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

Question

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) V 1= V 2 and R 1= R 2= R 3 (B) V 1= V 2 and R 1=2 R 2= R 3 (C) V 1=2 V 2 and 2 R 1=2 R 2= R 3 (D) 2 V 1= V 2 and 2 R 1= R 2= R 3

Tardigrade Admin · Accepted Answer

V 1=( R 1( V 1+ V 2)/ R 1+ R 3) ⇒ V 1 R 3= V 2 R 1 V 2=( R 3( V 1+ V 2)/ R 1+ R 3) ⇒ V 2 R 1= V 2 R 3

Q. Two ideal batteries of $e m f V_{1}$ 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

$V_{1} = V_{2}$ and $R_{1} = R_{2} = R_{3}$

$V_{1} = V_{2}$ and $R_{1} = 2 R_{2} = R_{3}$

$V_{1} = 2 V_{2}$ and $2 R_{1} = 2 R_{2} = R_{3}$

$2 V_{1} = V_{2}$ and $2 R_{1} = R_{2} = R_{3}$

$V_{1} = \frac{R _{1} ( V _{1} + V _{2} )}{R _{1} + R _{3}}$
$\Rightarrow V_{1} R_{3} = V_{2} R_{1}$
$V_{2} = \frac{R _{3} ( V _{1} + V _{2} )}{R _{1} + R _{3}}$
$\Rightarrow V_{2} R_{1} = V_{2} R_{3}$

Q. Two ideal batteries of emfV1​ and V2​ and three resistances R1​,R2​ and R3​ are connected as shown in the figure. The current in resistance R2​ would be zero if

V1​=V2​ and R1​=R2​=R3​

V1​=V2​ and R1​=2R2​=R3​

V1​=2V2​ and 2R1​=2R2​=R3​

2V1​=V2​ and 2R1​=R2​=R3​