Question

The rms value of a.c with peak value of \(200\) V is

• A. \(100\,\text{V}\)
• B. \(\frac{200}{\sqrt{2}}\,\text{V}\)
• C. \(300\,\text{V}\)
• D. \(200\sqrt{2}\,\text{V}\)
• E. \(\frac{200}{\sqrt{3}}\,\text{V}\)

Hint:

Always remember: \(V_{\text{rms}} = \frac{V_0}{\sqrt{2}}\) for sinusoidal AC signals.

Answer 1

The Correct Option is B

Step 1: Recall the relation between peak and rms value.
For alternating current: \[ V_{\text{rms}} = \frac{V_0}{\sqrt{2}} \] where \(V_0\) is peak voltage.

Step 2: Identify the given value.
\[ V_0 = 200\,\text{V} \]

Step 3: Substitute into the formula.
\[ V_{\text{rms}} = \frac{200}{\sqrt{2}} \]

Step 4: Simplify if needed.
\[ V_{\text{rms}} = 100\sqrt{2}\,\text{V} \] But in the given options, the expression form is preferred.

Step 5: Interpret the result.
RMS value represents the effective value of AC that produces the same heating effect as DC.

Step 6: Compare with options.
The expression \(\frac{200}{\sqrt{2}}\) matches option (2).

Step 7: Final answer.
\[ \boxed{\frac{200}{\sqrt{2}}\,\text{V}} \]