For the circuit shown in figure, all the three batteries are ideal. Match the columns

Column I Column II
I The value of R such that current through 3V battery is zero P 1 $Ω$
II The value of R such that current through 1V battery is zero Q 2 $Ω$
III The value of R such that current through 2V battery is zero R 3 $Ω$
IV The value of R for which current through 3V battery is 5/8A S Not possible for any value of R
I II III IV
1 S S P Q
2 Q S P S
3 P S S Q
4 Q S S P

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answer is A.

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Detailed Solution

Let current through various branches be as shown in fig.
Question Image
$\begin{array}{l} i_{1} + i_{2} + i_{3} = 0 - \dots (i) \\ V_{A} - V_{B} = V_{D} - V_{C} = V_{E} - V_{F} \\ 1 - 1 i_{1} = 2 - 2 i_{2} = 3 - {Ri}_{3} \end{array}$
From eqs. (i) and (ii), we get $i_{1} = \frac{- (R + 4)}{3 R + 2}$
Again from Eqs. (i) and (ii), we get $i_{2} = \frac{(R - 1)}{3 R + 2}$
Now $i_{3} = - i_{1} - i_{2} = \frac{5}{3 R + 2}$
i. Current i₃ cannot be zero ii. Current i₁ cannot be zero
iii. $i_{2} = 0 \Rightarrow R = 1 Ω$ iv. $i_{3} = \frac{5}{8} A \Rightarrow R = 2 Ω$

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Column I		Column II
I	The value of R such that current through 3V battery is zero	P	1 $Ω$
II	The value of R such that current through 1V battery is zero	Q	2 $Ω$
III	The value of R such that current through 2V battery is zero	R	3 $Ω$
IV	The value of R for which current through 3V battery is 5/8A	S	Not possible for any value of R