JEE Mains Physics · Moving Charges and Magnetism

Galvanometer, Ammeter and Voltmeter

In a moving coil galvanometer the torque NIAB is balanced by a spring, so the deflection is proportional to the current; a small shunt in parallel makes it an ammeter, a large resistor in series makes it a voltmeter.

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Why this matters

Thirty PYQs, twenty-five of them multiple choice, and three from 2026: the largest page in the chapter. Twelve are about the galvanometer itself: six on current and voltage sensitivity, four turn a deflection into a current, a constant or a resistance, one asks why the core is metal and one reads a half-deflection graph. Eighteen convert it: twelve into an ammeter with a shunt, six into a voltmeter with a series resistor.

Concept 1 of 3: Moving coil galvanometer: deflection and sensitivity

The coil sits in a radial field, so its plane always lies along the field and the torque on it is NIAB at every angle. A spring twists back with a torque Cθ. The coil stops where the two balance, so the deflection is proportional to the current. Sensitivity is how much deflection a given current, or a given voltage, produces.

Definition

Balance: $NIAB = C\theta$ , so $\theta = \dfrac{NAB}{C}I$ . C is the torsional constant, in N m/rad, with dimensions $ML^{2}T^{-2}$ .
Current sensitivity $\dfrac{\theta}{I} = \dfrac{NAB}{C}$ . Voltage sensitivity $\dfrac{\theta}{V} = \dfrac{NAB}{CR}$ , where R is the coil's resistance.
Current sensitivity rises with more turns, a stronger field, a larger area or a weaker spring.
More turns of the same wire also raise R in proportion, so the voltage sensitivity stays the same. If the gain is made while keeping R fixed (a different wire), it carries through to the voltage sensitivity.
Figure of merit K = I/θ, the current per division: the inverse of the current sensitivity.
The coil is wound on a metal (non-magnetic) frame: eddy currents in it damp the motion, so the pointer comes to rest quickly.

Balance and sensitivity

NIAB = C\theta \qquad \frac{\theta}{I} = \frac{NAB}{C} \qquad \frac{\theta}{V} = \frac{NAB}{CR}

Worked example

A galvanometer coil has 50 turns of area 4 cm² in a radial field of 0.2 T, a torsional constant of

2 \times 10^{-5}

N m/rad and a resistance of 40 Ω. Find its current sensitivity, the deflection for 1 mA, and its voltage sensitivity.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

JEE Mains · 2025 · 2 Apr 2025 · Q77Moderate

Example 1 · Moving Charges and Magnetism · Galvanometer, Ammeter and Voltmeter

In a moving coil galvanometer, two moving coils

M_{1}

and

M_{2}

have the following particulars:

R_{1}= 5\Omega,{\text{ }N}_{1}= 15,{\text{ }A}_{1}= 3.6 \times10^{- 3}{\text{ }m}^{2},{\text{ }B}_{1}= 0.25\text{ }T

R_{2}= 7\Omega,{\text{ }N}_{2}= 21,{\text{ }A}_{2}= 1.8 \times10^{- 3}{\text{ }m}^{2},{\text{ }B}_{2}= 0.50\text{ }T

Assuming that torsional constant of the springs are same for both coils, what will be the ratio of voltage sensitivity of

M_{1}

and

M_{2}

More turns also mean more resistance

Adding turns of the same wire raises NAB and R together. Current sensitivity grows, but voltage sensitivity, NAB/CR, does not change.

Figure of merit is the inverse of sensitivity

Current sensitivity is divisions per ampere; figure of merit is amperes per division. A more sensitive galvanometer has a smaller figure of merit.

Current and voltage sensitivity differ by R

θ/V = (θ/I)/R. Comparing two galvanometers' voltage sensitivity needs each one's resistance as well as N, A, B and C.

Drill 11 more on moving coil galvanometer: deflection and sensitivity

Concept 2 of 3: Converting a galvanometer into an ammeter with a shunt

A galvanometer reaches full scale at a tiny current Ig. To measure a large current I, most of it must go round the coil. A small resistance, the shunt, joined in parallel carries the extra I − Ig. The coil and the shunt have the same voltage across them, which fixes the shunt.

Definition

Same voltage across coil and shunt: $I_g G = (I - I_g)S$ , so $S = \dfrac{I_g G}{I - I_g}$ .
To make the range n times the full-scale current ( $I = nI_g$ ): $S = \dfrac{G}{n - 1}$ .
Resistance of the ammeter: $\dfrac{SG}{S + G}$ , smaller than S. An ideal ammeter has zero resistance.
Share of the total current through the coil: $\dfrac{I_g}{I} = \dfrac{S}{S + G}$ . A shunt that cuts the deflection to a fraction f of what it was gives $\dfrac{S}{S + G} = f$ .
An ammeter goes in series with the part whose current it measures.

