A train of pulses with each pulse 30 μs wide and having an inter-pulse separation of 20 μs is propagating through a transmission line. How long should the transmission line be in meters so that exactly three pulses are on the line at a time ? Assume propagation speed to be \(3 \times 10^{8}\) m/s.
MH SET - 2018, SET Exam - 2018,
Answer: D
The line should be 39 km long.
For exactly three pulses to be on the line, it must hold three pulse widths and the two gaps between them:
\[ \begin{aligned} t &= 3 \times 30 + 2 \times 20 = 130\ \mu\text{s} \\ L &= 3 \times 10^{8} \times 130 \times 10^{-6} \\ &= 39000\ \text{m} = 39\ \text{km} \end{aligned} \]
3.9 km is the same length with the power of ten slipped by one. 25 km is not a combination of three pulses, and 2.5 km would hold less than a single pulse, since one 30 μs pulse alone is 9 km long.
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