--- title: "Resistance switching numerical (220 kV, 600 Ω)" subject: "Switchgear and Protection" chapter: 6 key: "semester_6/switchgear_and_protection:resistance-switching-220kv" source: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/resistance-switching-220kv site: BCT Engineering --- # Resistance switching numerical (220 kV, 600 Ω) Switchgear and Protection · Chapter 6: Circuit Breakers - Asked in: 2072 Magh, 8 marks - Video: [54 Problem solution of Resistance Switching in Circuit Breakers](https://www.youtube.com/watch?v=RBBDs7S7dko) — Dr Padmini S Panneer Selvam - 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-220kv - Whole chapter: https://www.bctengineer.com/md/semester_6/switchgear_and_protection/chapter-6 ## Question In a 220 kV system the reactance and capacitance up to the location of circuit breaker is 8 Ω and 0.025 μF, respectively. A resistance of 600 Ω is connected across the contacts of the circuit breaker. Determine the following: (i) Natural frequency of oscillation (ii) Damped frequency of oscillation (iii) Critical value of resistance which will give no transient oscillation and (iv) The value of resistance which will give damped frequency of oscillation one-fourth of the natural frequency of oscillation. ## Short answer With L=25.46 mH, natural frequency is 6.31 kHz. With 600 Ω damping, damped frequency is 3.41 kHz. Critical resistance is 504.6 Ω, and the resistance giving f_d=f_n/4 is 521.2 Ω. ## Answer **Resistance switching** means connecting a resistor across the CB contacts (or arc) so that the restriking voltage transient is damped, its frequency is lowered and RRRV is reduced. #### 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* = 8 Ω, *C* = 0.025 μF, *R* = 600 Ω, *f* = 50 Hz. ```text L = 8 / 314.16 = 25.46 mH ``` #### (i) Natural frequency ```text 1/LC = 1/(25.46×10⁻³ × 0.025×10⁻⁶) = 1.5708×10⁹ f_n = √(1.5708×10⁹) / 2π = 6308 Hz ≈ 6.31 kHz ``` #### (ii) Damped frequency ```text 1/(4R²C²) = 1/(4 × 600² × (0.025×10⁻⁶)²) = 1.1111×10⁹ f_d = √(1.5708×10⁹ − 1.1111×10⁹) / 2π = 3412 Hz ≈ 3.41 kHz ``` #### (iii) Critical resistance ```text R_c = ½ √(25.46×10⁻³ / 0.025×10⁻⁶) = ½ × 1009.25 = 504.6 Ω ``` #### (iv) Resistance for f_d = f_n/4 ```text R = R_c / √(1 − 1/16) = 504.6 / 0.9682 = 521.2 Ω Check: f_d = 1577 Hz = 6308/4 ✓ ``` **Answer: (i) f_n = 6.31 kHz; (ii) f_d = 3.41 kHz; (iii) R_c = 504.6 Ω; (iv) R = 521.2 Ω.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What does a resistor across the CB contacts do? A. It raises the natural frequency and the RRRV B. It damps the restriking transient, lowers its frequency and reduces RRRV C. It increases arc current D. It replaces the arcing contacts Answer: B. Resistance switching damps the oscillation, lowering frequency and RRRV so the arc does not restrike. (Key point: Purpose of resistance switching) 2. The critical resistance for no oscillation is A. R_c = sqrt(L/C) B. R_c = 2 sqrt(L/C) C. R_c = (1/2) sqrt(L/C) D. R_c = sqrt(LC) Answer: C. Setting 1/LC = 1/(4R^2C^2) gives R_c = (1/2) sqrt(L/C) = 504.6 ohm here. (Key point: Critical resistance) 3. With X = 8 ohm (L = 25.46 mH) and C = 0.025 uF, f_n is about A. 63 kHz B. 630 Hz C. 3.41 kHz D. 6.31 kHz Answer: D. f_n = 1/(2 pi sqrt(LC)) = 6308 Hz. (Key point: Natural frequency) 4. With R = 600 ohm, the damped frequency is A. f_d = (1/2pi) sqrt(1/LC - 1/(4R^2C^2)) = 3.41 kHz B. 6.31 kHz, unchanged C. f_d = f_n x 600 D. 0 Hz because R > R_c Answer: A. sqrt(1.5708e9 - 1.1111e9)/2pi = 3412 Hz. R above R_c still gives a damped oscillation. (Key point: Damped frequency) ## Close variants set in other exams - [Resistance switching numerical (132 kV, 350 Ω)](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Aresistance-switching-132kv) — Switchgear and Protection, chapter 6, asked 2× ## Related in Switchgear and Protection - [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× - [RRRV from short circuit test (220 kV)](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Arrrv-220kv-test) — 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× - [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× ## Related in other subjects - [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× - [Reactance diagram: three generators, two 220 kV lines](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Areactance-diagram-three-gens-two-lines) — Power System Analysis I, chapter 3 - [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 - [Tower dimensions for 220 kV single circuit line](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Atower-dimensions-220kv) — Transmission and Distribution System Design, chapter 4, asked 2×