Question

The form factor for DC supply voltage is always

• A. Zero
• B. Unity
• C. Infinity
• D. Any value between 0 and 1

Hint:

For a DC quantity, \[ V_{\text{rms}}=V_{\text{avg}}. \] Hence the form factor of DC is always \[ 1. \] For a sinusoidal waveform, \[ \text{Form Factor}=\frac{1.11}{1}. \]

Answer 1

The Correct Option is B

Concept: Form factor is an important parameter used in AC circuit analysis. It is defined as the ratio of the RMS (Root Mean Square) value of a waveform to its average value. Mathematically, \[ \text{Form Factor} = \frac{\text{RMS Value}}{\text{Average Value}}. \] For alternating waveforms such as sinusoidal, triangular, or square waves, the RMS value and average value are generally different. However, for a DC quantity, both values are identical.

Step 1: Write the definition of form factor.
\[ \text{Form Factor} = \frac{V_{\text{rms}}}{V_{\text{avg}}}. \] This formula is valid for both voltage and current waveforms.

Step 2: Determine the RMS value of a DC voltage.
Let the DC voltage be \(V\). Since the voltage remains constant with time, \[ V(t)=V. \] Therefore, \[ V_{\text{rms}} = \sqrt{\frac{1}{T}\int_0^T V^2\,dt}. \] \[ = \sqrt{\frac{V^2T}{T}}. \] \[ = V. \] Hence, \[ V_{\text{rms}}=V. \]

Step 3: Determine the average value of the DC voltage.
The average value is \[ V_{\text{avg}} = \frac{1}{T}\int_0^T V\,dt. \] \[ = \frac{VT}{T}. \] \[ = V. \] Thus, \[ V_{\text{avg}}=V. \]

Step 4: Calculate the form factor.
Substituting into the formula, \[ \text{Form Factor} = \frac{V}{V}. \] \[ =1. \] Therefore, \[ \boxed{\text{Form Factor}=1} \] or \[ \boxed{\text{Unity}}. \]