--- title: "HRC fuse I²t and fuses in series" subject: "Switchgear and Protection" chapter: 3 key: "semester_6/switchgear_and_protection:hrc-fuse-i2t-series" source: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/hrc-fuse-i2t-series site: BCT Engineering --- # HRC fuse I²t and fuses in series Switchgear and Protection · Chapter 3: Fuses - Asked in: 2075 Baisakh, 6 marks - Video: [Understanding Current Limit Fuses and let through current](https://www.youtube.com/watch?v=P5hZ1WYfXB4) — Jonathan Gracey - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/hrc-fuse-i2t-series - Whole chapter: https://www.bctengineer.com/md/semester_6/switchgear_and_protection/chapter-3 ## Question Describe the time/current I²t characteristics of a HRC fuse and explain how they are used to select the ratings of fuses in series. ## Short answer HRC fuse time-current curve is inverse; for short times (<10 ms) melting depends on I²t energy. Pre-arcing I²t is constant at high currents. For series fuses, the downstream fuse's total let-through I²t must be less than the upstream fuse's pre-arcing I²t to prevent upstream melting, and time-current curves must not cross. ## Answer #### Time–current and I²t characteristics of an HRC fuse The **time–current characteristic** shows the operating time against current on log–log scales. It is inverse: long times for small overloads, a few milliseconds for heavy faults. For short operating times (less than about 10 ms) heat cannot escape from the element, so melting depends only on the energy **I²t** delivered: ```text Pre-arcing I²t = ∫₀^tp i² dt (energy to melt element) Arcing I²t = ∫tp^tt i² dt (energy during arc) Total I²t = pre-arcing I²t + arcing I²t ``` ```text I²t (A²s, log) │ total I²t ───────────── │ ╱ (rises with voltage; higher at low pf) │ pre-arcing I²t ──────── │ (constant at high current) └─────────────────────────► prospective I ``` - **Pre-arcing I²t** is practically constant for a given fuse at high currents (fixed by element mass and material). - **Total (let-through) I²t** depends on circuit voltage, power factor and prospective current. - Manufacturers give both values for each rating. #### Selection of fuses in series using I²t For a minor (downstream) fuse F2 and a major (upstream) fuse F1: ```text Supply ──[F1]──┬──[F2]── load fault after F2 ``` 1. Both fuses carry the same fault current. 2. For F1 not to blow or be damaged, the energy let through by F2 in clearing the fault must not melt F1: ```text Total I²t of F2 < Pre-arcing I²t of F1 ``` 3. At lower currents (long times) the **time–current curves must not cross**; the major fuse curve must lie above the minor fuse curve with a margin. 4. Choose F2 from the load current; then choose the smallest F1 that satisfies the I²t rule. In practice a rating ratio of about **1.6–2 : 1** is sufficient for gG fuses. *Example (illustrative values):* a 63 A fuse with total I²t ≈ 15 000 A²s and a 125 A fuse with pre-arcing I²t ≈ 30 000 A²s discriminate, since 15 000 < 30 000. The total I²t of the fuse must also be less than the withstand I²t (k²S²) of the protected cable or semiconductor, so the I²t data also fix the maximum fuse rating for a given cable. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is I2t used for short times? A. Below about 10 ms heat cannot escape, so melting depends on energy I2t B. Because current is constant C. Because voltage is zero D. Arc is absent Answer: A. Pre-arcing I2t is practically constant at high current. (Key point: Why I2t) 2. What is total I2t? A. Pre-arcing only B. Pre-arcing I2t + arcing I2t; depends on voltage and power factor C. Rated squared D. Constant for all Answer: B. Pre-arcing I2t is fixed by element mass; total depends on circuit. (Key point: Total I2t) 3. Condition for F2 downstream and F1 upstream? A. Pre-arcing of F2 > total of F1 B. Equal I2t C. Total I2t of F2 < pre-arcing I2t of F1 D. Total F1 < total F2 Answer: C. So F1 is not damaged. Example: 15 000 < 30 000 A2s. (Key point: Series rule) 4. What else must total I2t satisfy? A. Exceed it B. Equal rated current C. Nothing D. Be less than withstand I2t (k^2 S^2) of cable or semiconductor Answer: D. This fixes the maximum fuse rating for a cable. 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