JEE Physics 2026 Question with Solution

Given: The resistors in the two gaps are $2\,\Omega$ and $3\,\Omega$. The initial null point is on wire $XY$. After connecting an unknown resistor in parallel with the $3\,\Omega$ resistor, the null point shifts by $22.5\,\text{cm}$ towards $Y$.

Find: The value of the unknown resistance.

For a meter bridge at balance condition,

Initial balance condition:

Solving,

New balance length after the shift: Since the null point shifts $22.5\,\text{cm}$ towards $Y$,

Let the new effective resistance in the right gap be $R'$. Then,

So,

Now the unknown resistance $X$ is connected in parallel with $3\,\Omega$, so

Substituting $R' = 1.2\,\Omega$,

Thus,

Hence,

Therefore, the resistance of the unknown resistor is $2\,\Omega$. The correct option is A.

Given: Initially the bridge balances with resistors $2\,\Omega$ and $3\,\Omega$. Then the $3\,\Omega$ branch is replaced by its parallel combination with an unknown resistor.

Find: The unknown resistance.

Because the null point shifts towards $Y$, the balancing length measured from $X$ increases. That means the right-gap resistance has decreased, which is consistent with adding a resistor in parallel to $3\,\Omega$.

Initially,

which gives

So the corresponding lengths are $40\,\text{cm}$ and $60\,\text{cm}$.

After shifting,

and the other segment becomes

Hence the new ratio is

Therefore,

Now use the parallel-combination relation:

So,

Then,

Therefore, the unknown resistor has value $2\,\Omega$.