--- title: "Critical resistance, critical speed and shunt generator characteristics" subject: "Electrical Machines I" chapter: 3 key: "semester_4/electrical_machines_i:critical-resistance-speed-shunt-characteristics" source: https://www.bctengineer.com/q/semester_4/electrical_machines_i/critical-resistance-speed-shunt-characteristics site: BCT Engineering --- # Critical resistance, critical speed and shunt generator characteristics Electrical Machines I · Chapter 3: DC Generator - Asked in: 2080 Chaitra, 4+4 marks - Video: [Critical Field resistance and Critical speed of a DC shunt generators.](https://www.youtube.com/watch?v=DxY91S1e_3Y) — EEE Tutorials - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machines_i/critical-resistance-speed-shunt-characteristics - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines_i/chapter-3 ## Question Define the terms critical resistance and critical speed of self-excited DC shunt generator with appropriate diagrams. Draw the performance characteristics of DC shunt generator and comment on it. ## Short answer Critical resistance is the slope of the tangent to the OCC from the origin; the maximum field resistance allowing voltage build-up at a given speed. Critical speed is the minimum speed for build-up with a fixed field resistance, Nc = N·Rf/Rc. External characteristic: terminal voltage drops with load due to IaRa, armature reaction and reduced field current, turning back beyond critical load. ## Answer #### Critical field resistance The **critical field resistance** $R_c$ is the maximum resistance of the shunt field circuit at which a self-excited shunt generator will just build up voltage at a given speed. Graphically it is the slope of the **tangent** drawn from the origin to the initial (linear) part of the OCC. ```text E ^ Rc line (tangent) | / Rf < Rc line | / / | / / ____---- OCC (speed N) | / / .--' | / /.-' builds up here |/ ./ | ./ Rf > Rc: no build-up |/ +----------------------> If ``` - $R_f < R_c$: field line cuts the OCC at a high voltage, so the machine builds up. - $R_f > R_c$: field line lies above the OCC; voltage stays near residual value. #### Critical speed The **critical speed** $N_c$ is the speed at which a given field resistance $R_f$ becomes the critical resistance, i.e. the minimum speed at which the generator just builds up. Since the OCC ordinates are proportional to speed: $$ \frac{N_c}{N} = \frac{R_f}{R_c} \quad\Rightarrow\quad N_c = N\,\frac{R_f}{R_c} $$ ```text E ^ Rf line | / OCC at N | / ___---- | /.--' | // OCC at Nc: tangent = Rf line | // __--- | //.-' | /.' OCC below Nc: no build-up |/ +----------------------> If ``` **Example:** $R_c = 220\ \Omega$ at 1500 rpm, $R_f = 176\ \Omega$: $N_c = 1500 \times 176/220 = 1200$ rpm. #### Performance characteristics of DC shunt generator **1. Open-circuit characteristic (OCC, $E_0$ vs $I_f$):** starts at the residual voltage, rises linearly, then bends due to saturation. **2. External characteristic ($V$ vs $I_L$):** ```text V ^ E0 +----.___ | ''--.__ (a) drop: IaRa | '--. (b) drop: armature reaction | '. (c) drop: lower If | \ | Ic ,-' turn-back | <------' +------------------------> IL 0 (short circuit current small) ``` - Terminal voltage falls as load increases, because of (a) armature resistance drop $I_aR_a$, (b) armature reaction weakening flux, and (c) reduced field current since $I_f = V/R_f$ falls with $V$. - Beyond a critical load current $I_c$ (load resistance below critical), the curve **turns back**: further decrease in load resistance lowers both $V$ and $I_L$. On a dead short circuit, the current is small (only residual EMF acts), so a shunt generator protects itself. **3. Internal characteristic ($E$ vs $I_a$):** lies above the external curve by $I_aR_a$, showing the effect of armature reaction and reduced field current only. **Comment:** the shunt generator gives an almost constant voltage for normal loads (voltage drop about 5-15% from no load to full load), so it is used for battery charging, excitation of alternators and lighting where moderate regulation is acceptable. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Graphically, critical field resistance is: A. The slope of the tangent from the origin to the linear part of the OCC B. The slope of the OCC at saturation C. The intercept of the OCC D. The residual voltage Answer: A. The tangent from the origin to the initial straight part of the OCC has slope Rc. (Key point: Critical resistance graph) 2. With Rc = 220 ohm at 1500 rpm and Rf = 176 ohm, Nc is: A. 1875 rpm B. 1200 rpm C. 1500 rpm D. 176 rpm Answer: B. Nc = N Rf/Rc = 1500 x 176/220 = 1200 rpm. (Key point: Critical speed formula) 3. Which is NOT a reason for the terminal voltage drop of a shunt generator under load? A. Armature resistance drop B. Armature reaction C. Reduced field current D. Increase of residual flux Answer: D. The drops are Ia Ra, armature reaction and lower If due to lower V. (Key point: Reasons for voltage drop) 4. Beyond the critical load current, the external characteristic turns back because: A. Reducing load resistance lowers both V and IL B. Speed rises C. Field current increases D. Residual flux vanishes entirely Answer: A. Falling V reduces field current and flux sharply, so IL also falls; a dead short gives only a small current. 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