The moving coil galvanometer

What is a moving coil galvanometer?

In plain words: the galvanometer is a current loop held by a spring. The magnetic torque on the loop grows with the current, the spring resists more the further it is twisted, and the pointer stops where the two balance, so the angle tells you the current.

Coil in a radial magnetic field

• The coil turns about a fixed axis between the curved poles of a permanent magnet. A cylindrical soft iron core inside the coil makes the field radial and also stronger (NCERT page 129; Figure 4.20, page 130).
• A current I gives the coil a torque τ = NIAB (NCERT Eq. (4.20) with N turns, page 129). Because the field is radial, the plane of the coil always lies along the field, so sin θ = 1 at every deflection, where θ is the angle between the normal to the coil and the field (page 130).
• A spring S_p gives a counter-torque kφ, where k is the torsional constant, the restoring torque per unit twist. In equilibrium kφ = NIAB, so (NCERT Eq. (4.26), page 130):

• The bracket NAB/k is a constant for a given galvanometer, so the deflection is proportional to the current and the scale can be made even (reasoned from NCERT Eq. (4.26)).
• As a detector, as in the Wheatstone bridge, the pointer rests in the middle of the scale and swings right or left depending on the direction of the current (page 130).

Conversion to an ammeter with a shunt

The range-extension formula assumes I > I_g. The voltmeter series-resistance formula below requires V ≥ I_gR_G; a negative required resistance signals that this conversion cannot provide the requested range.

• A sensitive galvanometer cannot directly measure ordinary ampere-scale currents, for two reasons: it reaches full-scale deflection at a current of the order of a microampere, and, being connected in series, its large resistance would change the current it is meant to measure (NCERT page 130).
• A small resistance r_s, the shunt, is joined in parallel with the coil, so that most of the current goes through the shunt. The combination has resistance R_Gr_s/(R_G + r_s) ≈ r_s when R_G ≫ r_s (NCERT page 130, Figure 4.21).
• If r_s is small compared with the resistance of the rest of the circuit, putting the ammeter in changes the current very little (page 130).
• Choosing the shunt (beyond NCERT, from Ohm’s law): if the galvanometer gives full scale at I_g and the ammeter must read up to I, the shunt carries I − I_g at the same potential difference, so I_gR_G = (I − I_g)r_s, and r_s = I_gR_G/(I − I_g).

Conversion to a voltmeter

• To measure the potential difference across part of a circuit, the voltmeter is joined in parallel with it, and it must draw a very small current; usually the disturbance is kept below one per cent (NCERT page 131).
• So a large resistance R is joined in series with the galvanometer, and the voltmeter’s resistance is R_G + R ≈ R, large (NCERT page 131, Figure 4.22).
• Choosing the series resistance (beyond NCERT, from Ohm’s law): for a full-scale reading V at the full-scale current I_g, V = I_g(R_G + R), so R = V/I_g − R_G.
• Range raised n times (beyond NCERT, from the two formulas above): for an ammeter reading I = nI_g, r_s = R_G/(n − 1); for a voltmeter reading nI_gR_G, R = (n − 1)R_G.
• An ideal ammeter would have zero resistance and an ideal voltmeter infinite resistance (reasoned; NCERT Example 4.12(c) uses an ideal ammeter).

Current sensitivity and voltage sensitivity

When comparing changes in N, hold A, B and the spring constant k fixed. Doubling the coil wire length at the same gauge approximately doubles its resistance; a fixed total piece of wire cannot also preserve the area per turn when N doubles.

• The current sensitivity is the deflection per unit current (NCERT Eq. (4.27), page 130):

• The voltage sensitivity is the deflection per unit voltage. With V = IR_G, where R_G is the galvanometer’s own resistance (NCERT Eq. (4.28), page 131, writes it as R):

• As NCERT notes, more turns N raise the current sensitivity (page 130). Increasing B or A, or using a weaker spring (smaller k), also works (reasoned from NCERT Eq. (4.27)).
• Doubling N doubles the current sensitivity, but it also roughly doubles the length of wire and so the resistance. The voltage sensitivity then stays unchanged (NCERT page 131). So, as NCERT notes, the change needed to make an ammeter is different from the change needed to make a voltmeter (page 131).

Solved examples

Common mistakes to avoid

Quick revision summary

• A coil in a radial field (soft iron core) feels τ = NIAB at every angle; a spring balances it, kφ = NIAB, so φ = (NAB/k)I.
• Ammeter: a small shunt r_s in parallel, total resistance ≈ r_s; r_s = I_gR_G/(I − I_g).
• Voltmeter: a large resistance R in series, total ≈ R; R = V/I_g − R_G.
• Current sensitivity φ/I = NAB/k; voltage sensitivity φ/V = NAB/(kR_G).
• More turns raise the current sensitivity but not the voltage sensitivity, since the resistance rises too.

