In the arrangement shown, current through the galvanometer is zero. Current through the galvanometer will still be zero, if

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R₁ and R₃ are inter changed

R₁ and R₂ are inter changed

The battery and galvanometer are inter changed

Both (2) and (3) are right

answer is C.

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Detailed Solution

Initially the bridge is balanced, So $\frac{R_{1}}{R_{3}} = \frac{R_{2}}{R_{4}} \Rightarrow \frac{R_{1}}{R_{2}} = \frac{R_{3}}{R_{4}}$ (1).

If R₁ and R₂ are inter changed, no current flows through the galvanometer if $\frac{R_{2}}{R_{3}} = \frac{R_{1}}{R_{4}} i . e . if \frac{R_{1}}{R_{2}} = \frac{R_{4}}{R_{3}} .$

Which does not satisfy equation (1).

Again if R₁ and R₃ are interchanged, no current flows through the galvanometer if $\frac{R_{3}}{R_{1}} = \frac{R_{2}}{R_{4}}$ Which does not satisfy equation (1).

If the battery and the galvanometer are inter changed, then there will be no current through the galvanometer if $\frac{R_{1}}{R_{2}} = \frac{R_{3}}{R_{4}}$ which satisfies equation (1).

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