Transformer Voltage Transformation Ratio |

## How to define the voltage transformation ratio of a transformer?

The voltage transformation ratio of a transformer is nothing but the ratio of transformer core turn number or induced voltage onto the cores.

In our previous article about Transformer E.M.F. Equation and Derivation, we have equated 2 equation for induced voltage of the transformer primary and secondary windings.

E

_{1}= 4.44fN_{1}Φ_{m}= 4.44fN_{1}B_{m}AE

_{2}= 4.44fN_{2}Φ_{m}= 4.44fN_{2}B_{m}A### Definition of Transformer Voltage Ratio

The transformer voltage transformation ratio is defined as the ratio of the EMF in the secondary coil to that in the primary coil.Symbolically transformer voltage transformation ratio defined by letter "K".

K = E

_{2}/E

_{1}= (4.44fN

_{2}Φ

_{m})/(4.44fN

_{1}Φ

_{m})

Therefore,

K = E

_{2}/E

_{1}= N

_{2/}N

_{1....(equ-1)}

Now,

V

_{1}= E

_{1}+ voltage drop

E

_{2}= V

_{2}+ voltage drop

Due to the resistance in the windings and some leakage flux, there is some loss in voltage. This is called Voltage Drop.

But, in the ideal case, the voltage drop can be neglected.

Hence,

V

_{1}= E

_{1}

E

_{2}= V

_{2}

Hence,

E

_{2}/E

_{1}= V

_{2}/V

_{1}…..(equ-2)

Also, in a transformer, the power across the primary, as well as the secondary winding, is the same.

Hence,

V

V

_{1}I_{1}= V_{2}I_{2}V

_{1}/V_{2}= I_{2}/I_{1}……..(equ-3)Now, combining equation (1), (2) & (3), we get, transformer voltage transformation constant (K)

**K = E**

_{2}/E_{1}= N_{2/}N_{1}= V_{2}/V_{1}= I_{2}/I_{1}Where,

1 represents the primary coil;

2 represents the secondary coil;

E is emf in the respective coil;

V is the voltage in the respective coil;

I is the current in the respective coil;

N is the number of turns of the respective coils;

Φ

1 represents the primary coil;

2 represents the secondary coil;

E is emf in the respective coil;

V is the voltage in the respective coil;

I is the current in the respective coil;

N is the number of turns of the respective coils;

Φ

_{m}is the mutual flux in the core.#### How do the transformer coil turn number and induced voltage determine the transformer is step-up or step-down?

Derivated equation of the voltage transformation of a transformer from the above is-

**E**

_{2}/E_{1}= N_{2/}N_{1}=KThis constant K is known as voltage transformation

ratio.

- If N
_{2}> N_{1}i.e. K > 1, then transformer is called step-up transformer; - If N
_{2}< N_{1}i.e. K < 1, then transformer is known as step-down transformer.

Again, for an ideal transformer, input VA = output VA.

V

_{1}I_{1}= V_{2}I_{2}or I_{2 /}I_{1=}V_{1/}V_{2}Hence, currents are in the inverse ratio of the (voltage) transformation ratio.

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