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?
xR and xA are, respectively, the rms and average values of x(t) = x(t - T), and similarly, yR and yA are, respectively, the rms and average values of y(t) = kx(t), k, T are independent of t. Which of the following is true?
The voltage 'V' and current 'A' across a load are as follows.
V(t) = 100 sin(ωt)
i(t) = 10 sin(ωt - 60°) + 2 sin(3ωt) + 5 sin(5ωt)
The average power consumed by the load, in W, is___________.
The rms value of a sinusoidal ac current is numerically equal to its value at an angle of _______ degrees
A resistor connected to a DC supply of 20 V produces the same heating effect as an AC supply connected across the same resistor. What is the RMS value of the AC voltage?
