Answer
(a) $a:~~-100~V$
$b:~~60~V$
$c:~~80~V$
(b) Phasor $a:~~$ The magnitude of the emf is decreasing.
Phasor $b:~~$ The magnitude of the emf is decreasing.
Phasor $c:~~$ The magnitude of the emf is increasing.
Work Step by Step
(a) We can write the general expression for the emf:
$V = V_0~cos~(\omega t + \phi)$
The instantaneous value of the emf is the horizontal component of $V$
From the graph, we can find the instantaneous value of the emf for each phasor:
$a:~~-100~V$
$b:~~60~V$
$c:~~80~V$
(b) The phasors rotate counterclockwise. The magnitude of the emf is increasing when the phasor is getting farther away from the vertical axis and getting closer to the horizontal axis.
Phasor $a$ is getting farther away from the horizontal axis and getting closer to the vertical axis. Therefore, the magnitude of the emf is decreasing.
Phasor $b$ is getting farther away from the horizontal axis and getting closer to the vertical axis. Therefore, the magnitude of the emf is decreasing.
Phasor $c$ is getting farther away from the vertical axis and getting closer to the horizontal axis. Therefore, the magnitude of the emf is increasing.
