# Step-by-Step Solution ## **Given Data** - Transformer rating: \(100 \text{ kVA}\) - Primary voltage: \(10 \text{ kV}\) - Secondary voltage: \(380 \text{ V}\) - Copper losses during short-circuit test: \(P_{cu} = 1200 \text{ W}\) - Core losses during open-circuit test: \(P_{core} = 200 \text{ W}\) ## **Purpose** Show that **during the short-circuit test, the core (iron) losses can be neglected**. --- ## **Step 1: Understanding Test Procedures** ### **Open-Circuit (OC) Test** - Low current, rated voltage applied (usually to LV side). - Measures core (iron) losses, since magnetizing current is small. - **Copper losses are negligible** (because current is low). ### **Short-Circuit (SC) Test** - Short LV winding, apply voltage to HV winding. - Voltage is just enough to get rated current flowing. - **Copper losses dominate** (since current is rated). - **Core losses are low** (since applied voltage is much less than rated). --- ## **Step 2: Core Losses Depend on Voltage** - Core losses (\(P_{core}\)) depend on the applied voltage and frequency. - **At rated voltage** (\(10\,\text{kV}\)), core losses are \(200\,\text{W}\) (from OC test). - **During SC test**, the applied voltage (\(V_{sc}\)) is **much lower** than rated voltage. --- ## **Step 3: Estimate Voltage during SC Test** Let \(V_{sc}\) be the voltage applied during the SC test. - Typically, \(V_{sc}\) is about 5–10% of rated voltage. - Let's estimate at **10% of rated voltage**: \[ V_{sc} = 0.1 \times 10,000 = 1,000\,\text{V} \] --- ## **Step 4: Core Losses at SC Test Voltage** Core losses are proportional to the **square of the applied voltage**: \[ P_{core,sc} = P_{core,rated} \times \left( \frac{V_{sc}}{V_{rated}} \right)^2 \] Plug in values: \[ P_{core,sc} = 200\,\text{W} \times \left( \frac{1,000}{10,000} \right)^2 = 200\,\text{W} \times (0.1)^2 = 200\,\text{W} \times 0.01 = 2\,\text{W} \] --- ## **Step 5: Compare Core Losses and Copper Losses in SC Test** - **Copper losses during SC test:** \(1200\,\text{W}\) - **Core losses during SC test:** \(2\,\text{W}\) \[ \frac{P_{core,sc}}{P_{cu}} = \frac{2}{1200} = 0.00167 \approx 0.17\% \] --- ## **Step 6: Conclusion** - **Core losses during SC test are negligible** compared to copper losses (less than 0.2% of copper losses). - This justifies ignoring core losses in the short-circuit test. --- ## **Final Answer** **During the short-circuit test, the core losses are only \(2\,\text{W}\) compared to copper losses of \(1200\,\text{W}\), i.e., less than 0.2%. Therefore, the core losses can be neglected during the short-circuit test.**