Question

In a balanced wheatstone bridge, current in the galvanometer is zero. It remains zero when
$\left(1\right)$ The emf is increased
$\left(2\right)$ All resistance are increased by $10\Omega$
$\left(3\right)$ All resistance are made five times.
$\left(4\right)$ The battery and the galvanometer are interchanged.

• A. Only $\left(1\right)$ is correct.
• B. $\left(1\right)$ and $\left(3\right)$ are correct.
• C. $\left(1\right),\left(2\right)$ and $\left(3\right)$ are correct.
• D. $\left(1\right),\left(3\right)$ and $\left(4\right)$ are correct.

Answer 1

The correct option is D $\left(1\right),\left(3\right)$ and $\left(4\right)$ are correct.


The necessary condition for a balanced wheatstone bridge:

$\frac{R_1}{R_2}=\frac{R_4}{R_3}$

$\Rightarrow R_1{R}_3=R_2{R}_4....\left(i\right)$

We can observe that the emf of battery has nothing to do with the condition for a balanced wheatstone bridge.

$\therefore$ A balanced bridge remains unaffected from the change in emf of battery.

Hence statement $\left(1\right)$ is correct

When each resistance is increased by $10\Omega$, then equation $\left(i\right)$ will no longer hold. Thus balanced condition of wheatstone bridge will get altered.

$\Rightarrow (R_1+10)(R_3+10)\ne (R_2+10)(R_4+10)$,

Hence statement $\left(2\right)$ is incorrect

If all the resistances are increased five times, then the multiplication factor gets cancelled from the two sides of Eq.$\left(i\right)$, thus the balancing condition is maintained.

$\Rightarrow \left(5R_1\right)\left(5R_3\right)=\left(5R_2\right)\left(5R_4\right)$

$\text{Or,}{R}_1{R}_3=R_2{R}_4$

Hence statement $\left(3\right)$ is correct

When the position of battery and galvanometer are interchanged in a balanced wheatstone bridge, it will again lead to equal potential across the diagonal arm.

Since, $R_1{R}_3=R_2{R}_4$


Hence this is also a balanced wheatstone bridge.

Therefore statement $\left(4\right)$ is correct

Why this question? $\underset{–}{\text{Concept Involved}}$: Always remember that if position of battery and galvanometer are exchanged then also a balanced wheatstone bridge will remain balanced.