Calculate secondary voltage and turns ratio for an ideal transformer.Ideal transformers assume no losses; also use current ratio Is/Ip = Np/Ns and power conservation (Pp = Ps).
An ideal transformer is a theoretical linear transformer that is lossless and perfectly coupled. It has no core losses, no winding resistance, and no leakage flux.
The voltage ratio is directly proportional to the turns ratio, while the current ratio is inversely proportional to the turns ratio. This allows for stepping up or stepping down AC voltages.
Where V is voltage, N is number of turns, and the subscripts p and s refer to primary and secondary windings respectively.
Given:
Step 1: Calculate Turns Ratio
Step 2: Apply Voltage Ratio Formula
Result: The secondary voltage is 23 V (a step-down transformer reducing voltage by a factor of 10).
What is the difference between step-up and step-down transformers?
A step-up transformer increases voltage (Nₛ > Nₚ) and decreases current. A step-down transformer decreases voltage (Nₛ < Nₚ) and increases current. Power remains constant in an ideal transformer.
Why is it called an 'ideal' transformer?
An ideal transformer has no losses—all power transferred in equals power transferred out. In reality, real transformers have winding resistance, core losses, and eddy currents. Ideal transformers are theoretical models for calculations.
Can a transformer change DC voltage?
No. Transformers only work with AC. They rely on changing magnetic fields to induce voltage. DC produces a constant field, so transformers are ineffective for DC circuits.
What happens if turns ratio is 1:1?
A 1:1 transformer (equal turns) produces equal input and output voltage. It's used for isolation purposes—separating circuits while maintaining the same voltage level, improving safety and reducing electrical noise.
How does the turns ratio relate to current?
Current is inversely proportional to turns ratio. If turns ratio is 1:10 (step-down), secondary current is 10 times higher than primary current. Power is conserved: V₁I₁ = V₂I₂.
What is the efficiency formula for transformers?
Efficiency = (Power Output / Power Input) × 100%. For ideal transformers, efficiency is 100%. Real transformers are typically 95-99% efficient, with losses due to heat and magnetic effects.
Can transformers amplify power?
No. A transformer cannot create or amplify power. It only transforms voltage and current while maintaining power (in ideal case). High voltage means lower current, and vice versa.
What's the relationship between turns ratio and impedance?
Impedance ratio = (Turns ratio)². If turns ratio is 1:2, impedance increases by 4:1. This principle is used for impedance matching in audio and RF circuits to maximize power transfer.
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