Meaning of Shannon’s law in communications Shannon’s fundamental theorem relates which pair of quantities for a channel with a given bandwidth and noise level?

Introduction / Context:
Shannon’s channel capacity theorem sets an upper bound on error-free data rate over a noisy channel given its bandwidth and signal-to-noise ratio, forming the foundation of modern digital communication system design.

Given Data / Assumptions:

• Additive white Gaussian noise (AWGN) channel model.
• Bandwidth B and SNR are known.

Concept / Approach:
The theorem states C = B * log2(1 + S/N), where C is capacity in bits/s. It ties achievable information rate to both bandwidth and SNR, independent of modulation specifics, assuming ideal coding with arbitrarily low error probability.

Step-by-Step Solution:
Identify capacity formula: C = B * log2(1 + S/N).Thus capacity depends on both bandwidth and SNR.Select the option matching this relationship.

Verification / Alternative check:
As S/N → ∞, C grows approximately as B * log2(S/N); as S/N → 0, capacity trends to zero.

Why Other Options Are Wrong:
Other options cite unrelated pairs (antenna gain, losses) or omit bandwidth; Shannon’s law fundamentally involves capacity, SNR, and bandwidth.

Common Pitfalls:
Confusing capacity with throughput; practical systems approach but never reach Shannon capacity due to coding and implementation constraints.

Final Answer:
Information-carrying capacity to signal-to-noise ratio (and bandwidth)