Question E7D14:
What is the purpose of connecting equal-value resistors across power supply filter capacitors connected in series?  

Choices:  
A: Equalize the voltage across each capacitor  
B: Discharge the capacitors when voltage is removed  
C: Provide a minimum load on the supply  
D: All these choices are correct    

Correct Answer is  D: All these choices are correct  

To protect and stabilize series filter capacitors, equal-value resistors (often called balancing or bleeder resistors) across each capacitor serve three purposes. That’s why “All these choices are correct” is the right answer.

1) Why the correct answer is correct
- Equalize voltage across each capacitor: Real capacitors have different leakage currents, so series capacitors won’t share voltage equally by themselves. Equal-value resistors form a resistive divider that forces each capacitor to see approximately half the total voltage (or an equal fraction if more than two), preventing overvoltage on any one capacitor.
- Discharge the capacitors when voltage is removed: These resistors provide a discharge path so the stored energy bleeds off after power is turned off, improving safety.
- Provide a minimum load on the supply: The bleeder current improves regulation by preventing the no-load voltage from rising excessively and swamps capacitor leakage variations, ensuring stable operation.

2) Why the other choices are “incorrect” on their own
- A, B, and C are each true, but each is only part of the purpose. Since all are true simultaneously, the most complete answer is D: All these choices are correct.

3) Useful formulas and rules of thumb
- Voltage sharing with equal resistors:
  - For two series capacitors with equal resistors R across each, and total supply voltage $V_{\text{total}}$, the bleeder current is:
    $$I_{\text{bleed}} = \frac{V_{\text{total}}}{R + R} = \frac{V_{\text{total}}}{2R}$$
    Each capacitor sees approximately:
    $$V_C \approx \frac{V_{\text{total}}}{2}$$
- Choose resistor current to dominate capacitor leakage:
  - Rule of thumb: Make $I_{\text{bleed}} \ge 10 \times I_{\text{leak}}$ (worst case) to ensure good voltage equalization.
- Discharge time constant per capacitor:
  - $$\tau = R C$$
  - Voltage decays as: $$V(t) = V_0 e^{-t/\tau}$$
  - After about $5\tau$, the voltage is under 1% of $V_0$.
- Resistor power rating:
  - For each resistor (across one capacitor): $$P = \frac{V_C^2}{R}$$
  - Ensure adequate margin for both power and voltage rating.

Practical tip: Pick R to provide a reasonable bleeder current (often on the order of 0.5–2 mA for many HV supplies, adjusted for your design), verify discharge time is acceptable, and check each resistor’s power and voltage ratings.