--- title: "Resistance switching numerical (132 kV, 350 Ω)" subject: "Switchgear and Protection" chapter: 6 key: "semester_6/switchgear_and_protection:resistance-switching-132kv" source: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/resistance-switching-132kv site: BCT Engineering --- # Resistance switching numerical (132 kV, 350 Ω) Switchgear and Protection · Chapter 6: Circuit Breakers - Asked in: 2073 Magh, 8 marks - Video: [current chopping and resistance switching by u k trivedi](https://www.youtube.com/watch?v=XkhTSsrfU5A) — GPC Sawaimadhopur - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/resistance-switching-132kv - Whole chapter: https://www.bctengineer.com/md/semester_6/switchgear_and_protection/chapter-6 ## Question For a 132 kV system, the reactance and capacitance up to the location of circuit breaker is 5 Ω and 0.035 μF, respectively. A resistance of 350 Ω is connected across the contacts of the circuit breaker. Determine the (a) Natural frequency of oscillation (b) Damped frequency of oscillation (c) Critical value of resistance which will give no transient oscillation and (d) The value of resistance which will give damped frequency of oscillation one-third of the natural frequency of oscillation. ## Short answer With L=15.915 mH, natural frequency is 6.74 kHz. With 350 Ω damping, damped frequency is 1.81 kHz. Critical resistance is 337.2 Ω, and the resistance giving f_d=f_n/3 is 357.6 Ω. ## Answer A resistance across the CB contacts damps the restriking voltage oscillation; if it is at or below the critical value, the voltage rises without oscillation. #### Formulas (resistance *R* across the contacts, parallel *R*–*L*–*C* circuit) ```text Natural frequency f_n = 1 / (2π √(LC)) Damped frequency f_d = (1/2π) √(1/LC − 1/(4R²C²)) Critical resistance R_c = ½ √(L/C) (R ≤ R_c gives no oscillation) For f_d = f_n / k: 1/(4R²C²) = (1/LC)(1 − 1/k²) R = R_c / √(1 − 1/k²) ``` Inductance from reactance: *L* = *X*/(2π × 50). #### Data *X* = 5 Ω, *C* = 0.035 μF, *R* = 350 Ω, *f* = 50 Hz. ```text L = 5 / 314.16 = 15.915 mH ``` #### (a) Natural frequency ```text 1/LC = 1/(15.915×10⁻³ × 0.035×10⁻⁶) = 1.7952×10⁹ f_n = √(1.7952×10⁹) / 2π = 6743 Hz ≈ 6.74 kHz ``` #### (b) Damped frequency ```text 1/(4R²C²) = 1/(4 × 350² × (0.035×10⁻⁶)²) = 1.6660×10⁹ f_d = √(1.7952×10⁹ − 1.6660×10⁹) / 2π = 1809 Hz ≈ 1.81 kHz ``` #### (c) Critical resistance ```text R_c = ½ √(15.915×10⁻³ / 0.035×10⁻⁶) = ½ × 674.34 = 337.2 Ω ``` Since 350 Ω > 337.2 Ω, the given resistor still allows a (heavily damped) oscillation, as found in (b). #### (d) Resistance for f_d = f_n/3 ```text R = R_c / √(1 − 1/9) = 337.2 / 0.9428 = 357.6 Ω Check: f_d = 2248 Hz = 6743/3 ✓ ``` **Answer: (a) f_n = 6.74 kHz; (b) f_d = 1.81 kHz; (c) R_c = 337.2 Ω; (d) R = 357.6 Ω.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which resistance gives no transient oscillation across the contacts? A. R greater than R_c B. R equal or below R_c C. R very large D. Any R Answer: B. At R <= R_c the voltage rises without oscillation. (Key point: Condition for no oscillation) 2. For X = 5 ohm and C = 0.035 uF, R_c is about A. 674 ohm B. 337.2 ohm C. 168.6 ohm D. 350 ohm Answer: B. L = 15.915 mH, R_c = (1/2) sqrt(L/C) = 0.5 x 674.3 = 337.2 ohm. (Key point: Critical resistance value) 3. Why is there still an oscillation (f_d = 1.81 kHz) with R = 350 ohm? A. Because 350 ohm is greater than R_c = 337.2 ohm, so oscillation is only heavily damped B. Because the reactance is too large C. Because capacitance is neglected D. Because the frequency is 50 Hz Answer: A. R above R_c leaves 1/LC > 1/(4R^2C^2), giving a small damped frequency. (Key point: Damped frequency for R above R_c) 4. The resistance that gives f_d = f_n/3 is A. R_c x 3 = 1011 ohm B. R_c / sqrt(1 - 1/9) = 357.6 ohm C. R_c x sqrt(1 - 1/9) = 318 ohm D. R_c / 3 = 112 ohm Answer: B. From 1/(4R^2C^2) = (1/LC)(1 - 1/k^2), R = R_c / sqrt(1 - 1/9) = 357.6 ohm. (Key point: Resistance for f_d = f_n/3) ## Close variants set in other exams - [Resistance switching numerical (220 kV, 600 Ω)](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Aresistance-switching-220kv) — Switchgear and Protection, chapter 6, asked 2× ## Related in Switchgear and Protection - [RRRV from short circuit test (132 kV)](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Arrrv-132kv-test) — Switchgear and Protection, chapter 6, asked 2× - [Restriking voltage numerical (11 kV, 10 mH)](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Arestriking-11kv-10mh) — Switchgear and Protection, chapter 6, asked 2× - [Restriking voltage numerical (6.6 kV, 8 mH)](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Arestriking-6-6kv-8mh) — Switchgear and Protection, chapter 6, asked 2× - [Specifying breaker on 132/66 kV transformer](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Abreaker-x-specification) — Switchgear and Protection, chapter 6 - [IDMT relays across 132/11 kV transformer (3500 A)](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Aidmt-132-11kv-3500a) — Switchgear and Protection, chapter 7 - [IDMT relays across 132/33 kV transformer (2000 A)](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Aidmt-132-33kv-2000a) — Switchgear and Protection, chapter 7 ## Related in other subjects - [Current chopping overvoltage in 132 kV breaker](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Achopping-overvoltage-10a) — High Voltage Engineering, chapter 3 - [Damped LCR oscillation, damped frequency](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Adamped-lcr-frequency-significance) — Engineering Physics, chapter 1, asked 2× - [Inductive reactance of vertical 132 kV line](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Avertical-132kv-12mm-5m) — Power System Analysis I, chapter 4 - [Damped oscillation, mechanical vs e.m.](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Adamped-mechanical-versus-electromagnetic) — Engineering Physics, chapter 1