Transformer Formula with Examples
Last Updated :
22 Apr, 2025
A transformer is a device that converts energy from one circuit to another. Electromagnetic induction is responsible for this. It's referred to as a high-efficiency voltage converter since it can convert high voltage to low voltage and vice versa. A good-condition transformer is made up of two windings: primary and secondary windings. Step-up and step-down transformers are the two types of transformers.
A transformer is an electrical device that allows us to sustain power when the voltage in an alternating current electrical circuit is increased or decreased. The power entering the equipment is equal to the power received at the output in the event of a perfect transformer. Real-world machinery has a modest rate of losses. It is a device that converts the alternating electrical energy of one voltage level into alternating electrical energy of another voltage level, based on the phenomenon of electromagnetic induction.
The voltage is multiplied by the current intensity to compute the power of an electric circuit. In the case of a transformer, the value of the power in the primary is the same as the power in the secondary.
Vp × Ip = Vs × Is
The transformer output voltage may be calculated using the input voltage and the number of turns on the main and secondary coils.
Vp / Vs = Np / Ns
Where,
Vp = Primary voltage
Vs= Secondary voltage
Np = number of turns in the primary
Ns = number of turns in the secondary
Is= Input current on the secondary coil.
Ip= Input current on the primary coil.
Step-up Transformers: These devices are utilized to elevate the voltage of an electrical current. They achieve this by converting a low-voltage input into a higher-voltage output. This is facilitated by increasing the number of turns in the primary coil of the transformer.
A step-up transformer raises voltage levels by augmenting the number of turns in its primary coil. Illustrated with an input of 12 volts and an output of 120 volts, this process leads to a proportional increase in voltage with a decrease in current. Such transformation allows the utilization of thinner wires for transmitting power over long distances.
Moreover, the step-up transformer functions as a boost converter, converting low DC voltage into high-voltage AC voltage. This is particularly useful for powering equipment such as electric motors that necessitate high voltage. The operational principles of a step-up transformer are explained through a transformer formula.
Step-Down Transformers: Conversely, step-down transformers decrease the voltage of an electrical current. They achieve this by adding more turns to the secondary coil.
A step-down transformer reduces voltage levels by increasing the number of turns in its secondary coil. Demonstrated with a 120-volt input and a 12-volt output, this process underscores how a higher number of turns in the secondary coil results in lower resistance, minimized energy loss, and consequently, enhanced efficiency compared to coils with fewer turns. Additionally, there exists a transfer formula elucidating the functionality of step-down transformers.
The efficiency of a transformer, denoted by the symbol η, refers to the ratio between its output power (in watts or kW) and its input power (in watts or kW). This ratio, also termed commercial efficiency, is crucial for assessing the performance of the transformer.
Mathematically, transformer efficiency is calculated using the following formula:
Efficiency = (Output Power / (Output Power + Losses)) * 100%
Where:
- Output Power represents the electrical power delivered by the transformer.
- Losses encompass any energy dissipated during the transformation process.
This formula provides a straightforward way to gauge how effectively a transformer converts input power into usable output power, essential for various applications across industries.
- Converting lower voltages from solar panels or batteries to match higher voltage requirements of appliances or electrical equipment.
- Utilizing step-up converters to power 24 or 48 volt loads from 12 volt DC systems.
- Increasing voltage in AC systems to facilitate charging of lithium-ion or lead-acid batteries.
| Formula | Description |
|---|
| Transformer Ratio Formula for Voltage | K=V2/V1 |
| Where, |
| V1 = Primary Voltage |
| V2 = Secondary Voltage |
| Transformer Ratio Formula for Current | K=I2/I1 |
| Where, |
| ?1 = Primary Current |
| ?2 = Secondary Current |
| Step-up Transformer Formula | T1T2=V1V2 |
| Where, |
| V1 = Voltage in the Secondary Coil |
| V2 = Voltage in the Primary Coil |
| T1 = Turns on the Primary Coil |
| T2 = Turns on the Secondary Coil |
| Step Down Transformer Formula | Vs=NpNs×Vp |
| Where, |
| Vp = Primary Voltage |
| Vs = Secondary Voltage |
| Np = Number of Turns in the Primary Coil |
| Ns = Number of Turns in the Secondary Coil |
Problem 1: The number of primary and secondary windings is 80 and 120 respectively. The secondary voltage is given by 240V, determine the primary voltage.
Solution
Np = 80
Ns = 120
Vs = 240V
The transformer formula is given by,
Vp / Vs = Np / Ns
Vp = Np / Ns × Vs
= 80 / 120 x 240
Vp = 160 V
Problem 2: The number of primary and secondary windings is 60 and 100 respectively. The secondary voltage is given by 250V, determine the primary voltage.
Solution
Np = 60
Ns = 100
Vs = 250V
The transformer formula is given by,
Vp / Vs = Np / Ns
Vp = Np / Ns × Vs
= 60 / 100 x 250
Vp = 150 V
Problem 3: The number of primary and secondary windings is 100 and 350 respectively. The primary voltage is given by 200V, determine the secondary voltage.
Solution
Np = 100
Ns = 350
Vp = 200V
The transformer formula is given by,
Vp / Vs = Np / Ns
Vs = Vp × Ns / Np
Vs = 200 × 350 / 100
Vs = 700V
Problem 4: 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
Np = 90
Ns= 120
Vs = 310V
By using the transformer calculation formula we get,
Vp/Vs = Np/Ns
Vp = Np/Ns × VS
Vp = 90/120 x 310
Vp = 232.5 V
Problem 5: 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
Np = 110
Ns = 240
Vp = 300V
The Transformer Formula is Given By,
Vp/Vs = Np/Ns
Vs = Ns/Np × Vp
Vs = 240/110 × 300
Vs = 654.5 V
Problem 6: The number of primary and secondary windings is 70 and 140 respectively. The secondary voltage is given by 300V, which determines the primary voltage.
Solution
Np = 90
Ns = 120
Vs = 310V
By using the transformer calculation formula we get,
Vp/Vs = Np/Ns
Vp = Np/Ns × VS
Vp = 70/140 × 300
Vp = 150 V
Problem 1: A transformer has 1000 turns in its primary coil and 200 turns in its secondary coil. Calculate the turns ratio N.
Problem 2: If a transformer has a turns ratio of 5:1 and the primary voltage is 120 V, what is the secondary voltage?
Problem 3: A transformer has a turns ratio of 1:10. If the primary current is 5 A, what is the secondary current?
Problem 4: A transformer operates at an efficiency of 95%. If the primary power input is 1000 W, what is the secondary power output?
Problem 5: Calculate the secondary current in an ideal transformer if the primary voltage is 240 V, the primary current is 2 A, and the turns ratio is 1:20.
Problem 6: A transformer has a primary voltage of 110 V and a secondary voltage of 220 V. Calculate the percentage voltage regulation if the secondary voltage drops to 210 V under full load.
Problem 7: If a transformer has an input power of 2000 W and an output power of 1900 W, calculate its efficiency.
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