Question

A capacitor filled with dielectric of relative permittivity $\epsilon _{r}=2.1,$ loses half the charge acquired during a time $3.0$ min. Assuming the charge to leak only through the dielectric filled, calculate its resistivity.

• A. $1.4\Omega-m$
• B. $1.4\times 10^{13}\Omega-m$
• C. $7.2\times 10^{13}\Omega-m$
• D. $10\Omega-m$

Answer 1

Answer: (B)

$q=q_{0}e^{- t/\tau}$
$\frac{q_{0}}{2}=q_{0}e^{- t/\tau}$
$t=\tauln2$
$=\left(\frac{\left(\epsilon \right)_{0} K A}{d}\right)\frac{\rho d}{A}ln2$
$\rho =\frac{t}{\epsilon _{0} K ln 2}=\frac{3 \times 60}{8 . 85 \times 10^{- 12} \times 2 . 1 \times 0 . 693}$
$=1.4\times 10^{13}\Omega-m$