When L is variable, minimum attenuation is achieved at:

(Where: L is Inductance per unit length; C is Capacitance per unit length; R is Resistance per unit length; and G is Conductance per unit length.)

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  1. \(\rm L =\frac{R G}{C} H / k m \)
  2. \(\rm L =\frac{C R}{G} H / k m\)
  3. L = CRG H/km
  4. \(\rm L=\frac{C G}{R} H / k m\)

Answer (Detailed Solution Below)

Option 2 : \(\rm L =\frac{C R}{G} H / k m\)
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Detailed Solution

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Concept:

In transmission line theory, for minimum attenuation, the condition of matching the primary line constants must be satisfied.

Minimum attenuation is achieved when the characteristic impedance is purely resistive, which happens when:

\( R/L = G/C \Rightarrow L = \frac{CR}{G} \)

Where:

  •  L  = Inductance per unit length
  • C  = Capacitance per unit length
  • R = Resistance per unit length
  • G  = Conductance per unit length

Correct Answer:

\( \boxed{L = \frac{CR}{G}~\text{H/km}} \)

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