⚖ Transformer Equation

The fundamental relationship for an ideal transformer links voltage ratio to turns ratio:

Vs / Vp = Ns / Np = n

Where n is the turns ratio. The secondary voltage scales proportionally with the number of secondary turns relative to primary turns.

⚗ Turns Ratio

Current ratio is the inverse of the voltage ratio:

Ip / Is = Ns / Np = n

Power is conserved in an ideal transformer: Vp × Ip = Vs × Is. If voltage goes up, current goes down by the same factor, and vice versa.

▲ Step-Up n > 1

When Ns > Np (n > 1), the output voltage is higher than the input:

• Vs > Vp (voltage increases)
• Is < Ip (current decreases)
• Used in power transmission to reduce line losses
• Example: 11kV to 400kV transmission

▼ Step-Down n < 1

When Ns < Np (n < 1), the output voltage is lower than the input:

• Vs < Vp (voltage decreases)
• Is > Ip (current increases)
• Used in power adapters and distribution
• Example: 230V to 12V for electronics

⚖ Power Conservation

For an ideal transformer (100% efficient):

Pp = Vp × Ip = Vs × Is = Ps

For a real transformer, efficiency η = Ps/Pp is typically 95-99% for large units. The difference is lost as heat.

⚙ Real Transformers

Real transformers have losses that reduce efficiency below 100%:

• Copper loss (I²R) — resistive heating in windings, increases with load current squared
• Core loss — hysteresis loss (magnetic domain switching) and eddy current loss (circulating currents in core)
• Leakage flux — not all magnetic flux links both windings
• Magnetizing current — small current needed to establish the magnetic field

★ Key Points

• Transformers work only with AC (changing magnetic flux required)
• Frequency is unchanged between primary and secondary
• Iron core concentrates magnetic flux, coupling the windings
• Large power transformers achieve η > 99%
• Resonant converters can achieve very high efficiency at specific frequencies
• The animation speed shows relative current magnitude — faster = higher current

📈 Efficiency Formula

Efficiency depends on load resistance and transformer parameters:

η = Ps / Pp × 100%

With the real model here, η is assumed at 95%. Higher load resistance (lighter load) yields better apparent efficiency because copper losses (I²R) are lower.