Determine the maximum length of the cable (in km) for transmitting data at a…

Concept: In CSMA/CD (Ethernet), a station must still be transmitting when the earliest possible collision signal returns; otherwise it cannot detect the collision. The governing constraint is that the round-trip propagation time must not exceed the frame transmission time: 2 × Tp ≤ Tt. Here Tp = L / v (propagation), and Tt = (frame size) / (data rate). Combining these bounds the cable length.

1. Transmission time: Tt = frame size / data rate = 10,000 / (500 × 106) = 2 × 10-5 s = 20 μs.

2. Collision-detection constraint: 2 × Tp ≤ Tt, so the one-way propagation time Tp ≤ Tt / 2 = 10 μs.

3. Convert the limiting time to distance: Lmax = v × Tp = 200,000 km/s × 10 × 10-6 s = 2 km.

Cross-check: At L = 2 km the round-trip time is 2 × (2 / 200,000) = 20 μs, exactly equal to the 20 μs transmission time — the borderline case where collision detection is still guaranteed. Any longer cable pushes the round-trip beyond 20 μs and breaks detection, so the maximum length is 2 km.