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Home > News & Articles > Transformer Formula: Definition, Efficiency, Turn Ratio, Types (Step Up and Step Down) and Working Principle
Updated on 08th July, 2023 , 9 min read
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
A transformer is an electrical apparatus that utilizes the phenomenon of electromagnetic induction to transfer electrical energy between different coils of wire.
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.
(Input voltage on the primary coil) × (Input current on the primary coil)
(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:
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:
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
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.
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
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.
Transformers find extensive applications in various electrical systems and devices, including:
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.
Concept | Formula | Explanation | Example |
Turn Ratio | K = Np / Ns | The turn ratio is the ratio of the number of turns in the primary winding (Np) to the number of turns in the secondary winding (Ns). | If a transformer has 100 turns in the primary and 20 turns in the secondary, the turn ratio would be 100/20 = 5. |
Step-Up Transformer | Vs = K * Vp | In 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). | If the turn ratio of a step-up transformer is 10 and the primary voltage is 100V, the secondary voltage would be 10 * 100V = 1000V. |
Step-Down Transformer | Vs = Vp / K | In a step-down transformer, the secondary voltage (Vs) is less than the primary voltage (Vp). The voltage ratio is determined by the turn ratio (K). | If the turn ratio of a step-down transformer is 5 and the primary voltage is 100V, the secondary voltage would be 100V / 5 = 20V. |
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.
K = V1 / V2
In this equation:
K = I1 / I2
In this equation:
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By - Nikita Parmar 2023-08-25 09:48:44 , 11 min readThe transformer formula represents the relationship between the primary and secondary voltages in a transformer. It is given by the turn ratio formula: Vp / Vs = Np / Ns, where Vp is the primary voltage, Vs is the secondary voltage, Np is the number of turns in the primary winding, and Ns is the number of turns in the secondary winding.
The turn ratio in a transformer is calculated by dividing the number of turns in the primary winding (Np) by the number of turns in the secondary winding (Ns). The formula for turn ratio is: K = Np / Ns.
The turn ratio determines the voltage transformation in a transformer. A higher turn ratio results in a step-up transformer, where the secondary voltage is greater than the primary voltage. Conversely, a lower turn ratio leads to a step-down transformer, where the secondary voltage is lower than the primary voltage.
The transformer formula, Vp / Vs = Np / Ns, shows that the ratio of primary voltage to secondary voltage is equal to the ratio of turns in the windings. This formula helps in understanding how the transformer transforms voltage based on the number of turns in the primary and secondary windings.
No, the transformer formula is specifically related to voltage transformation. To calculate current transformation, the turns ratio and the load impedance of the transformer need to be considered.
By knowing the primary voltage (Vp), turn ratio (K), and using the formula Vs = Vp / K, you can calculate the secondary voltage (Vs) in a transformer.
The transformer formula is widely used in electrical engineering and power systems. It helps in designing and analyzing transformer configurations, understanding voltage transformation, and determining the appropriate turn ratios for desired voltage levels.
The basic transformer formula remains the same for different transformer types, whether it's a step-up or step-down transformer. However, the specific formulas may differ depending on the specific parameters being calculated, such as voltage ratios or current ratios.
The transformer formula does not directly relate to power transfer. However, by knowing the voltage and current on either side of the transformer, the power transfer can be calculated using the formula: Power = Voltage * Current.
The transformer formula assumes ideal transformer behavior, neglecting losses such as resistance, leakage inductance, and core losses. Additionally, it assumes a sinusoidal waveform and does not account for non-ideal factors that may affect the transformer's performance. Real-world transformers may have variations due to these factors.
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