Power and Energy Devices and Systems (PE)

Question Set 1: Energy Conversion and Reference Frame Theory

August 2012

## Contents

## Problem 1

# Solution

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## Problem 2

# Solution

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## Problem 3

# Solution

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## Trigonometric Identities

- $ \cos A \cos B = 0.5\left(\cos(A + B) + \cos(A - B)\right) $
- $ \sin A \sin B = 0.5\left(\cos(A - B) - \cos(A + B)\right) $
- $ \sin A \cos B = 0.5\left(\sin(A + B) + \sin(A - B)\right) $
- $ \cos(A \pm B) = \cos A \cos B \mp \sin A \sin B $
- $ \sin(A \pm B) = \sin A \cos B \pm \cos A \sin B $