Finding RMS Value from Peak Value of Sinusoidal Supply

The question asks us to determine the Root Mean Square (RMS) value of a sinusoidal AC supply given its peak value.

Understanding RMS Value

The RMS value of an alternating current (AC) or voltage represents the equivalent DC value that would produce the same amount of power dissipation in a resistive load. For a sinusoidal waveform, the RMS value is related to the peak (or maximum) value by a specific formula.

Formula for RMS Value

The relationship between the RMS value ($V_{rms}$) and the peak value ($V_p$) of a sinusoidal voltage is given by the formula:

$V_{rms} = \frac{V_p}{\sqrt{2}}$

Where:

• $V_{rms}$ is the RMS voltage.
• $V_p$ is the peak voltage (the maximum value the voltage reaches).

Calculation Steps

We are given the peak value of the sinusoidal supply:

$V_p = 50$ V

Now, we can substitute this value into the formula to find the RMS value:

1. Start with the formula: $V_{rms} = \frac{V_p}{\sqrt{2}}$
2. Substitute the given peak value ($V_p = 50$ V): $V_{rms} = \frac{50}{\sqrt{2}}$ V

Therefore, the RMS value of the sinusoidal supply is $\frac{50}{\sqrt{2}}$ Volts.

Identifying the Correct Option

Comparing our calculated RMS value, $\frac{50}{\sqrt{2}}$ V, with the provided options:

• Option 1: $50\sqrt{2}$
• Option 2: $\frac{50}{\sqrt{2}}$
• Option 3: $25\sqrt{3}$
• Option 4: $\frac{25}{\sqrt{2}}$

The calculated value matches Option 2.