Question

In an insulated cable having core diameter d and overall diameter D, the ratio of maximum to minimum dielectric stress is given by,

• A. $\left(\frac{D}{d}\right)$
• B. ${\left(\frac{D}{d}\right)}^{1/2}$
• C. $\left(\frac{d}{D}\right)$
• D. ${\left(\frac{D}{d}\right)}^2$

Answer 1

The correct option is A $\left(\frac{D}{d}\right)$

Maximum dielectric stress = ${\delta }_{max}$

${\delta }_{max}=\frac{V}{rln\left(\frac{R}{r}\right)}$

Minimum dielectric stress $={\delta }_{min}$

${\delta }_{min}=\frac{V}{Rln\left(\frac{R}{r}\right)}$
$\therefore$ The ratio of maximum to minimum dielectric stress

$=\frac{{\delta }_{max}}{{\delta }_{min}}$

or, $\frac{{\delta }_{max}}{{\delta }_{min}}=\frac{\frac{V}{rln\left(\frac{R}{r}\right)}}{\frac{V}{Rln\left(\frac{R}{r}\right)}}=\frac{R}{r}=\frac{D}{d}$