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

### Related Formula R_texteq = fracR_1 R_2R_1 + R_2 text (parallel)$$R_{\text{eq}} = \frac{R_1 R_2}{R_1 + R_2} \text{ (parallel)}$$ H = I^2 R t$H = I^2 R t$ I = fracVR_texteq + r$$I = \frac{V}{R_{\text{eq}} + r}$$ ### Core Logic The circuit is a balanced Wheatstone bridge between A and B, because the ratio of adjacent arms is frac12 = frac24$\frac{1}{2} = \frac{2}{4}$. Thus, the middle 1\,Omega$1\,\Omega$ resistor (if there is one connecting the middle nodes) is ineffective.

The equivalent resistance across AB (R_AB$R_{AB}$) involves the upper branch (1+2 = 3\,Omega$1+2 = 3\,\Omega$) and the lower branch (2+4 = 6\,Omega$2+4 = 6\,\Omega$) in parallel.

R_AB = frac3 times 63 + 6 = frac189 = 2\,Omega$$R_{AB} = \frac{3 \times 6}{3 + 6} = \frac{18}{9} = 2\,\Omega$$ ### Step 1: Calculate Current and Heat Total resistance in the circuit = R_AB + r_textinternal = 2 + 1 = 3\,Omega$R_{AB} + r_{\text{internal}} = 2 + 1 = 3\,\Omega$. Total current from the battery i = frac9textV3\,Omega = 3textA$i = \frac{9\text{V}}{3\,\Omega} = 3\text{A}$. The heat generated specifically between points A and B in 1 minute (60 seconds) is: H_AB = i^2 R_AB t = (3)^2 times 2 times 60$$H_{AB} = i^2 R_{AB} t = (3)^2 \times 2 \times 60$$ H_AB = 9 times 120 = 1080text J$$H_{AB} = 9 \times 120 = 1080\text{ J}$$ ### Pattern Recognition Check for balanced Wheatstone bridge first. Then use H = i^2 R t$H = i^2 R t$ strictly with the equivalent resistance of just the section AB$AB$ to find heat specifically generated across AB$AB$. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Current Electricity