---
title: "Channel capacity for 6 kHz, 6 dB"
subject: "Data Communication"
chapter: 1
key: "semester_5/data_communication:capacity-6khz-6db"
source: https://www.bctengineer.com/q/semester_5/data_communication/capacity-6khz-6db
site: BCT Engineering
---

# Channel capacity for 6 kHz, 6 dB

Data Communication · Chapter 1: Introduction

- Asked in: 2071 Shrawan, 3 marks
- Video: [Nyquist Bit Rate & Shannon Capacity | Signal-to-Noise Ratio | Computer Networks Course | Lecture 18](https://www.youtube.com/watch?v=_LxyNd-pDdk) — Mind Your Exam Channel
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/data_communication/capacity-6khz-6db
- Whole chapter: https://www.bctengineer.com/md/semester_5/data_communication/chapter-1

## Question

Calculate the channel capacity having bandwidth and SNR of 6 kHz and 6 dB respectively.

## Short answer

Given B = 6 kHz, SNR = 6 dB → S/N ≈ 3.98, Shannon capacity C = B log2(1 + S/N) = 6000 × log2(4.98) = 6000 × 2.316 ≈ 13.9 kbps.

## Answer

Given: B = 6 kHz, SNR = 6 dB. Use Shannon's formula C = B log₂(1 + S/N).

1. S/N = 10^(6/10) = 3.981
2. 1 + S/N = 4.981
3. log₂(4.981) = 2.316
4. C = 6000 × 2.316 = 13,899 bps

**Answer: C ≈ 13.9 kbps.**

## Check yourself

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

1. Which formula is used?
   A. C = B log2(1 + S/N)
   B. C = 2B log2 L
   C. C = B log2 L
   D. C = kTB
   Answer: A. It is a noisy channel with given SNR. (Key point: Formula)

2. 6 dB gives S/N of about
   A. 6
   B. 3.98
   C. 0.6
   D. 60
   Answer: B. 10^0.6 = 3.981. (Key point: SNR ratio)

3. The capacity is about
   A. 6 kbps
   B. 36 kbps
   C. 13.9 kbps
   D. 2.3 kbps
   Answer: C. 6000 x log2(4.981) = 6000 x 2.316 = 13.9 kbps. (Key point: Result)

## Related in Data Communication

- [Capacity for 3.1 kHz, SNR 0 dB](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Acapacity-3-1khz-0db) — Data Communication, chapter 1
- [Capacity and Nyquist levels, 3 to 4 MHz, 24 dB](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Anyquist-shannon-bandwidth-3-4mhz) — Data Communication, chapter 1

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