In the Shannon-Hartley theorem, if you increase the bandwidth while keeping SNR constant, how does the channel capacity change?

• A. Capacity increases proportionally with bandwidth
• B. Capacity increases logarithmically with SNR
• C. Capacity decreases
• D. Capacity increases linearly with bandwidth

Answer: (A)

The key idea here is how channel capacity depends on bandwidth when the signal-to-noise ratio is held constant. In the Shannon-Hartley formula, capacity equals bandwidth times the logarithm term log2(1 + SNR). If SNR stays the same, that logarithmic factor is constant, so the only changing variable is bandwidth. Therefore, capacity scales directly with bandwidth: doubling the bandwidth doubles the capacity, because C = B × [constant]. This makes sense because wider bandwidth allows more independent signal dimensions per second to carry information, assuming the same SNR.