## Transformer

The transformer converts electrical energy from one circuit to another. Electromagnetic induction is used to do this. It's known as a voltage converter because it can convert high voltage to low voltage and vice versa. A good-condition transformer is made up of two windings, the main and secondary windings. Step up and step down transformers are the two types of transformers provided.

### Transformer Formula

A transformer is an electrical device that allows us to maintain power when increasing or decreasing the voltage in an alternating current electrical circuit. In the case of a perfect transformer, the power entering the equipment is equal to the power received at the output. There is a small percentage of losses in real machinery. Based on the phenomena of electromagnetic induction, it is a device that transforms alternating electrical energy of one voltage level into alternating electrical energy of another voltage level.

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The power of an electric circuit is calculated by multiplying the voltage by the current intensity. The value of the power in the primary is the same as the power in the secondary, as in the case of a transformer.

[(input voltage on the primary coil) × (input current on the primary coil )] = [(output voltage on the secondary coil ) × (output current on the secondary coil)]

Transformer Equation Can be Written As,

V_{p} xI_{p}= V_{s} x I_{s}

If we know the input voltage and the number of turns on the primary and secondary coils, we can calculate the transformer output voltage.

\[\frac{Input\, Voltage\, on\, the\, Primary\, Coil}{Output\, Voltage\, on\, the\, Secondary\, Coil}\] = \[\frac{Number\, of\, turns\, of\, Wire\, on\, the\, Primary\, Coil}{Number\, of\, turns\, of\, Wire\, on\, the\, Secondary\, Coil}\]

Transformer Equation Can be Written As,

\[\frac{V_{p}}{V_{s}}\] = \[\frac{N_{p}}{N_{s}}\]

Where

V_{p} = Primary voltage,

V_{s}= Secondary voltage,

N_{p} = number of turns in the primary

N_{s} = number of turns in the secondary

I_{s}= Input current on the secondary coil.

I_{p}= Input current on the primary coil.

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### Efficiency of Transformer Formula

The efficiency of a transformer is denoted by the letter ‘η’ and is defined as the ratio of output in watts ( or kW) to input in watts ( or kW) ( and is also known as commercial efficiency ).

The efficiency of transformer formula is simply as follows,

Efficiency = \[\frac{Output\, Power}{Output \, Power + Losses}\] x 100%

### Transformer Turns Ratio Formula

The number of turns on the primary winding divided by the number of turns on the secondary coil is the transformer turns ratio. The transformer turns ratio affects the transformer's predicted functioning as well as the voltage required on the secondary winding. When a secondary voltage lower than the primary voltage is required step-down transformer – the number of turns on the secondary must be lower than in the primary, and vice versa for step-up transformers when the transformer turns ratio steps-down the voltage, it steps-up the current, and vice versa, so that the voltage and a current ratio of an ideal transformer are directly related to the number of turns on the secondary.

The Transformer Ratio Formula for Voltage is as Follows,

K= \[\frac{V_{1}}{V_{2}}\]

Where,

V_{1} = Primary voltage

V_{2} = Secondary voltage

The Transformer Ratio Formula for Current is as Follows,

K= \[\frac{I_{1}}{I_{2}}\]

Where,

I_{1} = Primary current

I_{2} = Secondary current

### Step Up Transformer Formula

A step-up transformer is a type of transformer that transforms low voltage (LV) and high current from the primary side to high voltage (HV) and low current on the secondary side.

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The primary coil turns are smaller than the secondary coil turns in a step-up transformer, which converts a low primary voltage to a high secondary voltage.

The step up transformer formula is as follows,

V_{S}= \[\frac{N_{S}}{N_{P}}\] x V_{P}

Where,

V_{p} = Primary voltage,

V_{s}= Secondary voltage,

N_{p} = number of turns in the primary

N_{s} = number of turns in the secondary

### Step Down Transformer Formula

A step-down transformer converts a high primary voltage to a low secondary voltage. The primary winding of a coil in a Step Down Transformer has more turns than the secondary winding.

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The Step Down Transformer Formula is as Follows,

V_{S}= \[\frac{N_{S}}{N_{P}}\] x V_{P}

Where,

V_{p} = Primary voltage,

V_{s}= Secondary voltage,

N_{p} = number of turns in the primary

N_{s} = Number of turns in the secondary

### Solved Examples

Ex.1. The number of primary and secondary windings is 90 and 120 respectively. The secondary voltage is given by 310V, which determines the primary voltage.

Solution:

Given:

N_{p} = 90,

N_{s}= 120

V_{s} = 310V

By using the transformer calculation formula we get,

\[\frac{V_{p}}{V_{s}}\] = \[\frac{N_{p}}{N_{s}}\]

V_{P}= \[\frac{N_{S}}{N_{P}}\] x V_{S}

V_{P} = \[\frac{90}{120}\] x 310

V_{p }= 232.5 volt

Ex.2. The number of primary and secondary windings is 110 and 240 respectively. The primary voltage is given by 300V, which determines the secondary voltage.

Solution:

Given:

N_{p} = 110,

N_{s}= 240

V_{p} = 300V

The Transformer Formula is Given By,

\[\frac{V_{p}}{V_{s}}\] = \[\frac{N_{p}}{N_{s}}\]

V_{S}= \[\frac{N_{S}}{N_{P}}\] x V_{P}

V_{S} = \[\frac{240}{110}\] x 300

V_{s} = 654.5 volts

Q.1) What is the Transformer Winding Formula?

Answer: Power grid distribution systems use transformers with simple designs that use coil wound around a magnetic core in various regions. These wire coils take incoming current and change the voltage according to the transformer turns ratio, which is a ratio of the number of turns in the transformer.

N_{p}/N_{s} = V_{p}/V_{s}

Where,

V_{p} = Primary voltage,

V_{s}= Secondary voltage,

N_{p} = number of turns in the primary

N_{s } = number of turns in the secondary

This transformer winding formula describes how a transformer changes incoming voltage by a fraction and how the voltage of a coil's winds is directly proportional to the number of coil windings.

Q.2) What is the Knee Point Voltage Formula?

Answer: Knee point voltage is the current transformer's saturation limit multiplied by a factor of 10. Each protection class CT must be used in the non-saturation mode. As a result, we must determine the maximum allowed voltage limit that can be applied to the current transformer's secondary winding. The Knee Point Voltage of a Current Transformer is defined by the IEC as the voltage at which a 10% increase in CT secondary voltage results in a 50% increase in secondary current.