In the diagram shown, the resistance between points A and B is ' $R_{1}$ ' when an ideal diode D is forward biased and is ' $R_{2}$ ' when ideal diode D is reverse biased. The ratio $R_{1} / R_{2}$ is

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When the ideal diode D is forward biased, it acts as a short circuit with zero resistance.

The circuit then consists of two $30 Ω$ resistors connected in parallel between points A and B.

The equivalent resistance $R_{1}$ is given by:

$R_{1} = \frac{30 \times 30}{30 + 30} = 15 Ω$

When the ideal diode D is reverse biased, it acts as an open circuit with infinite resistance.

No current flows through the top branch, so the equivalent resistance $R_{2}$ is simply the resistance of the bottom branch.

$R_{2} = 30 Ω$

The ratio $\frac{R _{1}}{R _{2}}$ is:

$\frac{R _{1}}{R _{2}} = \frac{15}{30} = \frac{1}{2}$

Answer: $\frac{1}{2}$

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