--- title: "Step-down chopper with 1 V drop: average and rms" subject: "Power Electronics" chapter: 4 key: "semester_7/power_electronics:step-down-chopper-1v-drop-rms" source: https://www.bctengineer.com/q/semester_7/power_electronics/step-down-chopper-1v-drop-rms site: BCT Engineering --- # Step-down chopper with 1 V drop: average and rms Power Electronics · Chapter 4: DC chopper - Asked in: 2075 Chaitra, 8 marks - Video: [SOLVED PROBLEMS OF CHOPPERS](https://www.youtube.com/watch?v=9U2TWnzduhA) — Prof. Barapate's Tutorials - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/power_electronics/step-down-chopper-1v-drop-rms - Whole chapter: https://www.bctengineer.com/md/semester_7/power_electronics/chapter-4 ## Question The supply voltage of a step down chopper is 230V dc, load resistance is 10 ohms. Take the voltage drop of 1V across chopper when it is ON. For a duty cycle of 0.4, calculate the average and rms value of output voltage. ## Short answer Pulse amplitude is 229 V. Average output voltage V_a = k × 229 = 0.4 × 229 = 91.6 V. RMS output voltage V_rms = √k × 229 = √0.4 × 229 ≈ 144.83 V. ## Answer With an ON-state drop $V_{ch}$, the load voltage is a pulse of height $(V_s - V_{ch})$ lasting $kT$ in every period, so the average and rms values follow directly from that pulse. **Given:** $V_s = 230$ V, $R = 10\ \Omega$, $V_{ch} = 1$ V, $k = 0.4$. ```text v0 229|_____ _____ | | | | 0 |_____|_____|_____|____ t kT T ``` #### Average output voltage $$ \begin{aligned} V_a &= \frac{1}{T}\int_0^{kT}(V_s - V_{ch})\,dt = k\,(V_s - V_{ch}) \\ &= 0.4\times(230-1) = 0.4\times229 = 91.6\ \text{V} \end{aligned} $$ #### RMS output voltage $$ \begin{aligned} V_{rms} &= \left[\frac{1}{T}\int_0^{kT}(V_s - V_{ch})^2dt\right]^{1/2} = \sqrt{k}\,(V_s - V_{ch}) \\ &= \sqrt{0.4}\times229 = 0.63246\times229 = 144.83\ \text{V} \end{aligned} $$ For reference, the load currents are $I_a = 91.6/10 = 9.16$ A and $I_{rms} = 14.48$ A. **Answer:** $V_a = 91.6$ V, $V_{rms} = 144.83$ V. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. With a 1 V switch drop, what is the load voltage pulse? A. (Vs - Vch) = 229 V for kT, zero for the rest B. 230 V for kT C. 1 V for kT D. 229 V for (1-k)T Answer: A. The conducting switch drops 1 V, so the load sees 229 V during ON. (Key point: Load voltage waveform) 2. What is the average output voltage? A. 92 V B. 91.6 V C. 229 V D. 144.83 V Answer: B. Va = 0.4 x 229 = 91.6 V. (Key point: Average voltage) 3. What is the formula for the rms output voltage? A. k (Vs - Vch) B. (Vs - Vch)/sqrt(k) C. sqrt(k) (Vs - Vch) D. k^2 (Vs - Vch) Answer: C. Squaring the pulse over kT and averaging over T gives sqrt(k) times the pulse height. (Key point: RMS formula) 4. What is the rms output voltage? A. 91.6 V B. 229 V C. 95.4 V D. 144.83 V Answer: D. sqrt(0.4) x 229 = 0.63246 x 229 = 144.83 V. (Key point: RMS value) ## Close variants set in other exams - [Step-down chopper with 2 V drop: average and rms](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Astep-down-chopper-2v-drop-rms) — Power Electronics, chapter 4, asked 2× ## Related in Power Electronics - [Step-down chopper with switch drop: efficiency](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Astep-down-chopper-efficiency-1v) — Power Electronics, chapter 4 - [Step-up chopper average and rms output](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Astep-up-chopper-avg-rms) — Power Electronics, chapter 4 - [Step-down chopper: fundamental of load current](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Astep-down-chopper-fundamental-load-current) — Power Electronics, chapter 4 - [Step-down chopper RLE load, 5 kHz](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Astep-down-chopper-rle-5khz) — Power Electronics, chapter 4 - [Step-down chopper variable frequency, 3 ms ON time](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Astep-down-chopper-variable-frequency-3ms) — Power Electronics, chapter 4 - [Step-down chopper with DC motor load](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Astep-down-chopper-dc-motor) — Power Electronics, chapter 4 ## Related in other subjects - [Chopper numerical: 220 V, 10 Ω, 50% duty](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Achopper-220v-10ohm) — Advanced Electronics, chapter 7, asked 4× - [Inverters; chopper numerical 220 V, 10 Ω](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Ainverters-chopper-220v-10ohm) — Advanced Electronics, chapter 7, asked 4× - [Step-down chopper with RL load](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Astep-down-chopper-rl) — Advanced Electronics, chapter 7 - [Chopper classification; step-down chopper RL load](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Aclassify-chopper-step-down-rl) — Advanced Electronics, chapter 7