Connect galvanometer with high series resistance R, observe deflection θ. Then add a shunt S until deflection is θ/2 — at this point the galvanometer resistance G = R·S/(R − S). Figure of merit k = E/((R+G)·θ) where E is cell emf. Use a fresh cell to keep E constant.
-- NCERT Physics Lab Manual Class 12, Part 6, p. 53Experiment 12 Galvanometer Half Deflect
8 MCQs9-step worked example
Source: NCERT Experimental SkillsOfficial key: NTA-verifiedLast updated: 27 Sep 2026
Experiment 12 Galvanometer Half Deflect, explained for NEET
The half-deflection method fails most often at one point: the shunt. S goes across the galvanometer, not in series with it, and R stays in series with the cell. Wire S in series and the whole derivation collapses — yet the halved deflection still appears, so the reading looks convincing.
The circuit is a cell of emf E, a high resistance box R in series with the galvanometer, and a low resistance box S connected in parallel with the galvanometer through its own key. With the S key open, adjust R until the deflection θ is a convenient whole number of divisions. Then close the S key and reduce S until the deflection is exactly θ/2. The NCERT Physics Lab Manual Class 12, Part 6, page 55 gives the working relation
G = RS / (R − S)
and this holds only while the current drawn from the cell is practically unchanged by inserting S — which needs R ≫ S. That is why R is set in thousands of ohms and S in tens.
The second quantity, the figure of merit, is the current needed for one division of deflection:
k = E / ((R + G) θ)
with units A div⁻¹. Note the G in the denominator. Dropping it because "G is small" is the commonest arithmetic slip here, and it biases k high by exactly G/R.
For NEET, this experiment is tested as a short reasoning or one-step numerical item — read the value asked for carefully, because G and k are different quantities from the same pair of readings and the options are usually built to swap them.
Watch-out: half deflection means half the deflection, not half the current through the galvanometer, and not S = G unless R is treated as infinite.
Can you answer these Experiment 12 Galvanometer Half Deflect 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
In the half-deflection experiment, the low resistance box S is connected:
Show answer and why every option is right or wrong
Answer: C. Option C is correct: S is a shunt across the galvanometer, so that closing its key diverts part of the current and halves the deflection, as set out in the circuit description in the NCERT Physics Lab Manual Class 12, Part 6, page 55.
Why A is wrong: A is incorrect: a series S would simply add to the circuit resistance and reduce the current everywhere; no current would be diverted, and the relation G = RS/(R − S) would not apply.
Why B is wrong: B is incorrect: S placed in series with the cell is electrically the same as adding to R, so it cannot produce the current split the method depends on.
Why D is wrong: D is incorrect: a box across the cell terminals loads the source rather than shunting the galvanometer, changing the effective supply instead of the galvanometer current.
MCQ 2Easy RecallPractice
In the half-deflection method, the galvanometer resistance G is obtained from the series resistance R and the shunt S as:
Show answer and why every option is right or wrong
Answer: A. Option A is correct. G = RS/(R − S) is the working formula stated for this experiment in the NCERT Physics Lab Manual Class 12, Part 6, page 55.
Why B is wrong: B is incorrect: RS/(R + S) is the equivalent resistance of R and S in parallel, a different quantity from the galvanometer resistance derived here.
Why C is wrong: C is incorrect: this is the reciprocal form and does not even carry the dimensions of resistance.
Why D is wrong: D is incorrect: R and S are not in series in this circuit; adding them is the error that follows from mis-wiring the shunt in series with the galvanometer.
MCQ 3Easy RecallPractice
The figure of merit of a galvanometer is defined as:
Show answer and why every option is right or wrong
Answer: D. Option D is correct: k = E/((R + G)θ) is the current per division, with units A div⁻¹, as defined for this experiment in the NCERT Physics Lab Manual Class 12, Part 6, page 56.
Why A is wrong: A is incorrect: deflection per unit current is the current sensitivity — the reciprocal of the figure of merit, with reciprocal units.
