Transformer Performance: Voltage ratio

Transformer Performance: Voltage ratio

1. What Voltage Ratio Is

Voltage ratio (turns ratio, transformation ratio)

for ideal transformer (no loss, no voltage drop). For practical,

slightly less than

due to winding resistance and leakage reactance drop.

• Step-up: $a<1$ ($N_2>N_1$ ⇒ $V_2>V_1$)
• Step-down: $a>1$ ($V_2<V_1$)
• Isolation: $a=1$ ($V_2≈V_1$)

2. Ideal vs Practical

Ideal:

Practical: Equivalent circuit includes $R_1, X_1$ (primary leakage), $R_2, X_2$, core branch $R_c$ (iron loss) + $X_m$ (magnetizing) in parallel. Then

⇒ voltage regulation.

3. Worked Examples

(a) Ideal N1=200, N2=1000, V1=230V ⇒ V2=1150V (step-up 5×) ✓

(b) Practical: E2=240V, I2=10A, R2=0.1Ω, X2=0.2Ω, load pf=0.8 lagging: V2= E2 - I2(R2 cosφ + X2 sinφ)? Actually phasor: V2 = E2 - I2(R2+jX2) ⇒ magnitude drop.

(c) Need to find a for 11kV/400V distribution: a=27.5 step-down.

4. Exam Points

• Define $a=V_1/V_2=N_1/N_2$ — 3-5 marks, very frequent.
• Distinguish ideal vs practical (drop due to $R,X$) — 5 marks, frequent.
• Solve $V_2$ for given $N$, $V_1$ — 3-5 marks, frequent.
• Mention current ratio inverse — 3 marks.