A sinusoidal voltage is given by the expression v = 300 \cos \left(120\pi t + 30^{°}\right).
a) What is the period of the voltage in milliseconds?
b) What is the frequency in hertz?
c) What is the magnitude of v at t = 2.778 ms?
d) What is the rms value of v ?
a) From the expression for v ,\omega=120 \pi \frac{rad}{s}.
Because \omega= \frac{2\pi}{T},T=\frac{2\pi}{\omega}=\frac{1}{60}s ,or 16.667 ms.
b) The frequency is \frac{1}{T} , or 60 Hz.
c) From (a),\omega= \frac{2\pi}{16.667}; thus, at t=2.778 ms, ωt is nearly 1.047 rad, or 60^{\circ }. Therefore,v(2.778 ms)= 300 \cos \left(60^{\circ } + 30^{\circ }\right)=0 V.
d) V_{rms}=\frac{300}{\sqrt{2}}= 212.13 V.