The heat generated in 1 minute between points A and B in the given circuit, when a battery of 9 V with internal resistance of 1Ω is connected across these points is ____ J

Wheatstone bridge between A and B.

$$R_{AB} = \dfrac{3 \times 6}{3+6}$$

$$R_{AB} = 2 \, \Omega$$

After solving we get the circuit as shown in figure
$$i = \dfrac{9}{2+1} \text{ A}$$

$$i=3A$$
$$t = 1 \text{ min} = 60 \text{ s}$$

Heat generated across a resistor $$R_{AB}$$ in time $$t$$ is $$H = i^2 R_{AB} t$$.

$$H = 9 \times 2 \times 60$$

$$H = 1080 \text{ J}$$