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538 ⏐⏐⏐ SINUSOIDAL ALTERNATING WAVEFORMS<br />

c. See Fig. 13.29.<br />

i � 2 cos(qt � 10°) � 2 sin(qt � 10° � 90°)<br />

� 2 sin(qt � 100°)<br />

i leads v by 110°, or v lags i by 110°.<br />

2<br />

d. See Fig. 13.30.<br />

i<br />

100°<br />

Note<br />

�sin(qt � 30°) � sin(qt � 30° � 180°)<br />

� sin(qt � 150°)<br />

v leads i by 160°, or i lags v by 160°.<br />

�<br />

–<br />

2<br />

10°<br />

Or using<br />

v<br />

0 � 3<br />

10° 2<br />

2 �<br />

�<br />

2<br />

–<br />

�t<br />

2<br />

� � �<br />

0<br />

110°<br />

150°<br />

160°<br />

FIG. 13.29<br />

Example 13.12; i leads v by 110°.<br />

2<br />

�<br />

2<br />

v<br />

�<br />

360°<br />

1<br />

200°<br />

3<br />

2 �<br />

i<br />

3<br />

2�<br />

FIG. 13.30<br />

Example 13.12; v leads i by 160°.<br />

Note<br />

�sin(qt � 30°) � sin(qt � 30° � 180°)<br />

� sin(qt � 210°)<br />

i leads v by 200°, or v lags i by 200°.<br />

e. See Fig. 13.31.<br />

5<br />

2 �<br />

By choice<br />

i ��2 cos(qt � 60°) � 2 cos(qt � 60° � 180°)<br />

� 2 cos(qt � 240°)<br />

2<br />

v<br />

–<br />

2<br />

3<br />

2 �<br />

2<br />

�<br />

2 5<br />

2 �<br />

� 0 �<br />

150°<br />

� 3�<br />

i<br />

FIG. 13.31<br />

Example 13.12; v and i are in phase.<br />

3<br />

3�<br />

�t<br />

�t

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