For the circuit shown in the figure. The equivalent resistance between point A and B for the 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)

Options

A. `25, oo`
B. `50 , oo`
C. `oo, 25`
D. `25,25`

Answer

To solve the problem of finding the equivalent resistance between points A and B in the given circuit with ideal diodes D1 and D2, we will analyze two cases based on the potential difference between points A and B.

### Step-by-Step Solution:

**Step 1: Analyze Case (i) where \( V_A > V_B \)**

1. In this case, point A is at a higher potential than point B. This means that diode D1 (connected to point A) will be forward-biased, and diode D2 (connected to point B) will also be forward-biased.
2. Since both diodes are forward-biased, they will act as short circuits (ideal diodes have zero resistance when forward-biased).
3. The resistors R1 and R2 are connected in parallel because both diodes are conducting.
4. The formula for equivalent resistance \( R_{eq} \) for resistors in parallel is given by:
\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} \]
5. Substituting the values of R1 and R2 (assuming both are 50 ohms):
\[ \frac{1}{R_{eq}} = \frac{1}{50} + \frac{1}{50} = \frac{2}{50} = \frac{1}{25} \]
6. Therefore, the equivalent resistance \( R_{eq} \) is:
\[ R_{eq} = 25 \, \Omega \]

**Step 2: Analyze Case (ii) where \( V_B > V_A \)**

1. In this case, point B is at a higher potential than point A. This means that diode D1 will be reverse-biased and diode D2 will also be reverse-biased.
2. When diodes are reverse-biased, they act as open circuits (ideal diodes have infinite resistance when reverse-biased).
3. Since both diodes are not conducting, there is no path for current to flow between points A and B.
4. Therefore, the equivalent resistance in this case is considered to be infinite:
\[ R_{eq} = \infty \, \Omega \]

### Final Answers:
- For case (i) \( V_A > V_B \): \( R_{eq} = 25 \, \Omega \)
- For case (ii) \( V_B > V_A \): \( R_{eq} = \infty \, \Omega \)