Two ideal batteries of emf and and three resistances , and are connected as shown in the figure. The current in resistance would be zero if [2014]

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 [2014]

Smart Achievers · Accepted Answer

(1, 2, 4)

No current is flowing through resistance $V_{2}$ .

Applying KVL in loop

$V_{1} - i R_{1} + V_{2} - i R_{3} = 0$

$∴$ $i = \frac{V_{1} + V_{2}}{R_{1} + R_{3}} \dots (i)$

Applying KVL in loop BCDEB

$V_{1} - i R_{1} = 0$

$∴$ $i = \frac{V_{1}}{R_{1}} \dots (i i)$

From eq. (i) & (ii)

$\frac{V_{1}}{R_{1}} = \frac{V_{1} + V_{2}}{R_{1} + R_{3}}$

$∴$ $V_{1} R_{1} + V_{1} R_{3} = V_{1} R_{1} + V_{2} R_{1}$

$\Rightarrow V_{1} R_{3} = V_{2} R_{1}$

$If V_{1} = V_{2}, then R_{1} = R_{3} = R_{2}$

$If V_{1} = V_{2}, then R_{1} = R_{3} = 2 R_{2}$

$If V_{1} = 2 V_{2}, then 2 R_{3} = R_{1}$

$If 2 V_{1} = V_{2}, then R_{3} = 2 R_{1} = R_{2}$

Solution

Q.
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 [2014]

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

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

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

4 $2 V_{1} = V_{2}$ and $2 R_{1} = R_{2} = R_{3}$

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Solution

Q. Two ideal batteries of emf V1 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 [2014]

1 V1=V2 and R1=R2=R3

2 V1=V2 and R1=2R2=R3

3 V1=2V2 and 2R1=2R2=R3