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Galvanometer resistance and figure of merit by half-deflection: NEET MCQs with answers

48 questions on this topic of Experimental Skills (NEET 2027 syllabus). Here are 12; tap one to see its answer and explanation.

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easy

1. In the circuit of the half-deflection method to determine galvanometer resistance G, key K₁ is in the main circuit with series resistance R, and key K₂ is in the shunt branch with shunt resistance S. What should be done first before closing key K₁?

  1. Keep R = 0 to allow maximum current
  2. Remove all plugs from the shunt resistance box S
  3. Close key K₂ with S = 0
  4. Take out a very high resistance from the resistance box R
Show answer and explanation

Answer: (D) Take out a very high resistance from the resistance box R

Before completing the circuit by closing the main key K₁, a very high resistance must be introduced from the series resistance box R. This ensures that the initial current flowing through the galvanometer is within its permissible limit, preventing potential burnout of the delicate coil.

medium

2. Statement I: In the half-deflection method, the deflection is deliberately kept between 20 and 30 divisions on a 30-division scale before introducing the shunt. Statement II: Keeping the initial deflection large minimizes the percentage error in measuring the deflection θ and half-deflection θ/2.

  1. Both Statement I and Statement II are correct and Statement II is the correct explanation of Statement I.
  2. Both Statement I and Statement II are correct but Statement II is not the correct explanation of Statement I.
  3. Statement I is correct but Statement II is incorrect.
  4. Statement I is incorrect but Statement II is correct.
Show answer and explanation

Answer: (A) Both Statement I and Statement II are correct and Statement II is the correct explanation of Statement I.

Reading deflection carries an observational reading error Δθ (typically half a division). The fractional error Δθ/θ decreases as θ increases, so using a large initial deflection (typically 20 to 30 divisions) significantly reduces the relative measurement error.

hard

3. A galvanometer gives 30 divisions with R = 4950 Ω and a 2 V cell of negligible resistance. If G = 50 Ω, its figure of merit is about:

  1. 1.33 × 10⁻⁵ A per division
  2. 4 × 10⁻⁴ A per division
  3. 2 × 10⁻³ A per division
  4. 6.7 × 10⁻² A per division
Show answer and explanation

Answer: (A) 1.33 × 10⁻⁵ A per division

I = E/(R + G) = 2/5000 = 4 × 10⁻⁴ A. Figure of merit = I/θ = 4 × 10⁻⁴/30 ≈ 1.33 × 10⁻⁵ A per division.

NCERT Class 11

medium

4. During a half-deflection experiment, a student records an initial deflection θ = 28 divisions with R = 4500 Ω. Upon introducing a shunt S = 90 Ω, the deflection becomes 14 divisions. The calculated resistance of the galvanometer is:

  1. 90.0 Ω
  2. 88.2 Ω
  3. 91.8 Ω
  4. 93.5 Ω
Show answer and explanation

Answer: (C) 91.8 Ω

The formula for galvanometer resistance is G = R·S / (R - S). Substituting the given values: G = (4500 × 90) / (4500 - 90) = 405000 / 4410 ≈ 91.84 Ω ≈ 91.8 Ω.

easy

5. During the determination of the figure of merit of a galvanometer, if a student doubles the total number of turns in the galvanometer coil while keeping the suspension fiber, magnetic field, and area unchanged, the figure of merit will:

  1. Be halved
  2. Be doubled
  3. Remain unchanged
  4. Become four times
Show answer and explanation

Answer: (A) Be halved

Figure of merit is given by k = C / (N A B), where C is the restoring torque per unit twist, N is the number of turns, A is the area, and B is the magnetic field. Since k is inversely proportional to N, doubling N halves the figure of merit.

hard

6. In a half-deflection experiment, a student obtains an initial deflection θ = 28 divisions with series resistance R = 2400 Ω. When a shunt S = 80 Ω is inserted, the deflection reduces to 14 divisions. If the student repeats the experiment using a series resistance R' = 4800 Ω, what shunt resistance S' will reduce the initial deflection to half its new value?

  1. 80.0 Ω
  2. 81.4 Ω
  3. 78.7 Ω
  4. 82.8 Ω
Show answer and explanation

Answer: (B) 81.4 Ω

First, determine the actual galvanometer resistance G from G = R·S / (R - S) = (2400 × 80) / (2400 - 80) = 192000 / 2320 = 82.76 Ω. Now, for the new series resistance R' = 4800 Ω, we have G = R'·S' / (R' - S'), which gives S' = (R' · G) / (R' + G) = (4800 × 82.76) / (4800 + 82.76) = 397248 / 4882.76 ≈ 81.36 Ω ≈ 81.4 Ω.

medium

7. In the half-deflection method, if the condition R >> G is not satisfied and R is comparable to G, then closing the shunt key K₂ causes the total current drawn from the battery to:

  1. Remain strictly constant
  2. Increase appreciably
  3. Decrease appreciably
  4. Become zero
Show answer and explanation

