Question

A telegraph wire $200\text{km}$ long has capacity $0.014\mu \text{F}$ per km and resistance $2\Omega /\text{km}$. If it carries an $AC$ of frequency $5\text{kHz}$ then what should be the inductance so that maximum power is delivered at the other end?

• A. $3.6\times {10}^{-4}\text{H}$
• B. $140\text{mH}$
• C. $1.4\text{mH}$
• D. $\text{none of these}$

Answer 1

Answer: (A)

$3.6\times {10}^{-4}\text{H}$

$X_L=X_C$
or $L=\frac{1}{C{\omega }^2}=\frac{1}{2.8\times {10}^{-6}\times (2\pi \times 5\times {10}^3{)}^2}$
$=\frac{1}{2.8\times 25\times 4{\pi }^2}=0.00036=3.6\times {10}^{-4}\text{H}$