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Question 2.2: Wall outlet voltage. Find an equation like (2.1) for the 120......

Wall outlet voltage. Find an equation like (2.1) for the 120-V, 60-Hz voltage delivered to your home.

i = I_{m} \cos \left(\omega t + \theta \right)     (2.1)

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From (2.11), the amplitude (magnitude, peak value) of the voltage is

\boxed{V_{rms}  =  V_{m}\sqrt{\frac{1}{2}}  =  \frac{V_{m}}{\sqrt{2} }}         (2.11)

V_{m}  =  \sqrt{2} V_{rms}  =  120 \sqrt{2}  =  169.7  V

The angular frequency ω is

\omega  =  2\pi f  =  2 \pi 60  =  377  {rad}/{s}

The waveform is thus

v = 169.7 cos 377t

It is conventional practice to treat the incoming voltage as having zero phase angle, so that all currents will have phase angles measured relative to that reference voltage.

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