Physics Class 12 Part I…
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Galvanometer Applications

🎓 Class 12 Physics CBSE Theory Ch 4 – Moving Charges and Magnetism ⏱ ~14 min
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Galvanometer Applications

4.12 The Moving Coil Galvanometer

The principle that a current-carrying coil placed in a magnetic field experiences a torque is exploited in the moving coil galvanometer (MCG). It detects (and measures) small electrical currents.

4.12.1 Construction

A rectangular coil of N turns is wound on a soft iron core and suspended (or pivoted) between the curved poles of a permanent magnet. The poles are concave so that the magnetic field is radial at every position of the coil - this means the plane of the coil always contains B, so the angle between the coil's normal n-hat and B is always 90°.

N S Soft iron core suspension wire restoring spring (k) mirror radial B
Fig 4.12 Moving coil galvanometer: a rectangular coil rotates between curved magnetic poles. A soft iron core makes the field radial.

4.12.2 Theory

Because the field is always perpendicular to the plane normal (theta = 90°), the torque on the coil due to current I is

\[\tau_{mag} = NIAB\]

The suspension provides a restoring torque proportional to the angular twist phi:

\(\tau_{spring} = k\phi\)

At equilibrium, magnetic torque = restoring torque:

\(NIAB = k\phi \quad\Longrightarrow\quad I = \dfrac{k}{NAB}\,\phi\)

So deflection is directly proportional to current. The scale can be marked uniformly.

4.12.3 Sensitivity

Current sensitivity:
\(I_S = \dfrac{\phi}{I} = \dfrac{NAB}{k}\) (deflection per unit current)
Voltage sensitivity:
\(V_S = \dfrac{\phi}{V} = \dfrac{\phi}{IR} = \dfrac{NAB}{kR}\) (deflection per unit voltage)

where R is the galvanometer resistance.

To increase sensitivity:

  1. Increase N (more turns) - both I_S and V_S go up.
  2. Increase A (larger coil area) or B (stronger magnet).
  3. Decrease k (softer spring/finer suspension).
  4. Note: increasing N also raises R, so V_S = NAB/(kR) does not necessarily improve - the two effects partly cancel.

Worked Example 4.10 - Galvanometer sensitivity

Example 4.10 L3 Apply

A galvanometer has 100 turns, coil area 5 cm², radial field 0.20 T, spring constant k = 5 x 10-7 N m / radian. Find the current sensitivity.

I_S = NAB / k = (100)(5 x 10-4)(0.20) / (5 x 10-7)

= 0.01 / 5 x 10-7 = 2 x 104 rad / A (a deflection of 1 rad for a current of 50 microampere).

4.12.4 Conversion of Galvanometer to an Ammeter

A galvanometer is highly sensitive but has a small full-scale current and a non-trivial internal resistance R_G. To measure currents much larger than full-scale, we connect a small shunt resistor r_s in parallel.

G R_G r_s shunt I I_g (small) -> (I - I_g) ->
Fig 4.13 Galvanometer + shunt = ammeter. Most of I bypasses the meter via r_s.

Voltage across galvanometer = voltage across shunt:

\(I_g R_G = (I - I_g) r_s \quad\Longrightarrow\quad r_s = \dfrac{I_g R_G}{I - I_g}\)

Effective resistance of the ammeter: \(R_A = \dfrac{R_G r_s}{R_G + r_s}\) - very small (good ammeter has low resistance so it does not disturb the circuit).

Worked Example 4.11 - Designing an ammeter

Example 4.11 L3 Apply

Convert a galvanometer of full-scale 5 mA and resistance 20 ohm into an ammeter reading 0-2 A.

I_g = 0.005 A, R_G = 20 ohm, I = 2 A.

r_s = I_g R_G / (I - I_g) = (0.005 x 20)/(2 - 0.005) = 0.10/1.995 = 0.0501 ohm.

So a tiny 0.05 ohm shunt converts the meter into a 2 A ammeter.

4.12.5 Conversion to a Voltmeter

To measure a voltage V we connect a high multiplier resistance R in series with the galvanometer. Now the same (small) full-scale current I_g flows through both, and

R (multiplier) G A B Voltage V_AB measured across the meter combination
Fig 4.14 Voltmeter: galvanometer + series multiplier resistor. Together they have a very high resistance.
\(V = I_g\,(R_G + R) \quad\Longrightarrow\quad R = \dfrac{V}{I_g} - R_G\)

Effective resistance of voltmeter: \(R_V = R_G + R\) - large (good voltmeter has very high resistance so it draws negligible current from the circuit being measured).

AspectAmmeterVoltmeter
Connected inSeries with circuit elementParallel with element
Extra resistorSmall shunt r_s in parallelLarge multiplier R in series
Ideal resistance0 (zero)Infinity
Practical resistanceVery smallVery large
Formular_s = I_g R_G / (I - I_g)R = V / I_g - R_G

Worked Example 4.12 - Designing a voltmeter

Example 4.12 L3 Apply

Convert the same galvanometer (I_g = 5 mA, R_G = 20 ohm) into a 0-150 V voltmeter.

R = V / I_g - R_G = 150 / 0.005 - 20 = 30000 - 20 = 29 980 ohm (~30 kohm).

Total voltmeter resistance ~30 kohm - much higher than typical circuit resistances, so it scarcely disturbs them.

Interactive: Galvanometer Deflection & Sensitivity L4 Analyse

Vary the parameters of the galvanometer and watch the pointer deflect according to phi = (NAB / k) I.

