JEE Advanced2023PhysicsAlternating CurrentActual
In a circuit shown in the figure, the capacitor C is initially uncharged and the key K is open. In this condition, a current of 1 A flows through the 1 Ω resistor. The key is closed at time t = t 0 . Which of the following statement(s) is(are) correct? [Given : e – 1 = 0 . 36 ]
Options
- AThe value of the resistance R is 3 Ω
- BFor t < t 0 , the value of current I 1 is 2 A
- CAt t = t 0 + 7 . 2 μ s , the current in the capacitor is 0 . 6 A
- DFor t → ∞ , the charge on the capacitor is 12 μ C
Correct answer
A. The value of the resistance R is 3 Ω
Step-by-step solution
From second branch, we can see the potential drop across the branch is 5 + 1 × 1 = 6   V . Now for the first branch, we can write 15 - I R = 6       . . . 1 and from third branch, we can write I 1 × 3 = 6 ⇒ I 1 = 2   A Now from Kirchoff's junction rule, I = I 1 + 1 = 3 Now, from equation(1), we can write 15 - 3 R = 6 ⇒ R = 3 Ω All three branches are in parallel, therefore we can write equivalent resistance as: 1 R eq = 1 3 + 1 3 + 1 ⇒ R eq = 3 5   &