Final answer:
To find the RMS value of the function v = 282.8(sin314t), we identify the peak voltage as 282.8 V and use the formula Vrms = Vo/√2 to calculate the RMS value, which results in 200 V.
Step-by-step explanation:
If the voltage is described by the equation v = 282.8(sin314t), to find the rms value of this sinusoidal voltage function, we use the formula for the peak voltage (Vo) and convert it to the root mean square (RMS) value. The formula for RMS value in the case of a sine wave is Vrms = Vo/√2. Given that Vo is the peak voltage, the RMS value can be calculated.
First, determine Vo. Since the given voltage function has the form v = Vo sin(ωt), we can see that Vo is the coefficient before the sine function, which in this case is 282.8 V. Now, we can use the equation to find the RMS voltage:
Vrms = Vo/√2
Vrms = 282.8 V / 1.414
Vrms = 200 V
Therefore, the RMS value of the given voltage is 200 V.