Transformer Formula

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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) x (Input current on the primary coil)


(Output voltage on the secondary coil) x (Output current on the secondary coil)


Transformer Equation can be Written As,

\[ V_{p} \times I_{p} = V_{s} \times I_{s} \]


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 Follows:

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

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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Definition of Transformer Formula

The formula calculates the efficiency of a transformer. The transformer is an electrical device that transfers electricity from one circuit to another circuit using magnetic induction. The transformer has two coils, a primary coil and a secondary coil instead of wires with voltage differences in it. Transformers are used daily by people for different purposes as they use them as inductors or motor protection devices. The transformer has two types of transformer, step up and step down.


Types of Transformer Formulas

  1. Step-up Transformer: A step-up transformer is used to increase the voltage of an electrical current. It does this by taking a low voltage input and increasing it to a higher voltage output. The step-up transformer accomplishes this by using a larger number of turns in the primary coil.


A step-up transformer takes a low voltage and steps it up to a higher voltage by increasing the number of turns on the primary coil. The image above shows how this is done with an input of 12 volts and an output of 120 volts. The increase in voltage is due to the increased number of turns on the primary coil which then causes a decrease in current. This is important as it allows for smaller wires to be used when transferring power over long distances.


The step-up transformer can also be used as a boost converter, which takes low DC voltage and converts it into high-voltage AC voltage. This is used to power devices that require a high voltage, such as an electric motor.


  1. Step-down Transformer: A step-down transformer is used to decrease the voltage of an electrical current. It does this by using a larger number of turns in the secondary coil.


A step-down transformer takes high voltage and steps it down to a lower voltage by increasing the number of turns on the secondary coil. The image above shows how this is done with an input of 120 volts and an output of 12 volts. The increase in Voltage is due to the increased number of turns on the secondary coil which then causes less resistance or loss of energy, resulting in higher efficiency compared to its counterpart (step-up Transformer).


Turn Ratio

A measure for describing how many more or fewer windings there are in the Transformer's secondary coil when compared to its primary. The ratio of turns is expressed as Ns/Np, where “Ns” represents the number of windings in the Secondary Coil and “Np” is equal to the number of windings on a Primary Coils


The Transformer Formula: Transformer Efficiency = Output Voltage / Input Voltage * Turn Ratio (Ns/Np)


An efficient transformer has a high turn ratio which means that it contains more coils or wires wrapped around each other inside with less resistance making them more power-efficient than low turn-ratio transformers. In addition, they can also be used for voltage step-up applications if their input is compared to the output. Transformers can be found in many devices such as microwaves, washers, and TVs.


The transformer formula is used to calculate the efficiency of a transformer. The transformer is an electrical device that transfers electricity from one circuit to another circuit using magnetic induction. The transformer has two coils, a primary coil and a secondary coil instead of wires with voltage differences in it. Transformers are used daily by people for different purposes as they use them as inductors or motor protection devices. The transformer has two types of the transformer, step up and step down


Some Common Applications for a Step-up Transformer Are as Follows

  • Converting low voltages from solar panels or batteries to a higher voltage required by appliances or electrical equipment

  • Step-up converter for 12 Volt DC systems to power 24 Volt or 48 Volt loads

  • Boosting the voltage of an Alternating Current (AC) system to charge lead acid or lithium-ion batteries


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:

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

Where,

\[N_{p}\] = number of turns in the primary

\[N_{s}\]  = number of turns in the secondN

\[V_{p}\] = Primary voltage,

\[V_{s}\] = Secondary voltage,


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

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

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:

Np = 90,

Ns= 120

Vs = 310V

By using the transformer calculation formula, we get:

Vp/Vs=Np/Ns

Vp=Ns/Np x VS

VP= 90/120  x 310

 Vp = 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:

\[N_{s}\] = 110,

\[N_{s}\]= 240

\[V_{p}\] = 300V

The transformer formula is given by

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

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

\[V_{s}\] =240/ 110 x 300

\[V_{s}\] = 654.5 volts

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FAQs (Frequently Asked Questions)

1. Who invented the transformer formula?

Transformer formula was invented by James Maxwell in the year 1873. The transformer is also known as “Maxwell's Transformed Circuit”.

2. What are the applications of transformers?

Transformers have different types of applications, they can be used to convert low voltage from solar panels or batteries to a higher voltage required by appliances or electrical equipment. It can also step up a converter for 12 Volt DC systems to power 24 Volt loads and boost AC system currents needed for lead-acid battery charging applications etc Transformers are used daily by people for different purposes as they use them as inductors or motor protection devices.

3. What is the reliability of the transformer formula?

Transformer formula is a very important and useful tool to calculate the Transformer Efficiency, Turn Ratio, and Voltage Step-up/down ratio. The transformer has two types of application such as step-up or step-down circuits which are used for different purposes in homes and industries.

4. What do transformers do?

Transformers can be used as inductors or motor protection devices. The transformer is an electrical device that transfers electricity from one circuit to another circuit using magnetic induction. Transformers are found in many appliances and electronic equipment. The transformer has two coils, a primary coil and a secondary coil instead of wires with voltage differences in it.

5. What is the difference between transformers and inductors?

Transformers are used to increase or decrease voltage levels, while inductors are used primarily to store energy in an electric current. Transformers are found in many appliances and electronic equipment. The transformer has two coils, a primary coil and a secondary coil instead of wires with voltage differences in it. Inductors have only one coil and are used to store energy in a magnetic field. The transformer has two types of application such as step-up or step-down circuits which are used for different purposes in homes and industries.

6. What is the transformer winding formula?

Power grid distribution systems use transformers with simple designs that use coil wounds 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.


Np/Ns = Vp/Vs


Where,


Vp = Primary voltage,


Vs= Secondary voltage,


Np = number of turns in the primary


Ns  = 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.

7.  What is the knee point voltage formula?

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.

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