--- title: "Equivalent circuit of 10 kVA 250/1000 V transformer" subject: "Electrical Machines I" chapter: 2 key: "semester_4/electrical_machines_i:oc-sc-10kva-250-1000-primary" source: https://www.bctengineer.com/q/semester_4/electrical_machines_i/oc-sc-10kva-250-1000-primary site: BCT Engineering --- # Equivalent circuit of 10 kVA 250/1000 V transformer Electrical Machines I · Chapter 2: Transformer - Asked in: 2073 Bhadra, 8 marks - Video: [EE213 - 09b - Determining equivalent circuit parameters for a transformer - numerical example](https://www.youtube.com/watch?v=b_6NbUb7U1o) — MAFarooqi - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machines_i/oc-sc-10kva-250-1000-primary - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines_i/chapter-2 ## Question The data obtained from the test of a 10 kVA, 250 V/1000 V single phase transformer are given below: No-load test (on L.V side): 250 V, 0.8 A, 80 watt Short circuit test (on H.V side): 80 V, 10 A, 120 watt Calculate the equivalent circuit parameters referred to primary side and draw the equivalent circuit. ## Short answer From OC test on LV side compute R0 = 781.25 ohm, X0 = 340.97 ohm. From SC test on HV side compute R02 = 1.2 ohm, X02 = 7.909 ohm, then refer to primary by factor 0.0625 giving R01 = 0.075 ohm, X01 = 0.494 ohm. ## Answer **Method.** The no-load (OC) test gives the shunt branch: $\cos\phi_0 = \frac{P_0}{V_0 I_0}$, $I_w = I_0\cos\phi_0$, $I_\mu = I_0\sin\phi_0$, $R_0 = \frac{V_0}{I_w}$, $X_0 = \frac{V_0}{I_\mu}$. The SC test gives the series branch: $Z = \frac{V_{sc}}{I_{sc}}$, $R = \frac{P_{sc}}{I_{sc}^2}$, $X = \sqrt{Z^2 - R^2}$. Values found on one side are moved to the other side by multiplying by the square of the voltage ratio. Primary = LV side (250 V). Rated HV current $= 10000/1000 = 10$ A, so the SC test is at full load. Factor HV to LV: $\left(\frac{250}{1000}\right)^2 = \frac{1}{16} = 0.0625$. #### No-load test (LV): 250 V, 0.8 A, 80 W $$ \begin{aligned} \cos\phi_0 &= \frac{80}{250 \times 0.8} = 0.4, \quad \sin\phi_0 = 0.9165 \\ I_w &= 0.8 \times 0.4 = 0.32\ \text{A}, \quad I_\mu = 0.8 \times 0.9165 = 0.733\ \text{A} \\ R_0 &= \frac{250}{0.32} = 781.25\ \Omega, \quad X_0 = \frac{250}{0.733} = 340.97\ \Omega \end{aligned} $$ #### SC test (HV): 80 V, 10 A, 120 W $$ \begin{aligned} Z_{02} &= \frac{80}{10} = 8\ \Omega, \quad R_{02} = \frac{120}{10^2} = 1.2\ \Omega \\ X_{02} &= \sqrt{8^2 - 1.2^2} = 7.909\ \Omega \end{aligned} $$ Referred to primary (× 0.0625): $$ \begin{aligned} R_{01} &= 1.2 \times 0.0625 = 0.075\ \Omega \\ X_{01} &= 7.909 \times 0.0625 = 0.494\ \Omega \\ Z_{01} &= 8 \times 0.0625 = 0.5\ \Omega \end{aligned} $$ #### Equivalent circuit referred to primary ```text I1 -> I0 I2' o-----+--------+---[ R01 ]---[ jX01 ]---o + | | + [ R0 ] [ jX0 ] load V1 | | V2' - | | - o-----+--------+------------------------o All values referred to primary (LV): R0 = 781.25 ohm, X0 = 340.97 ohm R01 = 0.075 ohm, X01 = 0.494 ohm ``` **Answer (primary side):** $R_0 = 781.25\ \Omega$, $X_0 = 340.97\ \Omega$, $R_{01} = 0.075\ \Omega$, $X_{01} = 0.494\ \Omega$, $Z_{01} = 0.5\ \Omega$. Useful extras: iron loss = 80 W, full-load copper loss = 120 W. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. From the OC test (250 V, 0.8 A, 80 W) the no-load power factor is: A. 0.2 B. 0.4 C. 0.8 D. 0.32 Answer: B. cos(phi0) = 80/(250 x 0.8) = 0.4. (Key point: Power factor at no load) 2. R0 and X0 are found from: A. V0 / I0 for both B. V0/Iw and V0/Imu respectively C. P0/I0^2 and Q0/I0^2 D. V0 Iw and V0 Imu Answer: B. R0 = V0/Iw = 781.25 ohm, X0 = V0/Imu = 340.97 ohm. (Key point: R0 and X0) 3. Primary is the 250 V side. SC values measured on the HV side are referred to the primary by multiplying by: A. 4 B. 16 C. 0.25 D. 0.0625 Answer: D. Impedances scale by the voltage ratio squared: (250/1000)^2 = 0.0625. (Key point: Referral factor) 4. R01 for this transformer is: A. 1.2 ohm B. 0.075 ohm C. 0.494 ohm D. 0.5 ohm Answer: B. R02 = 120/10^2 = 1.2 ohm; R01 = 1.2 x 0.0625 = 0.075 ohm. (Key point: SC parameters) ## Close variants set in other exams - [Equivalent circuit of 5 kVA 200/400 V transformer](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aoc-sc-5kva-200-400-primary) — Electrical Machines I, chapter 2, asked 2× ## Related in Electrical Machines I - [Equivalent circuit of 8 kVA 400/120 V transformer](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aoc-sc-8kva-400-120-hv) — Electrical Machines I, chapter 2 - [Equivalent circuit and half-load efficiency of 50 kVA transformer](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3A50kva-2500-250-test-secondary-half) — Electrical Machines I, chapter 2 - [Equivalent circuit of 20 kVA 250/2500 V transformer from tests](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aoc-sc-20kva-250-2500) — Electrical Machines I, chapter 2, asked 3× - [Equivalent circuit of 20 kVA 220/2200 V transformer](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aoc-sc-20kva-220-2200-primary) — Electrical Machines I, chapter 2 - [Transformer equivalent circuit referred to primary](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aequivalent-circuit-referred-primary) — Electrical Machines I, chapter 2 - [Induction motor equivalent circuit from no-load and blocked rotor tests](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aim-noload-blocked-400v-equivalent) — Electrical Machines I, chapter 5 ## Related in other subjects - [10 kVA 250/1000 V tests, equivalent circuit](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Atf-10kva-250-1000-parameters) — Electrical Machines, chapter 2 - [20 kVA 250/2500 V test parameters](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Atransformer-20kva-250-2500-primary) — Electrical Machine, chapter 2, asked 2× - [20 kVA 250/2500 V tests, equivalent circuit](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Atf-20kva-250-2500-parameters) — Electrical Machines, chapter 2, asked 2× - [25 kVA 250/2500 V tests, equivalent circuit](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Atf-25kva-250-2500-parameters) — Electrical Machines, chapter 2, asked 2×