JEE Main 2023 · 11 April · morning · Numerical answer · +4 / −0
In the circuit diagram shown in figure given below, the current flowing through resistance 3 Ω is x/3 A.
The value of x is ___________
Answer and solution
Answer 1
Solution
Physics sir · 4 steps
Look at which plate faces which: these two cells push against each other, so their emfs subtract.
- Read the polarities. The long plate is the positive terminal. The 4 V cell has its long plate on the left and the 8 V cell has its long plate on the right, so their negative terminals face each other. The cells oppose, and the net emf is 8 - 4 = 4 V, driving current the way the 8 V cell pushes.
- Total resistance. The 3 Ω and 6 Ω in parallel give (3 × 6)/(3 + 6) = 2 Ω. Everything else is in series, internal resistances included: 0.5 + 1 + 4.5 + 2 = 8 Ω.
I = (E₂ - E₁)/(r₁ + r₂ + R) = (8 - 4)/8 = 0.5 A
- Split the current. In a parallel pair, current divides in inverse ratio of the resistances. The 3 Ω branch takes 0.5 × 6/(3 + 6) = 1/3 A.
- So. x/3 = 1/3, which gives x = 1.
The common slip: 3. Adding the emfs as 4 + 8 = 12 V gives a main current of 1.5 A and 1 A in the 3 Ω resistor, so x = 3.
The idea to keep. Before adding emfs in a single loop, check the plates. Positive facing positive, or negative facing negative, means the cells oppose and you subtract. And never forget the internal resistances in the total.
Answer from the NTA final answer key. Solution by PrepWiser.