Wheatstone bridge formed by a uniform wire AB of length 100 cm. Resistance R in left gap, unknown X in right gap; balance point at length l from A gives X = R·(100 − l)/l. Measure wire length L and diameter d (screw gauge); ρ = (X·π·d²)/(4·L). Reverse the current and average to cancel thermo-emf.
-- NCERT Physics Lab Manual Class 12, Part 2, p. 28Experiment 10 Resistivity Metre Bridge
8 MCQs9-step worked example
Source: NCERT Experimental SkillsOfficial key: NTA-verifiedLast updated: 24 Sep 2026
Experiment 10 Resistivity Metre Bridge, explained for NEET
The metre bridge question that costs marks is not the bridge equation — it is what the balance point is allowed to be. A balance found at 8 cm or at 94 cm is arithmetically usable and experimentally poor: the fractional uncertainty in the ratio l : (100 − l) blows up near either end, because one of the two lengths is small while the metre-scale uncertainty stays the same. The instruction in the NCERT Physics Lab Manual Class 12, Part 2, page 28 is to adjust the resistance box until the null sits near the middle of the wire, roughly between 30 cm and 70 cm.
The bridge is a Wheatstone network laid flat. One gap holds the unknown wire, the other a resistance box; the uniform bridge wire between them supplies the other two arms in the ratio of their lengths. At the null,
X = R · l / (100 − l)
with l in centimetres measured from the end nearest the unknown. Nothing here depends on the cell's emf, which is why the bridge is a null method rather than a meter-reading method.
Resistivity then needs two more measurements that are not part of the bridge at all: the wire's length L and its diameter d, giving
ρ = X · πd² / (4L)
The diameter enters squared, so it dominates the final uncertainty — a point worth remembering before polishing the balance length to a tenth of a millimetre.
Three practical habits the manual insists on (page 28): press the jockey, never slide it, or the wire develops kinks and non-uniformity; keep the key closed only while taking a reading, so the wire does not warm and drift; and remember the thick copper strips in the gaps are there to make the connecting resistance negligible, not decorative.
Watch-out: interchanging the two gaps and averaging is the standard correction for end effects — not an optional extra trial.
Can you answer these Experiment 10 Resistivity Metre Bridge MCQs?
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
MCQ 1Easy RecallPractice
The metre bridge determines an unknown resistance on the basis of:
Show answer and why every option is right or wrong
Answer: C. C is correct: the metre bridge is a Wheatstone network in which the uniform wire on either side of the balance point forms two arms, as described in the NCERT Physics Lab Manual Class 12, Part 2, page 28.
Why A is wrong: A is wrong because no meter reading is used at balance — the galvanometer reads zero and the result is independent of the current supplied.
Why B is wrong: B is wrong because the potentiometer compares potential differences or emfs; the metre bridge compares resistances through a four-arm balance.
Why D is wrong: D is wrong because the junction rule alone gives no relation between the four arms; the balance condition comes from equating potentials across the galvanometer branch.
MCQ 2Easy RecallPractice
The bridge wire stretched along the metre scale is normally made of manganin or constantan because such an alloy has:
Show answer and why every option is right or wrong
Answer: A. A is correct: the alloy gives enough resistance per centimetre for a sharp null while keeping resistance nearly unchanged as the wire warms, as noted in the NCERT Physics Lab Manual Class 12, Part 2, page 28.
Why B is wrong: B is wrong because a near-zero resistance wire would give no measurable ratio between the two segments and no distinct balance point.
Why C is wrong: C is wrong because a drifting balance point is exactly the defect the alloy is chosen to avoid.
Why D is wrong: D is wrong because the bridge equation assumes a uniform wire of constant cross-section and resistivity; non-uniformity is an error source, not a feature.
MCQ 3Easy RecallPractice
Thick copper strips are fitted between the terminals that form the two gaps of a metre bridge in order to:
Show answer and why every option is right or wrong
Answer: D. D is correct: the strips are made thick and of copper so their own resistance can be neglected against the unknown and the box resistance, as stated in the NCERT Physics Lab Manual Class 12, Part 2, page 28.
