What is the RMS value of an AC voltage given by V(t) = V0 sin(ωt)?

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Question: What is the RMS value of an AC voltage given by V(t) = V0 sin(ωt)?

Options:

Correct Answer: V0/√2

Solution:

The RMS value of an AC voltage is given by V_rms = V0/√2.

What is the RMS value of an AC voltage given by V(t) = V0 sin(ωt)?

What is the RMS value of an AC voltage given by V(t) = V0 sin(ωt)?

Step 1: Understand that V(t) = V0 sin(ωt) represents an alternating current (AC) voltage, where V0 is the peak voltage.
Step 2: The RMS (Root Mean Square) value is a way to express the effective value of an AC voltage.
Step 3: The formula for the RMS value of a sinusoidal voltage is V_rms = V0 / √2.
Step 4: This means to find the RMS value, you take the peak voltage (V0) and divide it by the square root of 2 (approximately 1.414).
Step 5: Therefore, the RMS value of the given AC voltage V(t) = V0 sin(ωt) is V_rms = V0 / √2.

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