Formula & Calculator
Transformer Power Conservation
For an ideal transformer, power on the primary side equals power on the secondary side.
Interpretation
Transformer power conservation (ideal): input volt‑amps equal output volt‑amps, so V₁·I₁ = V₂·I₂.
This ignores losses; real transformers have slight inefficiencies.
Example: V₁=230V, I₁=1A, V₂=46V → I₂ = (230×1)/46 = 5A.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| V₁ | Primary winding RMS voltage | V |
| I₁ | Primary winding RMS current | A |
| V₂ | Secondary winding RMS voltage | V |
| I₂ | Secondary winding RMS current | A |
| S | Apparent power (VA) — identical on both sides for ideal transformer | VA |
What it means
For an ideal transformer, the input power equals the output power. This is expressed as V₁·I₁ = V₂·I₂, assuming no losses. This relationship follows from energy conservation. In a real transformer, there are losses due to winding resistance, core losses (hysteresis and eddy currents), and leakage flux, so the efficiency is less than 100%. However, the ideal power conservation equation is used for basic calculations and design. It shows that if the voltage is stepped down, the current is stepped up, and vice versa. This is the reason transformers are so important in power transmission: high voltage reduces current and thus reduces I²R losses. Example: With V₁=230V, I₁=1A, and V₂=46V (from previous example), the output current would be I₂ = (230*1)/46 = 5A, assuming an ideal transformer.
Worked example
Transformer Power Conservation – Practical Example
Real‑World| Parameter | Value |
|---|---|
| V₂ | 48 V |
| Apparent power S | 100 VA |
| Formula | V₁·I₁ = V₂·I₂ = S |
Common mistakes
- Ideal: Assumes no losses – V₁I₁ = V₂I₂.
- Efficiency: Real transformers have efficiency <100% – include losses.
- Power units: VA (apparent power) – not watts unless power factor =1.
- Sign: The formula holds for both directions (step‑up or step‑down).
- DC: Transformers do not work on DC – only AC.
Applications
Transformer power conservation (ideal) states that input volt‑amps equal output volt‑amps: V₁·I₁ = V₂·I₂. This relation holds for ideal transformers, neglecting losses. Engineers use it to calculate the secondary current from the primary current and voltage levels, and vice versa. It ensures that the transformer is properly rated for the load. In real transformers, losses reduce the efficiency, so a small correction is needed. This formula is the basis for the apparent power rating of transformers in kVA. By applying power conservation, professionals can design transformer‑based power supplies and distribution systems.
- Calculation of primary and secondary currents for given load
- Transformer sizing for power and voltage requirements
- Design of current transformers for measurement
- Understanding of transformer efficiency and losses
- Educational insight into transformer operation
Frequently Asked Questions
In an ideal transformer, V₁·I₁ = V₂·I₂, meaning the power on the primary side equals the power on the secondary side.
100% because no losses are assumed. Real transformers have efficiencies typically 95-99%.
Since V₁/V₂ = N₁/N₂ and I₁/I₂ = N₂/N₁, multiplying gives V₁I₁ = V₂I₂.
The output power is less than input; efficiency η = P_out/P_in.
The transformer rating is usually in VA (apparent power) because both real and reactive power are transformed.
The magnetizing current does not transfer power; it is needed to establish the magnetic field and causes a small phase shift.
It is the maximum VA (or kVA) the transformer can handle without overheating, based on thermal limits.
I₁ = (V₂/V₁) I₂, assuming ideal conditions.
At startup, the transformer can draw many times its rated current due to flux buildup, which affects protection settings.
Common errors include: 1) forgetting the conservation, 2) using real power instead of apparent power, 3) ignoring losses, 4) applying to non-ideal transformers without correction, and 5) using the wrong current relationship.