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In a long transmission line, if $r$, $l$, $g$, and $c$ are the resistance, inductance, shunt conductance, and capacitance per unit length, respectively, the condition for distortionless transmission is

1. $rc=lg$
2. $r=\sqrt{l/c}$
3. $rg=lc$
4. $g=\sqrt{c/l}$

Correct answer: $rc=lg$

Solution

A transmission line is distortionless when all frequency components experience the same phase delay and attenuation. The Heaviside condition for this is $\dfrac{r}{l}=\dfrac{g}{c}$, which is equivalent to $rc=lg$. Therefore, the correct condition is $rc=lg$.

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