JEE Main 2026 January: Metre-bridge and the shifted null point
The metre bridge appears every January because it tests three things at once: the null condition of a balanced Wheatstone bridge, reading a linear scale accurately, and the error that creeps in when the jockey is set off-centre.
Worked solution for the JEE Main January 2026 physics question on the metre bridge, where the null point landed at 38 cm instead of the textbook 40 cm and the second part asked for the resulting error.
How this actually works
Setting up the ratio
At the balance point the ratio of resistances equals the ratio of lengths, so with the unknown resistance R in one gap, a 10 Ω standard in the other, and a null point at 38 cm, the balance condition is R / 10 = 38 / 62. That is the only equation the question needs, but candidates lost marks writing the lengths backwards — the resistance on the left corresponds to the left length, not the right. Reading the diagram is the actual test here, not the arithmetic, and the arithmetic is a single division.
Where the percentage comes from
The second part asked for the percentage error introduced by assuming the null point was exactly at a round number. With a 38 cm reading the relative error is small in absolute terms, but it propagates directly into the calculated resistance, because the resistance is proportional to a length ratio. The standard fix, taught in the lab rather than the textbook, is to take the average of the balance points for the two-swap measurement, which cancels the systematic end-error of the bridge wire.
Why the two-swap exists
The bridge wire has non-uniform resistance per unit length near the ends and near the joints, so a null point found on one side of the wire is not directly comparable to one found on the other. Reversing the battery and galvanometer does not move the null point — at balance the galvanometer draws no current, so reversing the polarity reverses neither the potential drop nor the balance condition. The swap exists purely so that the same end-error appears in both readings and cancels in the average. Students who expected the null point to move after the swap wasted a minute rediscovering that it does not.
How to practise this pattern
Do one full metre-bridge problem a week for four weeks, always including the two-swap average and the percentage-error part. The first three are arithmetic; the fourth is where the marks are, and it is the part students skip because the answer to part one already looked right.
JEE Main 2026 January: Metre-bridge and the shifted null point: the facts to keep
| Apparatus | Metre bridge: a one-metre uniform wire, a jockey, a galvanometer and a 10 ohm standard resistor |
|---|---|
| Balance condition | R / R_standard = l / (100 - l), with l measured in centimetres from the left end |
| Null point here | 38 cm, giving R = 10 x 38 / 62 |
| The two-swap method | Reverse the battery and galvanometer, find the second null point, and average the two lengths |
| Why the swap works | At balance the galvanometer draws no current, so the null point does not move; the swap cancels the systematic end-error |
| The error question | A millimetre-scale reading error is a very small resistance error, because the resistance scales with a length ratio |
Questions students ask about this
Why does swapping the battery and galvanometer not change the null point?
At balance the galvanometer draws no current, so reversing the battery polarity reverses neither the potential drop nor the balance condition. The null point stays put; the swap is a check on the contact resistance of the wire.
What is the sensitivity of a metre bridge?
The fractional change in the unknown resistance equals the fractional change in the null point length, so a millimetre-scale reading error is a very small resistance error. The instrument is accurate precisely because the balance condition is null-based rather than deflection-based.