Refer to the circuit diagram given below. The heat generated across the 6 $$\Omega$$ resistance in 100 second is $$\frac{\alpha}{100}$$ J. The value of $$\alpha$$ is _______. (Nearest integer)

$$R_{\text{eq}} = \frac{R_1 R_2}{R_1 + R_2} = \frac{6 \times 4}{6 + 4} = \frac{24}{10} = 2.4\ \Omega$$

$$E_{\text{eq}} = \frac{\frac{E_1}{R_1} + \frac{E_2}{R_2}}{\frac{1}{R_1} + \frac{1}{R_2}} = \frac{\frac{3}{6} + \frac{0}{4}}{\frac{1}{6} + \frac{1}{4}} = \frac{0.5}{\frac{5}{12}} = \frac{0.5 \times 12}{5} = 1.2\text{ V}$$

$$R_{\text{total}} = 3 + R_{\text{eq}} = 3 + 2.4 = 5.4\ \Omega$$

$$E_{\text{total}} = 2\text{ V} - 1.2\text{ V} = 0.8\text{ V}$$

$$I_{\text{total}} = \frac{E_{\text{total}}}{R_{\text{total}}} = \frac{0.8}{5.4} = \frac{4}{27}\text{ A}$$

$$V_{\text{parallel}} = E_{\text{eq}} + I_{\text{total}}R_{\text{eq}}$$

$$V_{\text{parallel}} = 1.2 + \left(\frac{4}{27} \times 2.4\right) = \frac{6}{5} + \left(\frac{4}{27} \times \frac{12}{5}\right) = \frac{6}{5} + \frac{16}{45} = \frac{54 + 16}{45} = \frac{70}{45} = \frac{14}{9}\text{ V}$$

$$I = \frac{V_{\text{parallel}} - 3}{6} = \frac{\frac{14}{9} - 3}{6} = \frac{-\frac{13}{9}}{6} = -\frac{13}{54}\text{ A}$$

$$H = I^2 R t = \left(\frac{13}{54}\right)^2 \times 6 \times 100$$

$$H = \frac{169}{2916} \times 600 = \frac{101400}{2916} \approx 34.77\text{ J}$$

$$\frac{\alpha}{100} = 34.77 \implies \alpha \approx 3477$$