--- title: "Transformer no-load operation and ideal transformer properties" subject: "Electrical Machines I" chapter: 2 key: "semester_4/electrical_machines_i:transformer-no-load-ideal-properties" source: https://www.bctengineer.com/q/semester_4/electrical_machines_i/transformer-no-load-ideal-properties site: BCT Engineering --- # Transformer no-load operation and ideal transformer properties Electrical Machines I · Chapter 2: Transformer - Asked in: 2079 Chaitra, 4 marks - Video: [Ideal Transformer On No Load | Basic Concepts | Electrical Machines](https://www.youtube.com/watch?v=-31ANzeRim0) — ENGINEERING TUTORIAL - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machines_i/transformer-no-load-ideal-properties - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines_i/chapter-2 ## Question Explain no load operation of single phase transformers. What are properties of ideal transformer? ## Short answer At no load the primary draws a small current I0 with magnetising component Im lagging voltage by 90 degrees and core-loss component Ic in phase with voltage; no-load pf is low. An ideal transformer has zero resistance, no leakage flux, infinite permeability, no core loss, 100% efficiency, and V1/V2 = N1/N2 = I2/I1. ## Answer #### No-load operation of a single-phase transformer With the secondary open ($I_2 = 0$), the primary draws a small **no-load current** $I_0$ (2–5% of rated) from the supply. It does two jobs, so it has two components: - **Magnetising component** $I_m = I_0\sin\phi_0$: in phase with the flux, lags $V_1$ by 90°; it sets up the core flux. - **Core-loss (working) component** $I_c = I_0\cos\phi_0$: in phase with $V_1$; it supplies hysteresis and eddy losses (and a very small $I_0^2 R_1$). $$ I_0 = \sqrt{I_m^2 + I_c^2}, \qquad P_0 = V_1 I_0\cos\phi_0 \approx \text{core loss} $$ ```text V1 ^ | I0 | / Ic | / phi0 (about 75-85 deg) | / +--------> phi, Im | v E1, E2 ``` The no-load power factor is low (0.1–0.3 lag). The shunt branch of the equivalent circuit is $R_0 = V_1/I_c$ and $X_0 = V_1/I_m$. #### Properties of an ideal transformer 1. Zero winding resistance (no $I^2R$ loss). 2. No leakage flux; all flux links both windings. 3. Core of infinite permeability, so negligible magnetising current. 4. No hysteresis or eddy current loss. 5. 100% efficiency, zero regulation, and $V_1/V_2 = N_1/N_2 = I_2/I_1$. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. The no-load current I0 has which two components? A. Magnetising in phase with V1 and core-loss lagging V1 by 90 deg B. Two components both lagging V1 by 90 deg C. Magnetising (in phase with flux, lags V1 by 90 deg) and core-loss (in phase with V1) D. Load component and magnetising component Answer: C. Im sets up flux and lags V1 by 90 deg; Ic supplies core losses and is in phase with V1. (Key point: No-load current components) 2. What does the input power at no load mainly supply? A. Core (iron) loss B. Mechanical friction loss C. Load power D. Copper loss of the secondary Answer: A. P0 = V1 I0 cos(phi0) is approximately the core loss since I0^2 R1 is tiny. (Key point: No-load power) 3. What is the typical no-load power factor of a transformer? A. 0.9 lagging B. Unity C. 0.8 leading D. Low, 0.1 to 0.3 lagging Answer: D. Magnetising current dominates so phi0 is large (75-85 deg) and the pf is low and lagging. (Key point: No-load power factor) 4. Which set describes an ideal transformer? A. No leakage flux but 2% iron loss B. Small resistance, partial leakage flux, finite permeability C. Zero resistance but 5% regulation D. Zero resistance, no leakage flux, infinite permeability, no core loss Answer: D. An ideal transformer has no losses, no leakage, negligible magnetising current, 100% efficiency and zero regulation. 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