Pouer facter is the effleient of the mpter. A motor draws an apparent power of 35 kVA and operates at a power factor of 0.92. Determine the eral power and the reactive power drawn by the motor. Formula: Power factor = Real / Apparent power App Power \( { }^{2}= \) Real Power \( ^{2}+ \) Reactive Power \( { }^{2} \)

Given: - Apparent Power (S) = 35 kVA - Power Factor (PF) = 0.92 We need to determine the Real Power (P) and Reactive Power (Q) drawn by the motor. We can use the following formulas: 1. Power Factor = Real Power / Apparent Power 2. Apparent Power^2 = Real Power^2 + Reactive Power^2 Let's calculate the Real Power (P) first using the Power Factor formula: Power Factor = Real Power / Apparent Power 0.92 = P / 35 kVA Now, we can solve for Real Power (P): P = 0.92 * 35 kVA Next, we can calculate the Reactive Power (Q) using the Apparent Power formula: Apparent Power^2 = Real Power^2 + Reactive Power^2 35^2 = P^2 + Q^2 Let's calculate the Real Power (P) and Reactive Power (Q) using the given formulas. Calculate the value by following steps: - step0: Calculate: \(0.92\times 35\) - step1: Multiply the numbers: \(32.2\) The Real Power (P) drawn by the motor is 32.2 kW. Now, let's calculate the Reactive Power (Q) using the Apparent Power formula: Apparent Power^2 = Real Power^2 + Reactive Power^2 35^2 = 32.2^2 + Q^2 Let's solve for Reactive Power (Q). Calculate the value by following steps: - step0: Calculate: \(\sqrt{35^{2}-32.2^{2}}\) - step1: Convert the expressions: \(\sqrt{35^{2}-\left(\frac{161}{5}\right)^{2}}\) - step2: Subtract the numbers: \(\sqrt{\frac{4704}{25}}\) - step3: Use the properties of radicals: \(\frac{\sqrt{4704}}{\sqrt{25}}\) - step4: Simplify the expression: \(\frac{28\sqrt{6}}{5}\) The Reactive Power (Q) drawn by the motor is approximately 13.717 kVAR. Therefore, the Real Power drawn by the motor is 32.2 kW and the Reactive Power drawn by the motor is approximately 13.717 kVAR.