Why A is wrong: A is wrong because the strips lower, not raise, the circuit resistance; current limiting is the job of the series rheostat or resistance box.
Why B is wrong: B is wrong because no strip resistance is entered into the bridge equation — the design assumes it is negligible.
Why C is wrong: C is wrong because heating is controlled by keeping the key closed only briefly, not by the strips.
MCQ 4Direct ApplicationPractice
In a metre bridge the unknown wire is in the left gap and a resistance box set to 6.0 Ω is in the right gap. The galvanometer shows no deflection when the jockey is at 40.0 cm from the left end. The resistance of the wire is:
Show answer and why every option is right or wrong
Answer: B. B is correct: X = R·l/(100 − l) = 6.0 × 40.0/60.0 = 4.0 Ω, the balance relation given in the NCERT Physics Lab Manual Class 12, Part 2, page 28.
Why A is wrong: A is wrong because 3.0 Ω comes from halving the box value instead of scaling it by the length ratio.
Why C is wrong: C is wrong because it simply repeats the box setting; the unknown equals the box value only when the balance point is at 50.0 cm.
Why D is wrong: D is wrong because 9.0 Ω uses the inverted ratio 60.0/40.0 — the length measured from the end of the unknown's own gap must be the numerator.
MCQ 5Direct ApplicationPractice
A wire of resistance 4.0 Ω has length 1.00 m and diameter 0.50 mm. Its resistivity is:
Show answer and why every option is right or wrong
Answer: D. D is correct: ρ = X·πd²/(4L) = 4.0 × π × (5.0 × 10⁻⁴ m)² / (4 × 1.00 m) = 7.9 × 10⁻⁷ Ω m, the working set out in the NCERT Physics Lab Manual Class 12, Part 2, page 28.
Why A is wrong: A is wrong because it uses ρ = XL/A, inverting the relation; resistivity is resistance times area per unit length, not resistance times length per unit area.
Why B is wrong: B is wrong because it treats the measured diameter as the radius (equivalently, it drops the factor 4), which multiplies the area — and the answer — by four.
Why C is wrong: C is wrong because it omits the factor π/4 and uses d² itself as the cross-sectional area.
MCQ 6Direct ApplicationPractice
With the unknown wire in the left gap, a metre bridge balances at 40.0 cm measured from the left end. The contents of the two gaps are then interchanged and the balance is again measured from the same left end. The new balance length is:
Show answer and why every option is right or wrong
Answer: A. A is correct: interchanging the gaps swaps the roles of l and (100 − l), so the null moves to 100.0 − 40.0 = 60.0 cm from the same end — the check the NCERT Physics Lab Manual Class 12, Part 2, page 28 prescribes for end effects.
Why B is wrong: B is wrong because the balance point stays put only if the two gaps hold equal resistances, which is not the case here.
Why C is wrong: C is wrong because 50.0 cm is the balance point of equal arms, not the result of interchanging unequal ones.
Why D is wrong: D is wrong because it subtracts the two lengths instead of reflecting the balance point about the midpoint of the wire.
MCQ 7Concept TrapPractice
A student sets the resistance box to a value that puts the balance point at 8.0 cm from the end of the unknown's gap. The best course of action is to:
Show answer and why every option is right or wrong
Answer: C. C is correct: near either end one of the two lengths is small, so the same scale uncertainty produces a large fractional error in the ratio; the NCERT Physics Lab Manual Class 12, Part 2, page 28 directs the null to be brought near mid-wire.
Why A is wrong: A is wrong because exactness of the equation is not the issue — the uncertainty in l/(100 − l) grows sharply as either length becomes small.
Why B is wrong: B is wrong because it moves the balance further into the region of poorest precision.
Why D is wrong: D is wrong because the jockey should be pressed at chosen points and lifted between them; sliding under pressure scrapes the wire and destroys the uniformity the bridge equation assumes, and a continuously closed key heats the wire.
