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 ]
D. For t → ∞ , the charge on the capacitor is 12 μ C
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   Ω = 0 . 6   Ω As all branches are in parallel with the capacitor branch, potential drop across all three branches will be the same. Therefore, E eq = 6   V . Now, current variation in the circuit due to charging will be 6 3 5 + 3 e - t - t 0 C R At, t = t 0 + 7 . 2   μs , we get i = 6 × 5 18 e - 7 . 2 × 10 - 6 2 × 10 - 6 × 3 . 6 = 30 18 × e - 1 = 30 18 × 0 . 36 = 0 . 6   A At steady state, voltage across capacitor = 6   V . Q = 6 × 2 = 12 μ C .
Related: Physics — Alternating Current · All PYQ Banks