Final answer:
An oscilloscope with a bandwidth of 20MHz is not capable of displaying a signal with a rise time of 20 ns because its maximum rise time capacity of 17.5 ns is less than the signal's rise time.
Step-by-step explanation:
To determine if an oscilloscope with a bandwidth of 20MHz is capable of displaying a signal with a rise time of 20 ns, we can use the bandwidth-rise time relationship. The relationship is given by the approximate formula: bandwidth (in Hz) ≈ 0.35 divided by the rise time (in seconds). If we solve for the maximum rise time that a 20MHz oscilloscope can accurately display, we get:
rise time = 0.35 / bandwidth = 0.35 / 20 x 10^6 = 17.5 ns
Since 17.5 ns is less than 20 ns, the oscilloscope's response would not be fast enough to accurately display the full rise time of the signal in question. Hence, an oscilloscope with a bandwidth of 20MHz is not capable of adequately displaying a signal with a rise time of 20 ns.