JEE MainPhysicsCurrent Electricity
In a circuit, three parallel branches are connected between two nodes P and Q. Branch 1 contains an unknown resistor R in series with a 12 V battery, with the battery's negative terminal connected to node Q. Branch 2 contains a 2 , resistor. Branch 3 contains a 4 , resistor in series with a 6 V battery, with the battery's positive terminal connected to node Q. If the heat generated in the 2 , resistor in 5 s is 90 J
Correct answer
1
Step-by-step solution
Let the potential at node Q be 0 V and the potential at node P be V . The heat generated in the 2 , resistor in time t is given by H = V^2 R₂ t . Substituting the given values: 90 = V^2 2 5 V^2 = 180 5 = 36 V = 6 V Now, apply Kirchhoff's Current Law (KCL) at node P. The sum of currents leaving node P must be zero. For Branch 1, the potential at the junction of R and the 12 V battery is 12 V (since its negative terminal is at 0 V ). For Branch 3, the potential at the junction of the 4 , resistor and the 6 V battery