Transformer Formula: Definition, Efficiency, Turn Ratio, Types (Step Up and Step Down) and Working Principle

Transformer Formula Overview

The transformer formula is a fundamental concept in electrical engineering that governs the behavior and operation of transformers. A transformer is an electrical apparatus utilized to either increase or decrease voltage levels between circuits. They find widespread applications in power distribution, electrical systems, and various electronic devices. It operates as a passive device by utilizing electromagnetic induction to transfer electrical energy from one circuit to another. The transformer achieves this by adjusting the AC voltage between circuits while maintaining a constant frequency of the current. The formula for the transformer can be expressed as:

Vp / Vs = Np / Ns

What is a Transformer?

A transformer is an electrical apparatus that utilizes the phenomenon of electromagnetic induction to transfer electrical energy between different coils of wire. 

1. A transformer consists of two or more coils of wire, known as windings, which are linked by a magnetic field. 
2. Its primary function is to transfer electrical energy between circuits through electromagnetic induction. 
3. By employing Faraday's Law of Induction, a transformer converts electrical energy from one level to another. This conversion is achieved by linking multiple electrical circuits through a shared magnetic field that is generated within the transformer. 
4. Operating on the principle of mutual induction, a transformer functions based on the concepts of electromagnetic induction. 
5. The equation representing a transformer, often referred to as the transformer formula or transformer equation, can be expressed as Vp × Ip = Vs × Is.

Transformer Formula

A transformer is an electrical apparatus that enables us to modify the voltage in an alternating current electrical circuit while maintaining power continuity. In an ideal transformer, the power entering the device equals the power delivered at the output. However, in real-world transformers, there are minor losses due to various factors. By harnessing the principles of electromagnetic induction, a transformer converts alternating electrical energy from one voltage level to another.

The power of an electric circuit is determined by multiplying the voltage by the current. This principle applies to both the primary and secondary sides of a transformer.

• Formula for power on the primary side: 

(Input voltage on the primary coil) × (Input current on the primary coil)

• Formula for power on the secondary side: 

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

The power in an electric circuit can be determined by multiplying the voltage by the current intensity.

The relationship between the input voltage and current on the primary coil and the output voltage and current on the secondary coil can be expressed as follows:

(Input Voltage on Primary Coil) × (Input Current on Primary Coil) = (Output Voltage on Secondary Coil) × (Output Current on Secondary Coil)

The transformer formula is given by:

Vp/Vs = Np/Ns

Where:

• Vp represents the main voltage
• Vs represents the secondary voltage
• Np represents the number of turns in the primary coil
• Ns represents the number of turns in the secondary coil

The ratio Np/Ns, known as the turn ratio, indicates the difference in the number of turns between the primary and secondary coils.

For a step-up transformer, the formula is:

Vs = (Ns/Np) × Vp

Where Ns is greater than Np, resulting in an increase in voltage from the primary to the secondary side.

For a step-down transformer, the formula is:

Vs = (Ns/Np) × Vp

Here, Np is greater than Ns, leading to a decrease in voltage from the primary to the secondary side.

Let's consider an example to illustrate this equation:

Suppose we have a transformer with a primary voltage of 120V and a turns ratio of 1:4. To find the secondary voltage, we can use the voltage equation:

Solution:
V1/V2 = N1/N2
120/V2 = 1/4
Cross-multiplying:
1 x V2 = 120 x 4
V2 = 480V
Hence, the secondary voltage of the transformer is 480V.

Current Equation: I1/I2 = N2/N1

If we have a transformer with a primary current of 5A and a turns ratio of 3:1, we can calculate the secondary current using the current equation:

Solution:

I1/I2 = N2/N1
5/I2 = 1/3
Cross-multiplying:
1 x I2 = 5 x 3
I2 = 15A
Therefore, the secondary current of the transformer is 15A.

Types of Transformer Formula 

1. Step-up Transformer: A step-up transformer is employed to raise the voltage of an electrical current. This is achieved by taking a low voltage input and transforming it into a higher voltage output. The step-up transformer achieves this by incorporating a greater number of turns in the primary coil. By increasing the number of turns in the primary coil, a step-up transformer elevates the voltage while reducing the current. This reduction in current is crucial as it enables the utilization of smaller wires when transmitting power over long distances. Additionally, a step-up transformer can serve as a boost converter, converting low DC voltage into high-voltage AC voltage. This functionality is advantageous for powering devices that require a high voltage, such as electric motors.
2. Step-down Transformer: A step-down transformer is employed to lower the voltage of an electrical current. It achieves this by utilizing a greater number of turns in the secondary coil. By increasing the number of turns in the secondary coil, a step-down transformer reduces the voltage while increasing the current. The image above illustrates this process, showcasing an input of 120 volts and an output of 12 volts. The increased number of turns in the secondary coil allows for lower resistance and energy loss, resulting in higher efficiency compared to its counterpart, the step-up transformer.

Parts of Transformer 

1. A transformer consists of three main components: the magnetic core, primary winding, and secondary winding.
2. The primary winding is connected to a live AC power source, causing an oscillating magnetic field to form around the coil.
3. The secondary winding experiences an electromotive force (EMF) due to the changing magnetic field.
4. When the secondary winding circuit is closed, it allows AC current to flow through it.
5. The magnetic core, often made of laminated steel sheets, provides a low resistance path for the magnetic field and is shared by both windings.
6. The ratio of the number of turns between the primary and secondary windings corresponds to the ratio of output and input voltage.
7. In a step-down transformer, the secondary winding has fewer turns than the primary winding, while in a step-up transformer, the secondary winding has more turns.

