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For a 0∘ reference sine wave with an RMS value of 9 V, determine its instantaneous value at π/−8rad The result should be in V Calculate Answers to 2 decimal points

User Joeystdio
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Final answer:

To find the instantaneous voltage of a sine wave at π/-8 rad with an RMS value of 9 V, calculate the peak voltage using Vp = Vrms√2 and multiply this by sin(π/-8) to obtain the instantaneous voltage.

Step-by-step explanation:

To determine the instantaneous value of a 0° reference sine wave with a RMS value of 9 V at π/-8 rad, we will first need to calculate the peak (or amplitude) value of this sine wave. The relationship between the RMS value (Vrms) and the peak value (Vp) for a sine wave is Vrms = Vp/√2. Solving for Vp gives us Vp = Vrms √2. Therefore, if Vrms is 9 V, the peak value will be Vp = 9 V √2.

Next, we apply the sine function to find the instantaneous value at a specific point in the cycle, which is sin(π/-8) multiplied by the peak value. The instantaneous voltage Vi is given by Vi = Vp × sin(θ), where θ is the angle in radians. Therefore, Vi = 9 V√2 × sin(π/-8).

After calculating the sine of π/-8 radians and performing the multiplication, we can find the required instantaneous voltage at this particular phase of the sine wave.

User UiUx
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