Alternating Voltage Equation Analysis

The given equation for the alternating voltage is V(t) = 200 sin 377t V.

This equation is in the standard form of an alternating voltage:

\[ V(t) = V_0 \sin(\omega t) \]

Where:

• \(V_0\) is the peak voltage or maximum voltage.
• \(\omega\) is the angular frequency in radians per second.
• t is the time in seconds.

Identifying Peak Voltage and Angular Frequency

Comparing the given equation V(t) = 200 sin 377t V with the standard form \(V(t) = V_0 \sin(\omega t)\), we can identify the values:

• Peak voltage, \(V_0 = 200\) V
• Angular frequency, \(\omega = 377\) rad/s

Calculating RMS Voltage

The root mean square (r.m.s.) voltage for a sinusoidal alternating voltage is related to the peak voltage by the formula:

\[ V_{rms} = \frac{V_0}{\sqrt{2}} \]

Substitute the peak voltage \(V_0 = 200\) V into the formula:

\[ V_{rms} = \frac{200}{\sqrt{2}} \text{ V} \]

Calculating Frequency

The angular frequency (\(\omega\)) is related to the frequency (f) in Hertz (Hz) by the formula:

\[ \omega = 2\pi f \]

We have \(\omega = 377\) rad/s. We can rearrange the formula to solve for the frequency f:

\[ f = \frac{\omega}{2\pi} \]

Substitute the value of \(\omega\):

\[ f = \frac{377}{2\pi} \text{ Hz} \]

To find the numerical value, we can approximate \(2\pi \approx 2 \times 3.14159 = 6.28318\).

\[ f \approx \frac{377}{6.28318} \approx 59.99 \text{ Hz} \]

This value is very close to 60 Hz. In electrical engineering contexts, 377 rad/s is commonly used as an approximation for \(120\pi\) rad/s, which corresponds exactly to 60 Hz (\(120\pi \approx 376.99\)).

Therefore, the frequency is 60 Hz.

Summary of Results

Based on the calculations:

• R.M.S. voltage = \(\frac{200}{\sqrt{2}}\) V
• Frequency = 60 Hz

These values correspond to one of the given options.