Bandwidth constrains data rate and channel capacity. Which equation expresses channel capacity given bandwidth B and signal-to-noise ratio?

• A. C = log2(1 + S/N) / B
• B. C = B log2(1 + S/N)
• C. C = B / log2(1 + S/N)
• D. C = (S/N) log2(1 + B)

Answer: (B)

The capacity of a channel, in bits per second, depends on both the available bandwidth and the signal-to-noise ratio in a way described by the Shannon–Hartley theorem: C = B log2(1 + S/N). Here B is the bandwidth in Hz and S/N is the signal-to-noise ratio, a dimensionless value. This shows that widening the channel’s bandwidth increases capacity linearly, while increasing SNR boosts capacity logarithmically, meaning the gains taper off at higher SNR.

The other forms don’t reflect this relationship. Putting bandwidth in the denominator would imply capacity shrinks as bandwidth grows. Dividing by the logarithm would misrepresent how bandwidth and SNR combine. Using the logarithm of (1 plus bandwidth) with S/N outside the log also distorts the established dependence, since the log should take (1 + S/N) as its argument, not involve bandwidth inside the log.