JEE Advanced 2014 · Paper 1 · Physics Q10

← JEE Advanced 2014 · Paper 1

PhysicsMultiple correct+3Question 10 of 60

Two ideal batteries of emf $V_1$ and $V_2$ and three resistances $R_1$ , $R_2$ and $R_3$ are connected as shown in the figure. The current in resistance $R_2$ would be zero if

A ladder circuit. Left vertical wire: battery V₁ (positive plate up) between the top wire and a left middle node. Right vertical: R₁ from the top wire down to a right middle node. R₂ joins the left and right middle nodes. Below the right middle node, battery V₂ (positive plate down) leads to the bottom-right corner; R₃ runs along the bottom back to the left side, which is wired straight to the left middle node.

V_1=V_2

and

R_1=R_2=R_3

V_1=V_2

and

R_1=2R_2=R_3

V_1=2V_2

and

2R_1=2R_2=R_3

2V_1=V_2

and

2R_1=R_2=R_3

Answer and worked solution

Official answer: A, B, D

Condition for zero current in $R_2$ . Then the two middle nodes are at the same potential, and the rest of the circuit is one loop: $V_1$ , $R_1$ , $V_2$ and $R_3$ in series, with both batteries driving the same way:
$I=\frac{V_1+V_2}{R_1+R_3}.$

Equal potentials. Going from the left middle node up through $V_1$ and down through $R_1$ must bring us back to the same potential:
$V_1=IR_1\implies V_1(R_1+R_3)=(V_1+V_2)R_1\implies \frac{V_1}{V_2}=\frac{R_1}{R_3}.$
$R_2$ does not enter.

(A) $V_1/V_2=1$ , $R_1/R_3=1$ . Yes.
(B) $V_1/V_2=1$ , $R_1/R_3=1$ . Yes.
(C) $V_1/V_2=2$ , $R_1/R_3=\frac12$ . No.
(D) $V_1/V_2=\frac12$ , $R_1/R_3=\frac12$ . Yes.

(A), (B), (D)

Topics:Kirchhoff's laws

← Previous question Next question →

JEE Advanced 2014 · Paper 1, Physics question 10