Working Principle of Transformer Formula

The functioning of a transformer is primarily based on the concept of mutual inductance between two circuits that share a magnetic flux. A basic transformer consists of two separate but magnetically linked inductive coils connected through a common magnetic pathway. The diagram below illustrates the operating principle of a transformer.

Operating Principle of a Transformer

1. The core of the transformer is constructed using laminated strips, with small gaps visible along the cross-section of the core. The mutual inductance between the two coils is significantly high. 
2. When an alternating voltage is applied to one of the coils, it generates an alternating magnetic flux within the laminated core. This alternating flux induces a mutual electromotive force in the transformer. 
3. The mutual electromotive force is created when a large portion of the alternating flux generated by one coil is coupled with the other coil. 
4. The phenomenon can be explained using Faraday's equations of electromagnetic induction. As the second coil circuit is closed, a current flows through it, and electrical energy is transmitted magnetically from the first coil to the second coil.
5.  The first coil, which receives the alternating current source, is known as the primary winding.
6.  The second coil, referred to as the secondary winding, extracts energy from the transformer.

A transformer operates by utilizing the principle of mutual inductance, where electrical energy is transferred magnetically from the primary winding to the secondary winding through the magnetic coupling between the two coils.

Examples of Transformer Applications

Transformers find extensive applications in various electrical systems and devices, including:

1. Power Grids: Transformers play a vital role in power transmission and distribution systems. They step up the voltage for efficient long-distance transmission and step it down for local distribution.
2. Electrical Appliances: Transformers are used in electronic devices such as televisions, computers, audio systems, and mobile phone chargers to adapt the voltage to the required levels.
3. Industrial Equipment: Transformers are employed in industrial machinery and equipment to regulate voltage levels, ensuring smooth and safe operation.

Efficiency of Transformer Formula

The efficiency of a transformer refers to the ratio of output power to input power. It represents how effectively the transformer transfers electrical energy. Efficiency is influenced by factors such as core losses, copper losses, and the magnetic properties of the core material. Modern transformers are designed to have high efficiency to minimize energy losses and maximize overall system performance.

The efficiency of a transformer can be calculated using the following formula:

Efficiency (%) = (Output power / Output power + Losses) × 100

Where:

Output power = Output voltage × Output current Input power = Input voltage × Input current

To calculate the efficiency, you need to determine the output power and the input power of the transformer. The output power is the product of the output voltage and the output current, while the input power is the product of the input voltage and the input current. By dividing the output power by the input power and multiplying the result by 100, you can express the efficiency as a percentage.

It's important to note that real-world transformers have losses due to factors such as resistance, hysteresis, and eddy currents. These losses reduce the overall efficiency of the transformer.

Transformer Formula: Turn Ratio, Step Up, and Step Down

Transformer Turn Ratio Formula

The transformer turn ratio is determined by dividing the number of turns on the primary winding by the number of turns on the secondary coil. This ratio has a significant impact on the expected performance of the transformer and the voltage needed on the secondary winding. In the case of a step-down transformer, where a lower secondary voltage is desired, the number of turns on the secondary must be fewer than those on the primary. Conversely, for step-up transformers, when the transformer turn ratio decreases the voltage, it increases the current, and vice versa. Consequently, the voltage and current ratio of an ideal transformer are directly linked to the number of turns on the secondary coil.

The Transformer Ratio Formula for Voltage:

K = V1 / V2

In this equation:

1. V1 represents the primary voltage, which is the voltage applied to the primary winding of the transformer.
2. V2 represents the secondary voltage, which is the voltage obtained from the secondary winding of the transformer.
3. The ratio of V1 to V2, as represented by K, is called the transformer turn ratio.

The Transformer Ratio Formula for Current:

K = I1 / I2

In this equation:

• I1 represents the primary current, which is the current flowing through the primary winding of the transformer.
• I2 represents the secondary current, which is the current flowing through the secondary winding of the transformer.
• The ratio of I1 to I2, as represented by K, is called the transformer turns ratio.

Transformer Formula: Things to Remember

1. Turn Ratio Formula: The turn ratio formula is represented by K = Np / Ns, where Np is the number of turns in the primary winding and Ns is the number of turns in the secondary winding.
2. Step-Up Transformer Formula: For a step-up transformer, the secondary voltage (Vs) is greater than the primary voltage (Vp). The voltage ratio is determined by the turn ratio (K), and the formula is Vs = K * Vp.
3. Step-Down Transformer Formula: In a step-down transformer, the secondary voltage (Vs) is lower than the primary voltage (Vp). The voltage ratio is determined by the turn ratio (K), and the formula is Vs = Vp / K.
4. Mutual Inductance: The functioning of a transformer is based on mutual inductance, which represents the magnetic coupling between the primary and secondary windings. The formula for mutual inductance is M = √(Lp * Ls), where Lp is the self-inductance of the primary winding and Ls is the self-inductance of the secondary winding.
5. Importance of Turns: The number of turns in the windings plays a crucial role in determining the voltage transformation in a transformer. Increasing the number of turns in the secondary winding relative to the primary winding leads to a step-up transformer, while decreasing the number of turns results in a step-down transformer.
6. Application of Formulas: These formulas allow us to calculate and understand the relationship between voltage, turns, and the functioning of transformers in various electrical systems.