The figure shows a circuit having eight resistances of 1 Ω each, labelled R 1 to R 8 , and two ideal batteries with voltages ε 1 = 12 V and ε 2 = 6 V . Which of the following statement(s) is(are) correct?
D. The magnitude of current flowing through R 5 is 2 . 4   A .
Point A and B are at same potential so they can be merged/folded. Now, let x and y be the current flowing from 6   V and 12   V batteries. The current distribution is shown below. Applying Kirchhoff's voltage law, For loop 1 : - 1 2 x - 1 2 x + y - 1 x + 6 = 0 ⇒ - 2 x - y 2 = - 6 ⇒ - 4   x - y = - 12 ⇒ 4 x + y = 12         ⋯ 1 For loop 2 : 1 2 y + 1 y + 12 + 1 2 x + y = 0 3 2 y + y 2 + x 2 = - 12 2 y + x 2 = - 12 4 y + x = - 24       ⋯ 2 Using, 2 - 4 × 1 , we have 4 y + x - 16 x - 4 y = - 24 - 48 ⇒ - 15 x = - 72 ⇒ x = 72 15 Putting in equation 1 , 4 72 15 + y = 12 ⇒ y = 12 - 288 15 = 180 - 288 15 = - 108 15 = - 7 . 2   A Now, current in R 1 = 7 . 2   A Current in R 2 = x + y 2 = 72 15 - 108 15 1 2 = 1 2 36 15 = 2 . 4 2   A = 1 . 2   A Current in R 3 = x = 4 . 8   A Current in R 5 = 1 2 x = 2 . 4   A
Related: Physics — Current Electricity · All PYQ Banks