Why B is wrong: B is incorrect: the figure of merit is a current, not a resistance; G is found separately from the shunt readings.
Why C is wrong: C is incorrect: the full-scale current equals k multiplied by the total number of divisions, so it is a derived value rather than the definition.
MCQ 4Direct ApplicationPractice
In a half-deflection experiment the deflection obtained with R = 1.05 × 10³ Ω is halved when a shunt S = 50.0 Ω is connected across the galvanometer. The galvanometer resistance is:
Show answer and why every option is right or wrong
Answer: B. Option B is correct: G = RS/(R − S) = (1050 × 50.0)/(1050 − 50.0) = 52.5 Ω, using the working relation given in the NCERT Physics Lab Manual Class 12, Part 6, page 55.
Why A is wrong: A is incorrect: 47.7 Ω comes from RS/(R + S), the parallel-combination formula, instead of the half-deflection relation with R − S in the denominator.
Why C is wrong: C is incorrect: this assumes G = S, true only in the limiting case of infinite R; here R is finite and G exceeds S.
Why D is wrong: D is incorrect: 1.00 × 10³ Ω is R − S, the denominator alone, reported as if it were the answer.
MCQ 5Direct ApplicationPractice
A galvanometer of resistance 50.0 Ω is in series with R = 1.95 × 10³ Ω across a cell of emf 2.00 V, and shows a deflection of 20.0 divisions. The figure of merit is:
Show answer and why every option is right or wrong
Answer: A. Option A is correct: k = E/((R + G)θ) = 2.00/((1950 + 50.0) × 20.0) = 5.0 × 10⁻⁵ A div⁻¹, following the definition in the NCERT Physics Lab Manual Class 12, Part 6, page 56.
Why B is wrong: B is incorrect: this value corresponds to a deflection of 10.0 divisions, half the 20.0 divisions actually observed.
Why C is wrong: C is incorrect: this divides by 50 divisions rather than 20.0 — the total resistance is right but the deflection is not.
Why D is wrong: D is incorrect: this drops two powers of ten from the total resistance, treating R + G as 2.00 × 10¹ Ω.
MCQ 6Concept TrapPractice
The relation G = RS/(R − S) assumes the current drawn from the cell is practically the same before and after the shunt is connected. This assumption requires that:
Show answer and why every option is right or wrong
Answer: D. Option D is correct: with R ≫ S the series resistance dominates the circuit, so inserting the small shunt barely changes the total current — the condition under which the derivation in the NCERT Physics Lab Manual Class 12, Part 6, page 55 is valid.
Why A is wrong: A is incorrect: S larger than R makes R − S negative, giving a meaningless negative value of G.
Why B is wrong: B is incorrect: with S comparable to R the shunt changes the total resistance substantially, so the constant-current assumption breaks and G comes out badly in error.
Why C is wrong: C is incorrect: a small R makes the circuit current depend strongly on S, and the deflection would also run off scale; R is deliberately set in the kilohm range.
MCQ 7CalculationPractice
A galvanometer of resistance 60.0 Ω is connected in series with R = 1.94 × 10³ Ω across a 2.00 V cell and deflects through 25.0 divisions. Its scale carries 30.0 divisions on each side. The current needed for full-scale deflection is:
Show answer and why every option is right or wrong
Answer: B. Option B is correct: first k = 2.00/((1940 + 60.0) × 25.0) = 4.0 × 10⁻⁵ A div⁻¹, then the full-scale current is k × 30.0 = 1.2 × 10⁻³ A, using the figure-of-merit definition in the NCERT Physics Lab Manual Class 12, Part 6, page 56.
Why A is wrong: A is incorrect: 4.0 × 10⁻⁵ A is the figure of merit itself — the current for one division — with the second step, multiplication by 30.0 divisions, left undone.
Why C is wrong: C is incorrect: this uses the observed 25.0 divisions as the full-scale count instead of the 30.0 divisions the scale actually carries.