MCQ 8CalculationPractice
A wire balances at 50.0 cm against a resistance box whose setting may be treated as exact. Its length is 1.000 m measured to ±0.001 m, its diameter 0.60 mm measured to ±0.01 mm, and each of the two balance lengths carries an uncertainty of ±0.1 cm. The maximum percentage error in the resistivity is closest to:
Show answer and why every option is right or wrong
Answer: B. B is correct: the diameter contributes 2 × (0.01/0.60) = 3.33%, the length 0.1%, and the two balance lengths 0.1/50.0 + 0.1/50.0 = 0.4%, giving about 3.8% in ρ = X·πd²/(4L) as computed in the NCERT Physics Lab Manual Class 12, Part 2, page 28.
Why A is wrong: A is wrong because it stops at the diameter and length terms and forgets that l and (100 − l) each carry the scale uncertainty.
Why C is wrong: C is wrong because it counts the diameter once instead of twice; d appears squared, so its fractional error is doubled.
Why D is wrong: D is wrong because it multiplies the diameter's fractional error by four; the exponent of d in the resistivity expression is 2, not 4.
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How do you solve a Experiment 10 Resistivity Metre Bridge question? A worked example
- 1
Given
Resistance box setting R = 6.0 Ω; balance length from the unknown's end l = 45.0 cm on a bridge wire of total length 100 cm (exact, by definition of the scale); wire length L = 1.00 m; wire diameter d = 0.40 mm measured with a screw gauge.
- 2
Required
The resistivity ρ of the material of the wire.
- 3
Concept
At the null the bridge is a balanced Wheatstone network, so the ratio of the two gap resistances equals the ratio of the two wire segments. The unknown resistance so obtained is then converted to resistivity using the wire's own geometry — a separate measurement that the bridge itself does not supply.
- 4
Formula
X = R · l / (100 − l), then ρ = X · πd² / (4L)
- 5
Substitution
X = 6.0 × 45.0 / (100 − 45.0) = 6.0 × 45.0 / 55.0
ρ = X × π × (4.0 × 10⁻⁴ m)² / (4 × 1.00 m) - 6
Calculation
X = 4.909 Ω
Cross-sectional area = π × 1.6 × 10⁻⁷ m² / 4 = 1.2566 × 10⁻⁷ m²
ρ = 4.909 × 1.2566 × 10⁻⁷ / 1.00 = 6.169 × 10⁻⁷ Ω m
The 100 in the balance relation and the 4 in πd²/4 are exact — the first is the defined length of the bridge wire in centimetres, the second a counting factor from the area of a circle. Neither limits the number of significant figures; the two-significant-figure inputs (6.0 Ω, 0.40 mm) do. - 7
Final answer
ρ ≈ 6.2 × 10⁻⁷ Ω m.
- 8
Common trap
Carrying 4.909 Ω and 6.169 × 10⁻⁷ Ω m into the answer line. The box setting and the diameter were each given to two significant figures, so the reported resistivity gets two. The opposite error is just as common in this experiment — treating the balance length as the limiting measurement and rounding to three figures because the metre scale reads to 0.1 cm, when in fact the squared diameter dominates the uncertainty.
- 9
Similar NEET-style question
The same wire is now compared against a box setting of 3.0 Ω. Predict the new balance length, then state whether the resistivity you would calculate from that trial should come out the same, and why the two trials are nevertheless worth averaging.
What to remember before solving Experiment 10 Resistivity Metre Bridge questions
More in Experimental Skills: 6 exam traps and mistakes · 3 formulas · 1 question pattern from its other lessons.
Experiment 10 Resistivity Metre Bridge questions from past NEET papers
No question in our NEET 2020–2025 set targets this topic directly.
Sources
Page numbers are the ones printed in the current NCERT textbook (2023 rationalised edition), unless marked pre-2023. The books are free at ncert.nic.in.
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