Question

An R-C voltage divider has an HV arm capacitance, \( C_1 = 600 \) pF, resistance \( R = 400 \) \( \Omega \), and equivalent ground capacitance \( C_g = 240 \) pF. The effective time constant of the divider in nanoseconds is:

• A. 32
• B. 100
• C. 67
• D. 25

Hint:

The effective time constant of an R-C voltage divider is computed using: \[ \tau = R \cdot \frac{C_1 C_g}{C_1 + C_g} \] For accurate impulse response analysis in high-voltage systems.

Answer 1

The Correct Option is C

Step 1: Effective Capacitance Calculation The total effective capacitance for an R-C voltage divider is given by: \[ C_{\text{eff}} = \frac{C_1 C_g}{C_1 + C_g} \] Substituting given values: \[ C_{\text{eff}} = \frac{(600 \times 240)}{(600 + 240)} \text{ pF} \] \[ C_{\text{eff}} = \frac{144000}{840} = 171.43 \text{ pF} \] Step 2: Time Constant Calculation The time constant \( \tau \) is given by: \[ \tau = R \cdot C_{\text{eff}} \] \[ \tau = 400 \times 171.43 \text{ ps} \] \[ \tau = 68571.43 \text{ ps} = 68.57 \text{ ns} \approx 67 \text{ ns} \] Step 3: Evaluating options: - (A) Incorrect: 32 ns is too low.
- (B) Incorrect: 100 ns is an overestimation.
- (C) Correct: \( 67 \) ns matches the computed result.
- (D) Incorrect: 25 ns is too low.