Answered: A farm house is located at the end of a…

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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Question

A farm house is located at the end of a country road in northern Michigan. The Thévenin impedance seen looking back into the power line from the electrical distribution panel is 0.2+j0.2 Ω. The Thévenin voltage is 240 V rms 60 Hz ac. A 2-hp 240-V-rms capacitor-start motor is used for pumping water. We want to estimate the voltage drop observed in the house when the motor starts. Typically, such a motor has a power factor of 75 percent and an efficiency of 80 percent at full load. Also, the starting current can be estimated as six times the full-load current. Estimate the worst-case percentage voltage drop observed when the motor starts.

Expert Solution

Step 1

Given data:

$\begin{array}{rcl} P_{o u t} & = & 2 hp \\ V_{r m s} & = & 240 V \end{array}$

The expression for the output power is given as,

$\begin{array}{rcl} P_{o u t} & = & 2 h p \\ = & 2 \times 746 \\ = & 1492 W \end{array}$

The expression for the input power is given as,

$\begin{array}{rcl} % η & = & \frac{P_{o u t}}{P_{i n}} \times 100 \\ 80 & = & \frac{1492}{P_{i n}} \times 100 \\ P_{i n} & = & 1865 W \end{array}$

Step 2

Now the expression for the current is given as,

$\begin{array}{rcl} I & = & \frac{P_{i n}}{V \cos θ} \\ = & \frac{1865}{240 \times 0.75} \\ = & 10.36 A \end{array}$

The expression for the starting current is given as,

$\begin{array}{rcl} I_{s} & = & 6 I \\ = & 6 \times 10.36 \\ = & 62.16 A \end{array}$

Calculating thevenin's impedance,

$\begin{array}{rcl} Z_{t h} & = & 0.2 + 0.2 j \\ = & \sqrt{0 . 2^{2} + 0 . 2^{2}} ∠ - \tan^{- 1} (\frac{0.2}{0.2}) \\ = & 0.283 ∠ - 45^{°} \end{array}$

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