Electrical Machines and Circuits

In a transformer the change in the current in primary coil produces the change in the current in secondary coil because of electromagnetic induction. 

iron core is basically used to minimise flux leakage so that energy losses can be minimise.

Power= $VI$

efficiency of a transformer $=\frac { Power _{ output } }{ { Power } _{ input } } $ for having efficiency >1 is not allowed by law of conservation of energy and e$=$1 is only for cases.
so e<1.

A transformer is used to change the voltage low to high or vice versa depending upon the efficiency for power transfer and usage and since it is an application of the changing emf due to change in magnetic flux which is created by changing current it can be only applied to a.c. .

A transformer changes Voltages and current but the power remains constant but that is case only for ideal transformer, in general there is loss in power in form of heat , sound , vibrations, eddy currents , etc .Only the frequency remains constant.

In a transformer, source of alternating current is applied to the primary coil. Due to this, the current in the primary coil (called as magnetizing current) produces alternating flux in the core of transformer. This alternating flux gets linked with the secondary coil, and because of the phenomenon of mutual induction an emf gets induced in the secondary coil. 
Mutual induction:
An alternating current flowing in a coil produces alternating magnetic field around it. When two or more coils are magnetically linked to each other, then an alternating current flowing through one coil causes an induced emf across the other linked coils. This phenomenon is called as mutual induction.
From these principles, it can be derived that emf divided by number of turns is same for both primary and secondary winding.

Transformers are found everywhere alternating current is used. This includes both large power stations to the power cord for our laptop computer. A transformer is an electrical device that trades voltage for current in a circuit, while not affecting the total electrical power. This means it takes high-voltage electricity with a small current and changes it into low-voltage electricity with a large current, or vice-versa. That is, step up or step down the voltage in a circuit.
A step-up transformer turns low-voltage electricity into high-voltage electricity while dropping the current. A step-down transformer changes high-voltage electricity into low-voltage electricity.
For a transformer to work, the current in one coil has to somehow make current flow in the other coil and the circuit it's connected to. A DC current in one coil will make a magnetic field on the other coil, but a magnetic field by itself won't drive any electrons around. A changing magnetic field, however, does create an electric force which will accelerate those electrons in the other coil into carrying a current. This process is described by Faraday's law of induction. We get a changing field from an AC current, since the current which makes the field is changing. Hence, DC current cannot be used as a source for a generator.

This question is already present in ID: 177624.

Transformers are found everywhere alternating current is used. This includes both large power stations to the power cord for our laptop computer. A transformer is an electrical device that trades voltage for current in a circuit, while not affecting the total electrical power. This means it takes high-voltage electricity with a small current and changes it into low-voltage electricity with a large current, or vice-versa. That is, step up or step down the voltage in a circuit. 
A step-up transformer turns low-voltage electricity into high-voltage electricity while dropping the current. A step-down transformer changes high-voltage electricity into low-voltage electricity. 
For a transformer to work, the current in one coil has to somehow make current flow in the other coil and the circuit it's connected to. A DC current in one coil will make a magnetic field on the other coil, but a magnetic field by itself won't drive any electrons around. A changing magnetic field, however, does create an electric force which will accelerate those electrons in the other coil into carrying a current. This process is described by Faraday's law of induction. We get a changing field from an AC current, since the current which makes the field is changing. Hence, DC current cannot be used as a source for a generator.

A transformer takes high-voltage electricity with a small current and changes it into low-voltage electricity with a large current, or vice versa. That is, step up or step down the voltage in a circuit. A step-up transformer turns low-voltage electricity into high-voltage electricity while dropping the current. A step-down transformer changes high-voltage electricity into low-voltage electricity.
If we change the number of turns in the coils we change the induced emf. This allows you to change (transform) the voltage from the primary to the secondary coil.

$\text{Power source}=EI=240\times 0.7=166$
$\Rightarrow \eta =\dfrac{\text{Output}}{\text{Input}}=\cfrac{140}{166}$ $\Rightarrow \eta=83.3\%$

Step up transformer increases the voltage in secondary coil and decreases current in secondary coil. Transformer works only on ac current because in DC current, there is no change of flux associated with the coil

The efficiency of the transformer is defined as ratio of useful power output to the input power. The two being measured is the same unit. Its unit is either watts or kw. Transformer efficiency is denoted by $\eta$

$\eta = \dfrac{\text{output power}}{\text{input power}} = =\dfrac{\text{output power}}{\text{input power + losses}}$

$\eta  = \dfrac{\text{output power}}{\text{input power + iron losses of copper + losses}}$

$\eta = \dfrac{V _2I _2 \cos \phi _2}{V _2 I _2 \cos \phi _2 + P _i + P _c}$

Where

$V _2  = $ secondary terminal voltage

$I _2 = $ Full load secondary current.

$\cos \phi _2 = $ Power factor of the load

$P _i = $ Iron losses = constant loss = exactly current loss + hysteresis loss

$P _c = $ full load copper loss

The efficiency is a function of load i.e. lead current $I _2$ assuming $\cos \phi$ constant. The secondary terminal voltage $V _2$ is also assumed constant.

$\dfrac{d \eta}{d I _2} = 0$

Now $\eta = \dfrac{V _2I _2\cos \phi _2}{ V _2I _2\cos \phi _2 + P _i + I _2^2 R _{2e} }$

$\dfrac{d \eta}{d I _2} = \dfrac{d}{d I _2}(\dfrac{V _2I _2\cos \phi _2}{ V _2I _2\cos \phi _2 + P _i + I _2^2 R _{2e} }) = 0$

$( V _2I _2\cos \phi _2 + P _i + I _2^2 R _{2e}) \dfrac{d}{d I _2}( V _2I _2\cos \phi _2) – (V _2I _2\cos \phi _2) \dfrac{d}{d I _2}( V _2I _2\cos \phi _2 + P _i + I _2^2 R _{2e}) = 0$

$( V _2I _2\cos \phi _2 + P _i + I _2^2 R _{2e})(V _2 \cos \phi _2) – (V _2 I _2 \cos \phi _2)(V _2 \cos \phi _2 + 2 I _2 R _{2e}) = 0$

Cancelling $V _2 \cos \phi _ 2$ from both the terms we get

$ V _2I _2\cos \phi _2 + P _i + I _2^2 R _{2e} – V _2I _2\cos \phi _2 – 2I^2 R _{2e} = 0 $

$P _i – I^2 R _{2e} = 0$

$P _i = I^2 R _{2e} = P _{Cu}$

$P _i = P _{Cu}$

 So, condition to achieve maximum efficiency is that

Copper Loss = Iron Loss

$\mu =\frac { { V } _{ s }{ I } _{ s } }{ { V } _{ p }{ I } _{ p } } =0.8\Rightarrow { I } _{ p }=\frac { { V } _{ s }{ I } _{ s } }{ { V } _{ p }\mu  } =\frac { 440\times 2 }{ 220\times .8 } =5A$