---
title: "Inverters; chopper numerical 220 V, 10 Ω"
subject: "Advanced Electronics"
chapter: 7
key: "semester_4/advanced_electronics:inverters-chopper-220v-10ohm"
source: https://www.bctengineer.com/q/semester_4/advanced_electronics/inverters-chopper-220v-10ohm
site: BCT Engineering
---

# Inverters; chopper numerical 220 V, 10 Ω

Advanced Electronics · Chapter 7: Introduction to Power Electronics

- Asked in: 2074 Chaitra, 2+1+2+2 marks; 2073 Chaitra, 2+1+2+2 marks (asked 2 times)
- Video: [DC chopper numericals](https://www.youtube.com/watch?v=S2_KeZcQov8) — Yogesh Maharjan
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/advanced_electronics/inverters-chopper-220v-10ohm
- Whole chapter: https://www.bctengineer.com/md/semester_4/advanced_electronics/chapter-7

## Question

What are inverters? For the chopper shown below has a resistive load R = 10Ω, the input voltage is Vs = 220V, when the chopper remains on its voltage drop Vch = 2V and the chopping frequency is f = 1 kHz with duty cycle of 50%. Derive and determine a) The average output voltage b) The RMS value of output voltage c) The chopper efficiency. [Figure: dc source Vs (+ at top) connected through the chopper switch SW to a resistive load R; the output voltage vo appears across R and the load current io flows through it.]

## Short answer

Inverters convert DC to AC of desired voltage and frequency. For the chopper (Vs=220V, Vch=2V, duty 50%): average output voltage = 109V, RMS = 154.15V, efficiency = 99.09%.

## Answer

#### Inverters

An **inverter** is a power electronic circuit that converts **DC into AC** of desired voltage and frequency. Thyristors, MOSFETs or IGBTs are switched in sequence so that the load sees an alternating voltage. Examples: single-phase half-bridge and full-bridge inverters, used in UPS, solar systems and AC motor drives.

#### Chopper calculation

Given: Vs = 220 V, R = 10 Ω, Vch = 2 V, f = 1 kHz (T = 1 ms), k = 0.5, so kT = 0.5 ms.

Output voltage is (Vs − Vch) during 0 < t < kT and 0 during kT < t < T.

#### a) Average output voltage

```text
Va = (1/T)∫₀^(kT) (Vs − Vch) dt
   = (kT/T)(Vs − Vch) = k(Vs − Vch)
   = 0.5 × 218
Va = 109 V
```

#### b) RMS output voltage

```text
Vo,rms = √[ (1/T)∫₀^(kT) (Vs − Vch)² dt ]
       = √k · (Vs − Vch)
       = 0.7071 × 218
Vo,rms = 154.15 V
```

#### c) Chopper efficiency

```text
Po = (1/T)∫₀^(kT) (Vs − Vch)²/R dt = k(Vs − Vch)²/R
   = 0.5 × 218²/10 = 2376.2 W

Pi = (1/T)∫₀^(kT) Vs·i dt,  i = (Vs − Vch)/R
   = k·Vs(Vs − Vch)/R
   = 0.5 × 220 × 218/10 = 2398 W

η = Po/Pi = (Vs − Vch)/Vs = 218/220 = 0.9909
```

**Answer: Va = 109 V, Vo,rms = 154.15 V, η = 99.09 %**

The only loss is the 2 V drop across the switch, so the efficiency is very high. This is the main advantage of switching (chopper) control over resistive control.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What does an inverter do?
   A. Converts AC into DC
   B. Converts DC into AC of desired voltage and frequency
   C. Converts DC into a different DC level
   D. Converts AC into AC of the same frequency
   Answer: B. An inverter switches devices in sequence so the load sees alternating voltage. (Key point: Inverter definition)

2. Average output voltage for Vs = 220 V, Vch = 2 V, k = 0.5?
   A. 110 V
   B. 218 V
   C. 109 V
   D. 154.15 V
   Answer: C. Va = k(Vs − Vch) = 0.5 × 218. (Key point: Average voltage)

3. What is the RMS output voltage?
   A. 109 V
   B. 218 V
   C. 192.1 V
   D. 154.15 V
   Answer: D. Vo,rms = sqrt(0.5) × 218 = 0.7071 × 218 = 154.15 V. (Key point: RMS voltage)

4. The chopper efficiency equals which ratio?
   A. (Vs − Vch)/Vs = 99.09 %
   B. k = 50 %
   C. Vch/Vs
   D. Va/Vs
   Answer: A. Po/Pi = k(Vs−Vch)^2/R divided by k·Vs(Vs−Vch)/R = (Vs−Vch)/Vs. (Key point: Efficiency)

## Close variants set in other exams

- [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×

## Related in other subjects

- [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 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-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