting the material of core, which has a narrow hysterisis loop. Therefore core of transformer is made of soft iron. Now a days it is made of 'Permalloy' (Fe-22%, Ni-78%).

(iv) Magnetic flux leakage : Magnetic flux produced in the primary winding is not completely linked with secondary because few magnetic lines of force complete their path in air only. To minimize this loss secondary winding is kept inside the primary winding.

(v) Humming losses : Due to the passage of alternating current, the core of the transformer starts vibrating and produces humming sound. Thus, some part (may be very small) of the electrical energy is wasted in the form of humming sounds produced by the vibrating core of the transformer.

(10) Uses of transformer : A transformer is used in almost all ac operations e.g.

(i) In voltage regulators for TV, refrigerator, computer, air conditioner etc.

(ii) In the induction furnaces. (iii) Step down transformer is used for welding purposes.

(iv) In the transmission of ac over long distance.

(v) Step down and step up transformers are used in electrical power distribution.

(vi) Audio frequency transformers are used in radiography, television, radio, telephone etc.

(vii) Radio frequency transformers are used in radio communication.

(viii) Transformers are also used in impedance matching.