Question

Optimum number of stages for Cockcroft-Walton voltage multiplier circuit are:

• A. \( \sqrt{\frac{V_{\max}}{I f C}} \)
• B. \( \sqrt{\frac{I f C}{V_{\max}}} \)
• C. \( \sqrt{\frac{V_{\max} f}{I C}} \)
• D. \( \sqrt{\frac{V_{\max} f C}{I}} \)

Hint:

The optimum number of stages in a Cockcroft-Walton voltage multiplier is given by: \[ n_{\text{opt}} = \sqrt{\frac{V_{\max}}{I f C}} \] Balancing capacitance, frequency, and load current helps optimize voltage gain efficiency.

Answer 1

The Correct Option is A

Step 1: Cockcroft-Walton Voltage Multiplier The Cockcroft-Walton (CW) multiplier is a circuit that generates high DC voltages from an AC input using stages of capacitors and diodes. 
Step 2: Optimum Number of Stages The voltage drop in a CW multiplier increases with the number of stages, affecting efficiency. The optimal number of stages (\( n \)) is given by: \[ n_{\text{opt}} = \sqrt{\frac{V_{\max}}{I f C}} \] where:
- \( V_{\max} \) = Maximum output voltage,
- \( I \) = Load current,
- \( f \) = Frequency of AC supply,
- \( C \) = Capacitance of the multiplier capacitors. 
Step 3: Evaluating options: 
- (A) Correct: Matches the standard formula for optimal stage number.
- (B) Incorrect: Inverted ratio, incorrect formula.
- (C) Incorrect: Incorrect placement of terms.
- (D) Incorrect: Incorrect expression for capacitance impact.