For the circuit shown in the figure, the equivalent resistance between point \(A \& B\) for two cases (i) \(V_A>V_B\) (ii) \(V_B>V_A\), respectively is __________ \(\Omega\) and __________ \(\Omega\) respectively.
( \(D _1\) and \(D _2\) are ideal diodes)

A.\(25, \infty\)
For ideal diode forward bias resistance is zero and reverse bias resistance is zero.
(i) V \(_{\text {A }}>\) V \(_{\text {B }}\)
Diode \(D_{1}\) Forward biased
Diode \(\mathrm{D}_{2}\) Forward biased
\(\frac{1}{\mathrm{R}_{\mathrm{AB}}}=\frac{1}{50+0}+\frac{1}{50+0}\)
\(\therefore \quad \frac{1}{\mathrm{R}_{\mathrm{AB}}}=\frac{1}{50}+\frac{1}{50}\)
\(\therefore \quad \frac{1}{\mathrm{R}_{\mathrm{AB}}}=\frac{2}{50}=\frac{1}{25}\)
\(\therefore \quad R_{A B}=25 \Omega\)
(ii) \(\mathrm{V}_{\mathrm{B}}>\mathrm{V}_{\mathrm{A}}\)
Diode \(\mathrm{D}_{1}\) reverse biased
Diode \(\mathrm{D}_{2}\) reverse biased
\(
\begin{aligned}
\frac{1}{R_{A B}} =\frac{1}{50+\infty}+\frac{1}{50+\infty} \\
\therefore \frac{1}{R_{A B}} =\frac{1}{\infty}+\frac{1}{\infty} \\
\therefore \frac{1}{R_{A B}} =0 \\
\therefore R_{A B} =\infty \Omega
\end{aligned}\)