A system has bandwidth as 4000 Hz with rise time 2.5 seconds. If the rise time decreased to 1.25 seconds then the bandwidth is ___________Hza)8000b)5000c)4585d)3000Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Given:

Bandwidth (B₁) = 4000 Hz

Rise time (T₁) = 2.5 seconds

Rise time (T₂) = 1.25 seconds

To find:

The bandwidth (B₂) when the rise time is decreased to 1.25 seconds.

Solution:

The rise time and bandwidth are related by the formula:

Bandwidth (B) = 0.35 / Rise Time (T)

Step 1: Calculate the initial bandwidth (B₁)

Substituting the given values in the formula:

B₁ = 0.35 / T₁

B₁ = 0.35 / 2.5

B₁ = 0.14 Hz

Step 2: Calculate the new bandwidth (B₂)

Substituting the new rise time (T₂) in the formula:

B₂ = 0.35 / T₂

B₂ = 0.35 / 1.25

B₂ = 0.28 Hz

Step 3: Convert the bandwidth to Hz

Since bandwidth is measured in Hz, we need to convert the result from the previous step to Hz.

B₂ = 0.28 * 1000 Hz

B₂ = 280 Hz

Step 4: Compare the initial and new bandwidth

Comparing the initial and new bandwidth:

B₁ = 0.14 Hz

B₂ = 280 Hz

Therefore, the new bandwidth (B₂) when the rise time is decreased to 1.25 seconds is 280 Hz. However, none of the given options match this value. Hence, the correct answer cannot be determined from the given options.

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