Question

The internal inductance${\mathbf{L}}_{\mathbf{int}}$per unit-length of a solid cylindrical conductor is a constant, given by $\frac{\mathbf{1}}{\mathbf{2}}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{7}}\frac{\mathbf{H}}{\mathbf{m}}$in SI system of units.

(a) True

(b) False

Short answer

Therefore, the correct option is (b) True

Step-by-step solution

Step 1:  Determine the formula of flux linkage inside the conductor.

Write the formula of flux linkage inside the conductor.

${\mathbf{\lambda }}_{\mathbf{int}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{7}}\mathbf{l}\frac{\mathbf{H}}{\mathbf{m}}\mathbf{}$

Here, $\mathrm{l}$is a current flowing through the conductor.

Determine the formula of internal inductance inside the conductor.

Write the formula of internal inductance inside the conductor.

${\mathrm{L}}_{\mathrm{int}}=\frac{{\mathrm{\lambda }}_{\mathrm{int}}}{\mathrm{l}}$

Substitute the value and solve as,

$\begin{array}{rcl}{\mathrm{L}}_{\mathrm{int}}& =& \frac{{\displaystyle \frac{1}{2}}\times {10}^{-7}\mathrm{l}{\displaystyle \frac{\mathrm{H}}{\mathrm{m}}}}{\mathrm{l}}\\ & =& \frac{1}{2}\times {10}^{-7}\frac{\mathrm{H}}{\mathrm{m}}\end{array}$

Hence, correct option is (a) True.