Wheatstone Bridge and Metre Bridge
On this page
Direct answer
Bridge four resistances P, Q, R, S in a diamond, a galvanometer across the diagonal and a cell across the outer points: the network reads null — zero deflection — when the ratio arms balance, P/Q = R/S, at which the unknown follows from the other three and neither the cell's emf nor the galvanometer's resistance matters. The metre bridge is its laboratory embodiment — a uniform 1-metre wire of manganin or constantan replaces two arms, and l/(100 - l) = R/S converts a length into resistance. Because it is a null method — current in the detector vanishes at balance — it is far more accurate than deflection measurement, the point NEET keeps asking about.
What you must remember
- Balance condition: P/Q = R/S; derived from Kirchhoff's loop rule with zero galvanometer current, so the bridge is independent of the galvanometer's resistance and the cell's emf at balance.
- Metre bridge formula: S = R (100 - l)/l, where R is the known resistance in the left gap and l the balance length on the wire.
- Wire material: manganin or constantan (eureka) — high resistivity, low temperature coefficient — chosen so the resistance per unit length stays uniform and stable; copper fails on both counts.
- Null method advantage: at balance the galvanometer draws no current, so the measurement does not disturb the circuit; this is the same virtue that makes the potentiometer superior to a voltmeter.
- Sensitivity rule: the balance point should sit near the middle of the wire (l between roughly 35 and 65 cm); end errors dominate when it hugs either end.
- Balance is a ratio test: checking a candidate balance needs only the four values, not the supply voltage — the fastest way to eliminate options in a multiple-choice bridge question.
A metre bridge session, from balance to error
A 10 Ω resistance in the left gap balances at l = 40 cm against an unknown S in the right gap: l/(100 - l) = R/S gives 40/60 = 10/S, so S = 15 Ω. Now the examiner's extension: the balance point lies too far left (below 30 cm), where a small end error of 1 cm distorts the ratio badly — l/(100 - l) changes from 0.40/0.60 to 0.39/0.61 — so the experimenter should have used a 20 Ω standard to pull the point toward the middle. The systematic errors have names: end resistances at the strip connections shift the effective zero, non-uniformity of the wire's cross-section makes resistance non-proportional to length, and contact resistance at the jockey adds a spurious few hundredths of an ohm wherever it touches. This is why the standard procedure swaps the two gaps and averages the balance points, largely cancelling the end error.
The traps in the diamond
The commonest error treats the balance condition as a lucky formula rather than a Kirchhoff statement; when a question redraws the bridge with the cell and galvanometer interchanged (which preserves balance — the interchangeability theorem), candidates who memorised a picture rather than the loops reach for options that assume the bridge is now "unbalanced". The second trap is the ratio direction in the metre bridge: l corresponds to the resistance in the same gap, so S = R(100 - l)/l, not Rl/(100 - l); both values appear in the options separated by a reciprocal. Third, off-balance questions require real circuit analysis: with the galvanometer carrying current you must write two loop equations (or use nodal analysis), and a quick sanity check — S open-circuits the right branch — anchors the extreme cases. Finally, the interplay question: inserting the ammeter in the wrong position or using a copper wire is a favourite assertion-reason dressing, and the manganin rationale (low temperature coefficient keeping length proportional to resistance despite Joule heating) is the expected justification.
Frequently asked questions
What is the balanced condition of a Wheatstone bridge?
P/Q = R/S — the ratio of one pair of adjacent arms equals the ratio of the other, at which the galvanometer current is exactly zero.
Why is the bridge called a null method?
The measurement is made by adjusting until the detector reads zero, so at balance no current flows through the galvanometer and the circuit is left undisturbed.
How is unknown resistance measured with a metre bridge?
By the relation S = R(100 - l)/l with a known standard R and the balance length l read off the uniform wire that forms the two ratio arms.
Why is manganin used for the metre bridge wire?
Its high resistivity gives a workable resistance per centimetre while its very low temperature coefficient keeps the wire's resistance proportional to length even as it warms.
What goes wrong when the balance point lies near the end of the wire?
End corrections and contact resistances become comparable to the measured ratio, so the percentage error blows up; the standard remedy is to change the known resistance and re-balance near the middle.