In the electric network shown, when no current flows through the 4 $$\Omega$$ resistor in the arm EB, the potential difference between the points A and D will be:

$$V_E = V_B + 4 - (I_{EB} \times 4)$$

$$I_{EB} = 0$$

$$V_E = V_B + 4\ \text{V}$$

$$V_A - V_B = 9\ \text{V} \implies V_B = V_A - 9\ \text{V}$$

$$V_D = V_E$$

$$V_E = (V_A - 9\ \text{V}) + 4\ \text{V}$$

$$V_E = V_A - 5\ \text{V}$$

$$V_A - V_E = 5\ \text{V}$$

Since $$V_E = V_D$$, $$V_A - V_D = 5\ \text{V}$$

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