-max 0 +max
phi = 0.40 rad, I_S = 20000 rad/A
Activity 4.4 - DIY Galvanometer with a Compass L3 Apply

Wind 30-50 turns of insulated copper wire on a small frame around a magnetic compass. Connect a 1.5 V cell with a current-limiting resistor and switch.

Predict: what happens to the compass needle when you close the switch? What changes if you double the number of turns?

The compass deflects from N-S (Earth field only) toward an angle that depends on the coil's field. Doubling N doubles the field at the compass and so increases the deflection. This is exactly the principle of the original tangent galvanometer.

If you reverse the cell, the deflection reverses sign too - confirming that the direction of deflection depends on current direction.

Competency-Based Questions L3-L5

In a school physics lab, a student has a galvanometer of resistance 50 ohm and full-scale current 10 mA. She wants to use it (i) as an ammeter reading up to 1 A, and (ii) as a voltmeter reading up to 5 V.

Q1. Why is the magnetic field in a moving-coil galvanometer made radial?

  • (a) So torque is independent of orientation - giving a linear scale
  • (b) To minimise resistance
  • (c) To allow AC operation
  • (d) To prevent overheating
(a). With radial B, sin theta = 1 always; tau = NIAB is constant in form so deflection phi proportional to I and the dial divisions are uniformly spaced.

Q2. (Numerical) Find the shunt needed to convert the galvanometer to a 1 A ammeter.

r_s = I_g R_G / (I - I_g) = (0.010 x 50)/(1 - 0.010) = 0.5 / 0.99 = 0.505 ohm.

Q3. (Numerical) Find the multiplier needed for the voltmeter (0-5 V).

R = V/I_g - R_G = 5/0.010 - 50 = 500 - 50 = 450 ohm, in series.

Q4. (True/False) An ideal voltmeter has zero internal resistance.

False. An ideal voltmeter has infinite resistance so it draws no current. An ammeter is the one with ideal resistance zero.

Q5. (HOT) Explain why merely doubling the number of turns N does not necessarily double the voltage sensitivity, even though it doubles the current sensitivity.

I_S = NAB/k - linear in N. But the wire length doubles too, so R doubles. V_S = NAB/(kR) is unchanged. Voltage sensitivity benefits less from extra turns; one must also use higher B, larger A, or a smaller k.

Assertion-Reason Questions L4 Analyse

(a) Both A and R true, R explains A. (b) Both true, R does not explain A. (c) A true, R false. (d) A false, R true.

A: A galvanometer in series with a high resistance can act as a voltmeter.

R: The high resistance limits current so that I_g R_total = V at full scale.

(a). Series multiplier ensures only the small full-scale current flows even at the maximum voltage to be measured.

A: An ammeter is connected in parallel with the circuit element whose current is to be measured.

R: Ammeters have a small resistance to avoid disturbing the circuit current.

(d). Reason is correct (low R), but the assertion is false: ammeters are connected in series. Connecting them in parallel could short-circuit and damage the meter.

A: Soft iron is used as the core of a moving coil galvanometer.

R: Soft iron is highly permeable - it concentrates the field lines in the gap and makes B large and radial.

(a). The high permeability of soft iron strengthens the field in the air gap, increasing torque and giving the radial geometry needed for a linear scale.

Frequently Asked Questions - Galvanometer Applications

What is the main concept covered in Galvanometer Applications?
In NCERT Class 12 Physics Chapter 4 (Moving Charges and Magnetism), "Galvanometer Applications" covers the core principles and equations students need for board exam success. The MyAiSchool lesson explains the topic with definitions, derivations, worked examples, and interactive simulations. Key formulas and dimensional analysis are included to build conceptual depth and problem-solving skills aligned with the CBSE 2025-26 syllabus.
How is Galvanometer Applications useful in real-life applications?
Real-life applications of "Galvanometer Applications" from NCERT Class 12 Physics Chapter 4 include electronics, communication systems, medical imaging, solar energy, semiconductor devices, and modern technology. The MyAiSchool lesson links every concept to a tangible example so students see physics as a problem-solving framework for the physical world, not as abstract formulas.
What are the key formulas in Galvanometer Applications?
Key formulas in "Galvanometer Applications" (NCERT Class 12 Physics Chapter 4 Moving Charges and Magnetism) are derived step-by-step in the MyAiSchool lesson. Students should memorize the final formula AND understand its derivation for full board marks. Each formula is listed with its dimensional formula, SI unit, applicability range, and common pitfalls. The Summary section at the end of each part includes a quick-reference formula card.
How does this part connect to other parts of Chapter 4?
NCERT Class 12 Physics Chapter 4 (Moving Charges and Magnetism) is structured so each part builds on the previous one. "Galvanometer Applications" connects directly to neighbouring parts via shared definitions, units, and methodology. The MyAiSchool lesson cross-references related concepts with internal links so students can navigate the whole chapter as one connected story rather than disconnected fragments.
What types of CBSE board questions come from Galvanometer Applications?
CBSE board questions from "Galvanometer Applications" typically include: (1) 1-mark MCQs on definitions and formulas, (2) 2-mark short-answer derivations or applications, (3) 3-mark numerical problems with units, (4) 5-mark long-answer derivations followed by application. The MyAiSchool lesson tags each Competency-Based Question (CBQ) with Bloom level (L1-L6) so students know how to study for each weight.
How can students use the interactive simulation effectively?
The interactive simulation in the "Galvanometer Applications" lesson allows students to adjust input parameters (sliders or selectors) and see physical quantities update in real time. To use it effectively: (1) try extreme values to understand limiting cases, (2) compare with the analytical formula, (3) check unit consistency, (4) test special configurations from worked examples. The simulation reinforces conceptual intuition that pure formula manipulation cannot.
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