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JEE MainPhysicsCurrent Electricity

Three parallel branches are connected between a common node A and the ground. Branch 1 contains a 2 resistor and a 12 V battery with its positive terminal facing node A. Branch 2 contains a 1 resistor and a battery of unknown emf E with its positive terminal facing node A. Branch 3 contains a 2 resistor and a 4 V battery with its negative terminal facing node A. The other ends of all three branches are grounded. If t

Correct answer

8

Step-by-step solution

Let the potential at node A be V_A = 6 V . Applying Kirchhoff's Current Law (KCL) at node A, the sum of currents leaving the node must be zero: V_A - 12 2 + V_A - E 1 + V_A - (-4) 2 = 0 Substitute V_A = 6 V into the equation: 6 - 12 2 + 6 - E 1 + 6 + 4 2 = 0 -6 2 + 6 - E + 10 2 = 0 -3 + 6 - E + 5 = 0 8 - E = 0 E = 8 Answer: 8

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