Let's understand the relationship between the maximum value (peak voltage) and the peak-to-peak voltage of a sinusoidal waveform.

Understanding Sinusoidal Voltage Peaks

A sinusoidal voltage is a type of alternating voltage that varies smoothly over time, resembling a sine wave when plotted on a graph. Key values associated with a sinusoidal voltage include:

• Maximum Value (\(V_p\)): This is the highest instantaneous voltage reached during a cycle. It is also often called the peak voltage.
• Minimum Value: This is the lowest instantaneous voltage reached during a cycle. For a standard sinusoidal waveform centered around zero, the minimum value is the negative of the maximum value (\(-V_p\)).
• Peak-to-Peak Voltage (\(V_{pp}\)): This is the total voltage difference between the maximum (positive peak) and the minimum (negative peak) values in one cycle.

Relating Maximum Value and Peak-to-Peak Voltage

For a symmetrical sinusoidal waveform, the peak-to-peak voltage is twice the maximum value (peak voltage). This is because the waveform goes from \(-V_p\) to \(+V_p\).

The relationship can be expressed mathematically as:

\(V_{pp} = V_p - (-V_p)\)

\(V_{pp} = V_p + V_p\)

\(V_{pp} = 2 \times V_p\)

Calculating the Peak-to-Peak Voltage

The question provides the maximum value of the sinusoidal voltage as 110 V.

Given:

• Maximum Value, \(V_p = 110\) V

We need to find the peak-to-peak voltage, \(V_{pp}\).

Using the formula \(V_{pp} = 2 \times V_p\):

\(V_{pp} = 2 \times 110\) V

\(V_{pp} = 220\) V

Therefore, the peak-to-peak voltage is 220 V.