Which of the following factor have value of 1.1 for sinusoidal alternating current only?
Form factor
Understanding Factors for Sinusoidal Alternating Current
When analyzing alternating current (AC) waveforms, certain factors are used to describe their characteristics based on their peak, RMS (Root Mean Square), and average values. The question asks about a specific factor that has a value of approximately 1.1 for a sinusoidal AC only. Let's examine the key factors:
- Form factor: This is defined as the ratio of the RMS value to the average value (usually taken over a half-cycle for symmetrical waveforms like a sinusoid, as the average over a full cycle is zero).
- Crest factor (also known as Peak factor or Amplitude factor): This is defined as the ratio of the peak value to the RMS value.
Calculating Factors for a Sinusoidal Waveform
Let's consider a sinusoidal voltage waveform given by \( v(t) = V_p \sin(\omega t) \), where \( V_p \) is the peak voltage.
- The peak value is \( V_p \).
- The RMS value for a sinusoidal waveform is \( V_{rms} = \frac{V_p}{\sqrt{2}} \).
- The average value over a half-cycle (or average of the absolute value over a full cycle) for a sinusoidal waveform is \( V_{avg} = \frac{2V_p}{\pi} \).
Form Factor Calculation
The Form factor is the ratio of the RMS value to the average value:
\[ \text{Form factor} = \frac{V_{rms}}{V_{avg}} = \frac{\frac{V_p}{\sqrt{2}}}{\frac{2V_p}{\pi}} = \frac{V_p}{\sqrt{2}} \times \frac{\pi}{2V_p} = \frac{\pi}{2\sqrt{2}} \]Now let's calculate the approximate numerical value:
\[ \text{Form factor} \approx \frac{3.14159}{2 \times 1.41421} \approx \frac{3.14159}{2.82842} \approx 1.1107 \]This value, approximately 1.11, is very close to 1.1.
Crest Factor Calculation
The Crest factor is the ratio of the peak value to the RMS value:
\[ \text{Crest factor} = \frac{V_{p}}{V_{rms}} = \frac{V_p}{\frac{V_p}{\sqrt{2}}} = \sqrt{2} \]Now let's calculate the approximate numerical value:
\[ \text{Crest factor} \approx 1.414 \]Comparing Values and Identifying the Factor
We calculated the following values for a sinusoidal alternating current:
- Form factor \(\approx 1.11\)
- Crest factor \(\approx 1.414\)
- Peak factor = Amplitude factor = Crest factor \(\approx 1.414\)
The question asks which factor has a value of 1.1 for sinusoidal alternating current. Comparing our calculated values to the options, the Form factor is approximately 1.11, which is the value closest to 1.1 among the common factors. Therefore, the factor with a value of approximately 1.1 for sinusoidal AC is the Form factor.
Important Questions from RMS Value of Time Varying Waveforms
RMS value is defined based on which of the following?
Which of the following methods used for average value determination is convenient for non-sinusoidal waves?
For a sinusoidal waveform, the RMS value of current will be _______ times the maximum value of current.
An alternating voltage has the equation V(t) = 200 sin 377t V. What is the value of r.m.s. voltage and frequency?
Which of the following factors indicates that wave departs from a sinusoidal condition?
