Determine the maximum length of the cable (in km) for transmitting data at a rate of 500 Mbps in an Ethernet LAN with frames of size 10,000 bits. Assume the signal speed in the cable to be 2,00,000 km/s.

In an Ethernet LAN using CSMA/CD, the condition for collision detection is:

where:

• $T_t = \frac{\text{Frame size}}{\text{Bandwidth}} = \frac{L}{B}$

• $T_p = \frac{\text{Distance}}{\text{Propagation speed}} = \frac{d}{v}$

Substitute the given values:

Given:

• Frame size $L = 10{,}000\text{ bits} = 10^4\text{ bits}$

• Bandwidth $B = 500\text{ Mbps} = 500 \times 10^6\text{ bps} = 5 \times 10^8\text{ bps}$

• Speed $v = 2{,}00{,}000\text{ km/s} = 2 \times 10^5\text{ km/s}$

Hence, the maximum length of the cable is 2 km (Option B).