In the figure, potential difference between A and B is:

Biasing verification based on the $$30\text{ V}$$ battery orientation:

$$\text{Anode connected towards high potential side } \implies \text{Forward-biased (short circuit)}$$

Parallel combination of the two identical resistors branch between A and B: $$R_{AB} = \frac{10 \times 10}{10 + 10} = 5\text{ k}\Omega$$

Total resistance connected to the source network: $$R_{\text{total}} = 10 + R_{AB} = 10 + 5 = 15\text{ k}\Omega$$

Potential difference across the parallel block using the voltage divider rule: $$V_{AB} = V \times \frac{R_{AB}}{R_{\text{total}}} = 30 \times \frac{5}{15} = 10\text{ V}$$