The intensity of a light pulse travelling along a communication channel decreases exponentially with distance x according to the relation I = I0e-ax, where I0is the intensity at x = 0 and α is the attenuation constant. (a) Show that the intensity reduces by 75% after a distance of (In4/α). (b) Attenuation of a signal can be expressed in decibel (dB) according to the relation dB=10 log10(I/I0).What is the attenuation in dB/km for an optical fibre in which the intensity falls by 50% over a distance of 50 km?

This is a Long Answer Type Questions as classified in NCERT Exemplaras we know that I= I0 e - ∝ x And I= 25%of I0=I=I0/4I0/4= I0 e - ∝ x I0 cancel from both sides¼= e - ∝ x Taking log on both sides log1 -log4= - ∝ x logeX= log4/ ∝

This is a Long Answer Type Questions as classified in NCERT Exemplaras we know that I= I0 e - ? x And I= 25%of I0=I=I0/4I0/4= I0 e - ? x I0 cancel from both sides¼= e - ? x Taking log on both sides log1 -log4= - ? x logeX= log4/ ?

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Physics NCERT Exemplar Solutions Class 12th Chapter Fifteen Physics Class 12th Communication Systems

The intensity of a light pulse travelling along a communication channel decreases exponentially with distance x according to the relation I = I₀e^-ax, where I₀is the intensity at x = 0 and α is the attenuation constant.
(a) Show that the intensity reduces by 75% after a distance of (In4/α).
(b) Attenuation of a signal can be expressed in decibel (dB) according to the relation dB=10 log₁₀(I/I₀).What is the attenuation in dB/km for an optical fibre in which the intensity falls by 50% over a distance of 50 km?

3 Views | Posted 4 months ago

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Answered by

alok kumar singh | Contributor-Level 10

4 months ago

This is a Long Answer Type Questions as classified in NCERT Exemplar

as we know that I= I_{0
$e^{- \propto x}$}

And I= 25%of I₀=

I=I₀/4

I₀/4= I_{0
$e^{- \propto x}$}

I₀cancel from both sides

¼= $e^{- \propto x}$

Taking log on both sides log1 -log4= - $\propto x$ loge

X= log4/ $\propto$

0 Upvotes 0 Downvotes

Answered by

alok kumar singh | Contributor-Level 10

4 months ago

This is a Long Answer Type Questions as classified in NCERT Exemplar

as we know that I= I_{0
$e^{- ? x}$}

And I= 25%of I₀=

I=I₀/4

I₀/4= I_{0
$e^{- ? x}$}

I₀cancel from both sides

¼= $e^{- ? x}$

Taking log on both sides log1 -log4= - $? x$ loge

X= log4/ $?$

0 Upvotes 0 Downvotes

2 Answers

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