Questions students ask

Are the moving coil galvanometer and its conversion to an ammeter and voltmeter in the JEE and NEET syllabus?

Yes, the moving coil galvanometer, its sensitivity and its conversion to an ammeter and a voltmeter are in both syllabuses: Unit 13 of the JEE Main syllabus lists “Moving coil galvanometer, its sensitivity and conversion to ammeter and voltmeter”, and Unit 13 of NEET (UG) 2026 has almost the same words. NCERT Class 12 Physics Part I covers them in Section 4.10 (pages 129–132). Finding a galvanometer’s resistance and figure of merit by the half-deflection method is listed separately, in Unit 20, Experimental Skills, of both.

Why can a moving coil galvanometer not measure alternating current?

An ordinary moving coil galvanometer does not directly indicate the magnitude of rapidly alternating zero-mean current because its torque, NIAB, reverses with the current: on 50 Hz mains it would push the coil one way and then the other a hundred times a second, too fast for the coil and pointer to follow, so they respond only to the average torque, zero over a cycle (beyond the NCERT text, reasoned from NCERT page 130 and the zero average of an alternating current). The pointer stays near zero, perhaps quivering; sufficiently slow current reversals can be followed by the pointer. Meters for alternating current rectify it before it reaches a moving coil, or use a movement whose deflection does not reverse with the current.

What would happen if a galvanometer’s magnetic field were uniform instead of radial?

In a uniform field a galvanometer’s scale would not be even: with the plane of the coil along the field at zero deflection, a deflection φ turns its normal to 90° − φ from the field, so the torque falls to NIAB cos φ and the balance becomes kφ = NIAB cos φ (beyond the NCERT text, reasoned from NCERT Eqs. (4.21) and (4.26)). Equal steps of current would then give smaller and smaller steps of deflection, and a deflection of 60° would need twice the current it needs in a radial field, since cos 60° = 0.5. The deflection could never reach 90°, where the torque would vanish.

Which has the highest resistance: a galvanometer, an ammeter or a voltmeter?

Of a galvanometer and the ammeter and voltmeter made from it, the voltmeter has the highest resistance, the ammeter the lowest and the galvanometer lies in between: the shunt brings the ammeter’s resistance down to R_GI_g/I, while the series resistor raises the voltmeter’s to V/I_g (reasoned from NCERT pages 130–131). For a galvanometer of 80 Ω giving full scale at 0.50 mA, a 0–1 A ammeter has 0.040 Ω and a 0–15 V voltmeter 30 kΩ. The larger an ammeter’s range, the lower its resistance, so for conversions of the same movement a milliammeter has a lower resistance than a microammeter; unrelated instruments need not follow that ordering (the NCERT Laboratory Manual Physics Class XII sets both questions, Experiment 6, page 58).

What are the SI units of the current sensitivity and voltage sensitivity of a galvanometer?

The current sensitivity of a galvanometer, NAB/k, is measured in radians per ampere (rad A^⁻¹) and its voltage sensitivity, NAB/(kR_G), in radians per volt (rad V^⁻¹), being deflections per unit current and per unit voltage (NCERT Eqs. (4.27)–(4.28), pages 130–131). They follow from the torsional constant k in N m rad^⁻¹ (NCERT table, page 134): m^² × T/(N m rad^⁻¹) = rad A^⁻¹, as 1 T = 1 N A^⁻¹ m^⁻¹. In the laboratory, deflections are read in scale divisions, so the current sensitivity is given in divisions per ampere, the reciprocal of the figure of merit.

Practice questions

Try each question first, then open the answer to check your working.

1. Q1. A galvanometer coil has 100 turns of area 2.0 × 10⁻⁴ m² in a radial field of 0.50 T, and a spring of torsional constant 1.0 × 10⁻⁶ N m per radian. Find its current sensitivity.

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   φ/I = NAB/k = 100 × 2.0 × 10⁻⁴ × 0.50/(1.0 × 10⁻⁶) = 1.0 × 10⁴ rad/A, that is 0.01 rad per µA: a current of 100 µA turns the coil through 1 rad (NCERT Eq. (4.27), page 130).

2. Q2. Why must an ammeter have a small resistance and a voltmeter a large one?

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   An ammeter goes in series, so a large resistance would change the current; a voltmeter goes in parallel, so a small resistance would draw current and change the voltage being measured (NCERT pages 130–131).

3. Q3. How is the neutral position of a galvanometer’s pointer arranged when it is used as a current detector?

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   In the middle of the scale, so that it can swing either way depending on the direction of the current (NCERT page 130).