## Translation **10p B)** Find the efficiency of a motor, which has the following values on its label: three-phase triangle, 380 volts, 4.5 kW, 10 A, Cosφ .86, 145 rpm, 50 Hz, and also find the torque in **Newton-meters**. --- ## Step-by-Step Solution ### **Given Data** - Voltage (\( V \)) = 380 V - Power (\( P \)) = 4.5 kW = 450 W - Current (\( I \)) = 10 A - Power factor (\( \cos\phi \)) = .86 - Rotational speed (\( n \)) = 145 rpm - Frequency (\( f \)) = 50 Hz --- ### **1. Input Apparent Power Calculation** For a three-phase system: \[ S = \sqrt{3} \cdot V \cdot I \] \[ S = \sqrt{3} \cdot 380 \cdot 10 = 1.732 \cdot 380 = 6581.6 \text{ VA} \] --- ### **2. Input Active Power Calculation** \[ P_{\text{input}} = \sqrt{3} \cdot V \cdot I \cdot \cos\phi \] \[ P_{\text{input}} = 1.732 \cdot 380 \cdot 10 \cdot .86 = 1.732 \cdot 380 \cdot .86 = 6581.6 \cdot .86 = 566.2 \text{ W} \] --- ### **3. Efficiency Calculation** \[ \eta \frac{P_{\text{output}}}{P_{\text{input}}} \] \[ \eta =frac{450}{566.2} = .796 \approx 79.6\% \] --- ### **4. Torque Calculation in Newton-meters** The mechanical power output: \[ P_{\text{output}} = 2\pi n T / 60 \] where: - \( P_{\text{output}} \) = output power (W) - \( n \) = speed (rpm) - \( T \) = torque (Nm) Rearranged for torque: \[ T = \frac{P_{\text{output}} \times 60}{2\pi n} \] Substitute values: \[ T = \frac{450 \times 60}{2 \pi \times 145} \] \[ T = \frac{270000}{911.6} \approx 29.64 \text{ Nm} \] --- ## **Summary of Answers** - **Efficiency (\( \eta \))**: **79.6%** - **Torque (\( T \))**: **29.6 Nm** (rounded to 1 decimal place)