JEE Main 2026 — Physics Electromagnetism

Taking the right-hand wire as the reference node at $0\text{ V}$0 V, let the left junction (where the $3\,\Omega$3Ω, $4\,\Omega$4Ω and $6\,\Omega$6Ω resistors meet) be Node A at potential $V_A$VA​.

Bottom branch: The positive terminal of the $2\text{ V}$2 V battery is at the reference, so its negative terminal (and hence the left end of the $3\,\Omega$3Ω resistor) is at $-2\text{ V}$−2 V.

Top branch: The positive terminal of the $3\text{ V}$3 V battery is at the reference, so its negative terminal (and hence the node between the $6\,\Omega$6Ω resistor and the $3\text{ V}$3 V battery) is at $-3\text{ V}$−3 V.

Applying KCL at Node A (sum of currents leaving the node is zero):

$$\dfrac{V_A - 0}{4} + \dfrac{V_A - (-2)}{3} + \dfrac{V_A - (-3)}{6} = 0$$4VA​−0​+3VA​−(−2)​+6VA​−(−3)​=0

$$\dfrac{V_A}{4} + \dfrac{V_A + 2}{3} + \dfrac{V_A + 3}{6} = 0$$4VA​​+3VA​+2​+6VA​+3​=0

Multiplying throughout by $12$12:

$$3V_A + 4(V_A + 2) + 2(V_A + 3) = 0$$3VA​+4(VA​+2)+2(VA​+3)=0

$$3V_A + 4V_A + 8 + 2V_A + 6 = 0$$3VA​+4VA​+8+2VA​+6=0

$$9V_A + 14 = 0 \Rightarrow V_A = -\dfrac{14}{9}\text{ V}$$9VA​+14=0⇒VA​=−914​ V

Current through the $6\,\Omega$6Ω resistor (from Node A towards the $-3\text{ V}$−3 V point):

$$I_6 = \dfrac{V_A - (-3)}{6} = \dfrac{-\dfrac{14}{9} + 3}{6} = \dfrac{\dfrac{13}{9}}{6} = \dfrac{13}{54}\text{ A}$$I6​=6VA​−(−3)​=6−914​+3​=6913​​=5413​ A

Heat generated in the $6\,\Omega$6Ω resistor in $t = 100\text{ s}$t=100 s:

$$H = I_6^2 \cdot R \cdot t = \left(\dfrac{13}{54}\right)^2 \cdot 6 \cdot 100$$H=I62​⋅R⋅t=(5413​)2⋅6⋅100

$$H = \dfrac{169}{2916} \cdot 600 = \dfrac{169 \cdot 100}{486} = \dfrac{16900}{486}\text{ J}$$H=2916169​⋅600=486169⋅100​=48616900​ J

Given $H = \dfrac{\alpha}{100}\text{ J}$H=100α​ J:

$$\dfrac{\alpha}{100} = \dfrac{16900}{486}$$100α​=48616900​

$$\alpha = \dfrac{16900 \cdot 100}{486} = \dfrac{1690000}{486} \approx 3477.37$$α=48616900⋅100​=4861690000​≈3477.37

Rounding to the nearest integer:

$$\alpha = 3477$$α=3477

Hence, the answer is $3477$3477.