Why D is wrong: D is incorrect: it multiplies the figure of merit by 60.0 divisions — both sides of the scale — instead of the 30.0 divisions on one side; full-scale deflection is 30.0 divisions.
MCQ 8Direct ApplicationPractice
A student computes the figure of merit as E/(Rθ), leaving the galvanometer resistance out of the denominator. With R = 1.00 × 10³ Ω and G = 50.0 Ω, the reported value is:
Show answer and why every option is right or wrong
Answer: C. Option C is correct: the reported value divided by the true value is (R + G)/R = 1050/1000 = 1.05, so leaving G out inflates the figure of merit by 5.0%, since the definition on the NCERT Physics Lab Manual Class 12, Part 6, page 56 uses the total resistance R + G.
Why A is wrong: A is incorrect: 4.8% is G/(R + G), the share of the total resistance that G represents; the error relative to the true k is measured against R and comes to 5.0%.
Why B is wrong: B is incorrect in direction: a smaller denominator gives a larger quotient, so omitting G raises the reported k rather than lowering it.
Why D is wrong: D is incorrect: G appears only once, in the figure-of-merit expression, so there is nothing for it to cancel against; the bias is present in every trial.
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How do you solve a Experiment 12 Galvanometer Half Deflect question? A worked example
- 1
Given.
Cell emf E = 2.00 V, taken as constant over the readings. With the shunt key open, series resistance R = 1.50 × 10³ Ω produces a galvanometer deflection θ = 30.0 divisions. Closing the shunt key and adjusting the shunt box to S = 60.0 Ω brings the deflection to 15.0 divisions.
- 2
Required.
(i) The galvanometer resistance G. (ii) The figure of merit k.
- 3
Concept.
With S across the galvanometer and R ≫ S, the total current from the cell is essentially unchanged when the shunt key is closed. Halving the deflection therefore means half the original current now passes through the galvanometer and half through S, so the two parallel branches carry equal currents across the same potential difference — which fixes G in terms of R and S. The figure of merit then follows from the unshunted reading, where the whole circuit current E/(R + G) produced θ divisions.
- 4
Formula.
G = RS/(R − S), and k = E/((R + G) θ).
- 5
Substitution.
G = (1.50 × 10³ × 60.0)/(1.50 × 10³ − 60.0); k = 2.00/((1.50 × 10³ + 62.5) × 30.0).
- 6
Calculation.
G = 9.00 × 10⁴ / 1.44 × 10³ = 62.5 Ω. Then R + G = 1.5625 × 10³ Ω, and (1.5625 × 10³) × 30.0 = 4.6875 × 10⁴, so k = 2.00 / 4.6875 × 10⁴ = 4.266… × 10⁻⁵ A div⁻¹. The 30.0 scale divisions are a counted number and the factor 2 implicit in "half deflection" is exact; neither limits the significant figures, which are set by E, R and S at three each.
- 7
Final answer.
G = 62.5 Ω and k = 4.27 × 10⁻⁵ A div⁻¹, both quoted to three significant figures.
- 8
Common trap.
Substituting R + S instead of R − S in the denominator. That gives 57.7 Ω here — close enough to 62.5 Ω to look plausible, which is exactly why it survives a quick glance. The minus sign comes from the requirement that the shunt branch and the galvanometer branch carry equal currents; R + S answers a different question. The second trap is dropping G from the figure of merit and using R alone, which here would return 4.44 × 10⁻⁵ A div⁻¹, high by 4.2%.
- 9
Similar NEET-style question.
A galvanometer in series with 2.00 × 10³ Ω across a 3.00 V cell deflects through 25.0 divisions; a shunt of 1.00 × 10² Ω across the galvanometer halves the deflection. Find G and k, and state the percentage by which k would be overestimated if G were omitted from the total resistance.
What to remember before solving Experiment 12 Galvanometer Half Deflect questions
More in Experimental Skills: 6 exam traps and mistakes · 3 formulas · 1 question pattern from its other lessons.
Experiment 12 Galvanometer Half Deflect 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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