Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bart Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bart A three-phase 1000 HP, 4160 V induction motor operates at an efficiency Bartieby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartieby Bartleby Bart of 95% and a power factor of 0.85 lagging. If the motor is delivering the Tueby Bart rated power to a load, Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bart a) Calculate P, Q. and IL.leby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bart b) A 300 KVAB capacitor bank is added in parallel with motor, calculate Bart the new line current. Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bart Bale c) Draw the power triangle to demonstrate the power factor reduction. Rartlahu Rartlahu Rartlahu Rartlahu Rartlahu RartlohuRartleby Bart Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bart Notes: Rated motor power is 1000 HP. 1 HP = 746 watts. Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bart Efficiency is defined as n=Pout/Pin Lrartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bart Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bartleby Bart Bartleby Bartlehy Bartleby Bartleby Bartlehy Bartleby Bartlehy Bartleby Bartlehy Bartlehy Bart

Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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**Title: Understanding Power Factor and Efficiency in Induction Motors**

**Introduction:**

This educational module focuses on the analysis of a three-phase 1000 HP, 4160 V induction motor. This motor operates at an efficiency of 95% and a power factor of 0.85 lagging. The goal is to explore the effects of these parameters on the motor's performance when it delivers rated power to a load.

**Content:**

**1. Calculating Power Parameters:**

*a) Calculate P, Q, and IL:*

- **P (Active Power):** The real power delivered to the load, measured in watts (W) or kilowatts (kW).
- **Q (Reactive Power):** The power stored and released by the inductive components of the load, measured in volt-amperes reactive (VAR) or kilovar (kVAR).
- **IL (Line Current):** The current flowing through the power line to the motor.

**2. Adding a Capacitor Bank:**

*b) A 300 kVAR capacitor bank is added in parallel with the motor, calculate the new line current:*

- The addition of the capacitor bank improves the power factor, reducing the reactive power demand on the supply system and thus affecting the line current.

**3. Power Factor Reduction:**

*c) Draw the power triangle to demonstrate the power factor reduction:*

- The power triangle visually represents the relationship between active power (P), reactive power (Q), and apparent power (S). By incorporating a capacitor bank, the triangle changes, showcasing reduced reactive power.

**Notes:**

- Rated motor power is 1000 HP. 
- 1 HP = 746 watts.
- Efficiency is defined as η = Pout / Pin

**Conclusion:**

This exploration illustrates the significance of efficiency and power factor in the performance and economic operation of induction motors. By enhancing the power factor, overall efficiency improves, leading to cost savings and reduced energy losses.
Transcribed Image Text:**Title: Understanding Power Factor and Efficiency in Induction Motors** **Introduction:** This educational module focuses on the analysis of a three-phase 1000 HP, 4160 V induction motor. This motor operates at an efficiency of 95% and a power factor of 0.85 lagging. The goal is to explore the effects of these parameters on the motor's performance when it delivers rated power to a load. **Content:** **1. Calculating Power Parameters:** *a) Calculate P, Q, and IL:* - **P (Active Power):** The real power delivered to the load, measured in watts (W) or kilowatts (kW). - **Q (Reactive Power):** The power stored and released by the inductive components of the load, measured in volt-amperes reactive (VAR) or kilovar (kVAR). - **IL (Line Current):** The current flowing through the power line to the motor. **2. Adding a Capacitor Bank:** *b) A 300 kVAR capacitor bank is added in parallel with the motor, calculate the new line current:* - The addition of the capacitor bank improves the power factor, reducing the reactive power demand on the supply system and thus affecting the line current. **3. Power Factor Reduction:** *c) Draw the power triangle to demonstrate the power factor reduction:* - The power triangle visually represents the relationship between active power (P), reactive power (Q), and apparent power (S). By incorporating a capacitor bank, the triangle changes, showcasing reduced reactive power. **Notes:** - Rated motor power is 1000 HP. - 1 HP = 746 watts. - Efficiency is defined as η = Pout / Pin **Conclusion:** This exploration illustrates the significance of efficiency and power factor in the performance and economic operation of induction motors. By enhancing the power factor, overall efficiency improves, leading to cost savings and reduced energy losses.
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