GATE CS 2007 Q66 — Data Link Layer: Framing, Error Detection, MAC, Ethernet Bridging

To find the physical length of cable equivalent to a $1$-bit delay, we need to calculate how far a signal travels along the cable during the time it takes to transmit a single bit.

Step 1: Calculate the duration of $1$ bit ($T_b$)
The transmission speed (bandwidth) is $R = 10^7\text{ bps}$.
The time required to transmit $1$ bit is: $$T_b = \frac{1}{R} = \frac{1}{10^7\text{ bits/sec}} = 10^{-7}\text{ seconds} = 0.1\ \mu\text{s}$$

Step 2: Calculate the equivalent distance ($d$)
The propagation speed of the signal through the cable is $v = 200\text{ meters}/\mu\text{s}$.
Using the relation $\text{Distance} = \text{Speed} \times \text{Time}$: $$d = v \times T_b$$ $$d = 200\text{ meters}/\mu\text{s} \times 0.1\ \mu\text{s} = 20\text{ meters}$$

Therefore, a $1$-bit delay in this network is equivalent to $20$ meters of cable.