Question

A long two-wire line composed of solid ground conductors is 0.5 cm and the distance between their centres is 2 m. If this distance is doubled, then the inductance per unit length _______.

• A. Halves
• B. Increases but does not double
• C. Doubles
• D. Decreases but does not halve

Hint:

Inductance in transmission lines depends on \( \ln(d/r) \), so doubling distance increases inductance, but not linearly.

Answer 1

The Correct Option is B

Step 1: Understand inductance per unit length in transmission lines
The inductance per unit length \( L \) of a two-wire line is given approximately by: \[ L = \frac{\mu_0}{\pi} \ln\left( \frac{d}{r} \right) \] where:
\( d \) = distance between wire centers,
\( r \) = radius of the conductor,
\( \mu_0 \) = permeability of free space.
Step 2: See the effect of doubling the distance \( d \)
If \( d \to 2d \), then: \[ L' = \frac{\mu_0}{\pi} \ln\left( \frac{2d}{r} \right) = \frac{\mu_0}{\pi} \left[ \ln\left( \frac{d}{r} \right) + \ln(2) \right] \] \[ L' = L + \frac{\mu_0}{\pi} \ln(2) \] So the new inductance is higher than before, but not double. Therefore, Option (2) is correct.