Explanation

(b) The impedance (Z) of an R – L – C series circuit is given by
$Z = \sqrt{R^{2} + \left( \omega L - \frac{1}{\omega C} \right)^{2}}$
As frequency of alternating emf applied to the circuit is increased, $X_{L}$ goes on increasing and $X_{C}$ goes on decreasing.
For a particular value of $\omega = (\omega_{r}\ $say$)$
$\ \ \ \ \ \ X_{L} = X_{C}$
ie, $\ \ \omega_{r}L = \frac{1}{\omega_{r}C}$
or ${\ \ \omega}_{r} = \frac{1}{\sqrt{LC}}$
or $2\pi v_{r} = \frac{1}{\sqrt{LC}}$
or $v_{r} = \frac{1}{2\pi\sqrt{LC}}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v = \frac{1}{2 \times 3.14 \times \sqrt{5 \times 80 \times 10^{- 6}}}$
$= \frac{1}{2 \times 3.14 \times \sqrt{(400 \times 10^{- 6})}}$
$= \frac{1}{2 \times 3.14 \times 2 \times 10^{- 2}}$
$= \frac{100}{3.14 \times 4}$
$= \frac{25}{3.15} = \frac{25}{\pi}Hz$