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Determine the maximum length of the cable $\text{(in km)}$ for transmitting data at a rate of $\text{1 Gbps}$ in an $\text{Ethernet LAN}$ with frames of size $\text{4000 bits}$. Assume the signal speed in the cable to be $\text{2,00,000 km/s}$.

1. $\text{100 meters}$
2. $\text{200 meters}$
3. $\text{400 meters}$
4. $\text{500 meters}$
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@Subarna Das @Mk Utkarsh pls give solution..i got this question wrong.

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Thanks..

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For avoiding collision in LAN (Ethernet), we should take care of the Transmission time-- it should be greater than twice the propagation time.

$\therefore \text{Transmission time} \geq 2 \times \text{Propagation time} \\ \implies \dfrac{L}{B} \geq 2 \times \dfrac{d}{v} \\ \implies \dfrac{4000}{10^9} \geq 2 \times \dfrac{d}{2 \times 10^5} \\ \implies \dfrac{4000}{10^9} \times 10^5 \geq d \\ \implies d \leq 0.4 \ km$

So, the maximum length of the cable should be $\text{0.4 km} \approx 400 \ meters$