The value of current I in the electrical circuit as given below, when potential at A is equal to the potential at B, will be ____ A.

$$V_A = V_B$$

Balanced bridge condition:

$$\frac{10}{R} = \frac{20}{40}$$

$$R = \frac{10 \times 40}{20} = 20\ \Omega$$

Equivalent resistance of upper branch: $$R_{\text{upper}} = 10 + 20 = 30\ \Omega$$

Equivalent resistance of lower branch: $$R_{\text{lower}} = R + 40 = 20 + 40 = 60\ \Omega$$

Total equivalent resistance: $$R_{\text{eq}} = \frac{R_{\text{upper}} \times R_{\text{lower}}}{R_{\text{upper}} + R_{\text{lower}}}$$

$$R_{\text{eq}} = \frac{30 \times 60}{30 + 60} = \frac{1800}{90} = 20\ \Omega$$

Total circuit current: $$I = \frac{V}{R_{\text{eq}}}$$

$$I = \frac{40}{20} = 2\text{ A}$$