A transformer is an electrical device that transfers energy between two circuits using magnetic fields, altering the voltage level by stepping it up or down. It achieves this by passing alternating current through coils of wire, creating a changing magnetic field that induces voltage in a second coil. This device is essential for efficient power transmission and regulation in electrical systems.
Transformer Formula
A transformer is an electrical device that maintains power while adjusting the voltage in an alternating current circuit, either increasing or decreasing it. In an ideal transformer, the power entering the device equals the power received at the output, though real-world transformers experience some energy losses.
This device operates by converting alternating electrical energy from one voltage level to another through electromagnetic induction. Power in an electric circuit is calculated by multiplying voltage by current, and in a transformer, the power in the primary coil is equal to the power in the secondary coil.
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. The following formula can mathematically represent the operation of a transformer:
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.
The Efficiency of Transformer Formula
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 important 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.
Here are various formulas used for different types of transformers, which help in understanding the relationship between voltage, current, and the number of turns in the coils. These formulas are essential for calculating the performance and function of transformers in electrical systems :
| 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, | |
| I1 = Primary Current | |
| I2 = Secondary Current | |
| Step-up Transformer Formula | T1/T2=V1/V2 |
| 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 |
Solved Examples on Transformer Formula
Example 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
Example 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
Example 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
Example 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
Example 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
Example 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 = 70
Ns = 140
Vs = 300V
By using the transformer calculation formula we get,
Vp/Vs = Np/Ns
Vp = Np/Ns × VS
Vp = 70/140 × 300
Vp = 150 V
Practice Questions
Question 1: A transformer has 1000 turns in its primary coil and 200 turns in its secondary coil. Calculate the turns ratio N.
Question 2: If a transformer has a turns ratio of 5:1 and the primary voltage is 120 V, what is the secondary voltage?
Question 3: A transformer has a turns ratio of 1:10. If the primary current is 5 A, what is the secondary current?
Question 4: A transformer operates at an efficiency of 95%. If the primary power input is 1000 W, what is the secondary power output?
Question 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.
Question 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.
Question 7: If a transformer has an input power of 2000 W and an output power of 1900 W, calculate its efficiency.