Answer: (B) Increase appreciably

When shunt S is connected across G, the equivalent resistance of the parallel combination is G·S / (G + S) < G. If R is not much larger than G, this drop significantly reduces the total circuit resistance from (R + G) to [R + G·S/(G + S)], which causes the total battery current to increase appreciably.

hard

8. A galvanometer coil has resistance G = 90 Ω. In a half-deflection experiment, a series resistance R = 910 Ω is used. If the simple formula G_calc = S is used instead of the exact relation G = R·S / (R - S), the percentage error in the determined value of G is:

  1. -9.9%
  2. +9.0%
  3. -9.0%
  4. +10.0%
Show answer and explanation

Answer: (C) -9.0%

The exact relation is G = (R × S) / (R - S), which gives S = (G × R) / (R + G) = (90 × 910) / (910 + 90) = 81900 / 1000 = 81.9 Ω. If the student approximates G_calc = S = 81.9 Ω, the error is G_calc - G = 81.9 - 90 = -8.1 Ω. The percentage error is (-8.1 / 90) × 100% = -9.0%.

easy

9. In a moving coil galvanometer, the deflecting torque is τ = NIAB. Which of the following parameters does NOT directly affect the figure of merit k = C / (NAB)?

  1. Restoring couple per unit twist (C) of the suspension wire
  2. Magnetic field strength (B)
  3. Resistance of the series resistance box (R) connected in the circuit
  4. Number of turns of the coil (N)
Show answer and explanation

Answer: (C) Resistance of the series resistance box (R) connected in the circuit

The figure of merit is an intrinsic constructional constant of the galvanometer given by k = C / (NAB), depending only on restoring torsion constant C, turn count N, coil area A, and magnetic flux density B. The external series resistance R changes the current flowing through it, but does not alter k itself.

medium

10. In a half-deflection circuit, a cell of emf 2.0 V is connected in series with a resistance of 3950 Ω and a galvanometer. The deflection produced is 20 divisions. A shunt resistance of 50 Ω reduces the deflection to 10 divisions. If R >> G is assumed, what is the figure of merit of the galvanometer?

  1. 5.0 × 10⁻⁵ A div⁻¹
  2. 2.5 × 10⁻⁵ A div⁻¹
  3. 1.0 × 10⁻⁴ A div⁻¹
  4. 2.0 × 10⁻⁴ A div⁻¹
Show answer and explanation

Answer: (B) 2.5 × 10⁻⁵ A div⁻¹

The approximate galvanometer resistance is G ≈ S = 50 Ω. Total circuit resistance is R + G = 3950 + 50 = 4000 Ω. Current I = E / (R + G) = 2.0 / 4000 = 5.0 × 10⁻⁴ A. Since this current produces a deflection θ = 20 divisions, the figure of merit k = I / θ = 5.0 × 10⁻⁴ / 20 = 2.5 × 10⁻⁵ A div⁻¹.

hard

11. A galvanometer has a resistance of 80 Ω and 30 divisions on each side of zero. When connected in series with a resistance of 2920 Ω across a 1.5 V cell, it deflects by 25 divisions. To convert this galvanometer into an ammeter of range 0 to 3 A, the required shunt resistance is approximately:

  1. 0.027 Ω
  2. 0.016 Ω
  3. 0.040 Ω
  4. 0.080 Ω
Show answer and explanation

Answer: (B) 0.016 Ω

Total initial resistance = 2920 + 80 = 3000 Ω. Current for 25 divisions = 1.5 / 3000 = 5.0 × 10⁻⁴ A. Figure of merit k = (5.0 × 10⁻⁴) / 25 = 2.0 × 10⁻⁵ A div⁻¹. Full-scale deflection current Ig = 30 × (2.0 × 10⁻⁵) = 6.0 × 10⁻⁴ A. Shunt required S ≈ (Ig × G) / I = (6.0 × 10⁻⁴ × 80) / 3 = 0.048 / 3 = 0.016 Ω.

medium

12. A cell of emf 1.5 V and negligible internal resistance is connected in series with a resistance of 2900 Ω and a galvanometer. The deflection is 30 divisions. When a shunt of 100 Ω is connected across the galvanometer, the deflection drops to 15 divisions. What is the figure of merit of the galvanometer?

  1. 1.67 × 10⁻⁵ A/div
  2. 2.50 × 10⁻⁵ A/div
  3. 5.00 × 10⁻⁴ A/div
  4. 3.33 × 10⁻⁵ A/div
Show answer and explanation

Answer: (A) 1.67 × 10⁻⁵ A/div

Using G = R·S / (R - S) = 2900 × 100 / (2900 - 100) = 290000 / 2800 ≈ 103.57 Ω. Initial current I = E / (R + G) = 1.5 / (2900 + 103.57) ≈ 1.5 / 3003.57 ≈ 4.994 × 10⁻⁴ A. Since this gives 30 divisions, the figure of merit k = I / θ = 4.994 × 10⁻⁴ / 30 ≈ 1.67 × 10⁻⁵ A/div.

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