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23 votes
23 votes

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.

  1. $1$
  2. $2$      
  3. $2.5$     
  4. $5$
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5 Answers

44 votes
44 votes
Best answer

$\text{transmission time} \geq \text{round trip time of 1 bit}$

$\text{transmission time} \geq 2 \times \text{propagation time}$

$\dfrac{10,000\ bits}{500\ Mbps} \geq 2 \times \dfrac{d}{2\times 10^{5}\text{ km per sec}}$

$ 2 \text{ km} \geq d $ 

Option B is correct.

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4 Comments

@Amar, Why you've multiplied 2 with the propagation time??
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edited by

@Arjun sir please clear this doubt the reason we considering that transmission time ≥ 2* propagation delay because in ethernet protocol such as CSMA there is no ack mechanism and to detect if there is any collision the sender should have packet length of 2*propagation delay so thst if there is any collision it could be detected.

Please clear pratyush doubt as well he also have same question

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edited by
@devshree coz propagation delay is one way latency to get round trip time we need to multiply it by 2 and add queuing delay + processing delay + transmit time of ack is involved at receiver or else it is considered as negligible
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13 votes
13 votes

In Ethernet LAN, there is a relation that transmission time >= 2*propagation time (To detect collision)
=> 10000/(500*1000000) >= 2*length/200000
=> length = 2km
so,
Answer is B i.e 2 Km

4 votes
4 votes
The question clearly states that we are considering Ethernet LAN (IEEE 802.3)

Ethernet LAN follows CSMA CD (Collision Detection)

Hence, Transmission time >= 2 * Propagation Time

As Transmission time = Length of frame / Bandwidth  = 10^3/(500 * 10^6)

And, Propagation time = Distance / Speed = d (say)/ 20 * 10^4

So, substituting these values in the above formula we get d <= 2 Km.

 

Hence, max value of d is 2 Km
0 votes
0 votes
Tt >= 2*Tp
L/B >= 2*(d/v)
10000/500000000 >=2*d/200000
(100000*10000)/500000000>=d
d<=2Km
Answer:

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