A communications channel has a bandwidth of 4,000 hz and a signal-to-noise ratio (snr of 30 db. what is the maximum possible data rate?

Through Shannon's Theorem, we can calculate the capacity of the communications channel using the value of its bandwidth and signal-to-noise ratio. The capacity, C, can be expressed as

C = B * log₂ (1 + S/N)

where B is the bandwidth of the channel and S/N is its signal-to-noise ratio.

Since the given SN ratio is in decibels, we must first express it as a ratio with no units as

SN (in decibels) = 10 * log (S/N)

30 = 10log (S/N)

log (S/N) = 3

S/N = 10³ = 1000

Now that we have S/N, we can solve for its capacity (in bits per second) as

C = 4000 * log₂ (1 + 1000)

C = 39868.91 bps

Thus, the maximum capacity of the channel is 39868 bps or 40 kbps.

Answer: 40 kbps