JEE Advanced 2022 — Paper 1 — PHY-II solution

JEE Advanced2022Paper 1PHY-II

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?

A
The magnitude of current flowing through $R_{1}$ is 7.2 A.
B
The magnitude of current flowing through $R_{2}$ is 1.2 A.
C
The magnitude of current flowing through $R_{3}$ is 4.8 A.
D
The magnitude of current flowing through $R_{5}$ is 2.4 A.

Solution

By symmetry, the top vertex $A$ and bottom vertex $B$ of the rhombus are at the same potential, so they can be merged. The folded network becomes two parallel branches from $C$ (left node) through the merged node $A / B$ to $D$ (right node), where each branch has resistance $1/2 Ω$ .

Let $x$ be the current entering at $C$ through $R_{3}$ branch (with 6 V source) and $y$ be the current leaving at $D$ through $R_{1}$ branch (with 12 V source). Applying KVL to the two loops:

Loop 1: $- \frac{x}{2} - \frac{x + y}{2} - x + 6 = 0 \Rightarrow 4 x + y = 12$ .

Loop 2: $\frac{y}{2} + y + 12 + \frac{x + y}{2} = 0 \Rightarrow 4 y + x = - 24$ .

Solving: $x = 72/15 = 4.8$ A, $y = - 108/15 = - 7.2$ A.

Current in $R_{1} = ∣ y ∣ = 7.2$ A. Current in $R_{3} = ∣ x ∣ = 4.8$ A.

Current in $R_{2} = \frac{∣ x + y ∣}{2} = \frac{∣72/15 - 108/15∣}{2} = \frac{36/15}{2} = 1.2$ A.

Current in $R_{5} = \frac{∣ x ∣}{2} = 2.4$ A.

All four statements are correct.

← Back to full paper

Practice more PHY-II

Concept-wise practice with instant solutions on Fundamenthol.

Start practicing →