Shunt

S = \frac{I_g G}{I - I_g} \qquad R_A = \frac{SG}{S + G}

Worked example

A galvanometer of resistance 50 Ω reaches full scale at 2 mA. Find the shunt that turns it into an ammeter of range 1 A, and the resistance of the ammeter.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

JEE Mains · 2026 · 24 Jan 2026 Shift 2 · Q13Moderate

Example 2 · Moving Charges and Magnetism · Galvanometer, Ammeter and Voltmeter

A moving coil galvanometer of resistance

100\Omega

shows a full scale deflection for a current of 1 mA . The value of resistance required to convert this galvanometer into an ammeter, showing full scale deflection for a current of 5 mA , is

\_\_\_\_

\Omega

The shunt carries I − Ig, not I

S = IgG/(I − Ig). Using I in the denominator gives a slightly smaller shunt, and with a small range like 5 mA against 1 mA the error is large.

A shunt goes in parallel

The shunt is joined across the galvanometer. A resistor in series raises the range for voltage, not current.

The ammeter's resistance is less than the shunt

The coil and shunt are in parallel, so the meter's resistance SG/(S + G) is below both. It is not S + G.

Drill 11 more on converting a galvanometer into an ammeter with a shunt

Concept 3 of 3: Converting a galvanometer into a voltmeter, compared with an ammeter

A voltmeter is a galvanometer that reaches full scale when the voltage V is across it. A large resistance in series limits the current to Ig at that voltage. The two conversions are mirror images: a small resistance in parallel for current, a large one in series for voltage, and the finished meters go into the circuit the opposite way round.

Definition

Voltmeter: $I_g(G + R) = V$ , so $R = \dfrac{V}{I_g} - G$ . Its resistance is $G + R = V/I_g$ .
To raise a voltmeter's range from $V_1$ to $V_2$ , add $R_V\left(\dfrac{V_2}{V_1} - 1\right)$ in series, where $R_V$ is its own resistance.
A coil tested once with a shunt and once with a series resistor: write Ig from each arrangement and set them equal to find G.
In an Ohm's-law experiment, the galvanometer with the large series resistor goes across the resistor (voltmeter); the one with the tiny shunt goes in series with it (ammeter).

Property	Ammeter	Voltmeter
What it measures	Current, up to I	Potential difference, up to V
Resistance added	Shunt $S = \dfrac{I_g G}{I - I_g}$	Series $R = \dfrac{V}{I_g} - G$
How it is joined to the galvanometer	In parallel	In series
How the meter goes into the circuit	In series with the part	In parallel, across the part Mirror images: swap both connections when you swap meters.
Resistance of the finished meter	$\dfrac{SG}{S + G}$ , less than S	$G + R$ , large
Ideal resistance	Zero	Infinite
Range made n times larger	Shunt $\dfrac{G}{n - 1}$	Add $(n - 1)$ times the meter's resistance in series
For G = 100 Ω and Ig = 1 mA	1 A range: S ≈ 0.1 Ω	10 V range: R = 9900 Ω

A small resistance in parallel for current; a large resistance in series for voltage.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

JEE Mains · 2026 · 6 Apr 2026 Shift 2 · Q23Moderate

Example 3 · Moving Charges and Magnetism · Galvanometer, Ammeter and Voltmeter

A moving coil of a galvanometer when shunted with

2\Omega

resistance gives a full-scale deflection for a current of 500 mA . When a resistance of

470\Omega

is connected in series it gives a full-scale deflection for 10 V potential applied on it. The value of resistance of galvanometer coil is

\_\_\_\_

\Omega

Subtract the galvanometer's own resistance

The series resistor is V/Ig − G. V/Ig alone is the whole voltmeter's resistance, coil included.

Raising a voltmeter's range uses the meter's resistance

To multiply the range by n, add (n − 1) times the voltmeter's total resistance, not (n − 1) times the bare galvanometer's.

A voltmeter in series reads almost the whole supply

Its large resistance takes nearly all the voltage and lets almost no current through. A voltmeter must go across the part, in parallel.

Drill 5 more on converting a galvanometer into a voltmeter, compared with an ammeter

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Moving coil galvanometer: deflection and sensitivity
Balance and sensitivity
$NIAB = C\theta \qquad \frac{\theta}{I} = \frac{NAB}{C} \qquad \frac{\theta}{V} = \frac{NAB}{CR}$
Converting a galvanometer into an ammeter with a shunt
Shunt
$S = \frac{I_g G}{I - I_g} \qquad R_A = \frac{SG}{S + G}$

Reference tables (1)

Converting a galvanometer into a voltmeter, compared with an ammeter8 rows

Property	Ammeter	Voltmeter
What it measures	Current, up to I	Potential difference, up to V
Resistance added	Shunt $S = \dfrac{I_g G}{I - I_g}$	Series $R = \dfrac{V}{I_g} - G$
How it is joined to the galvanometer	In parallel	In series
How the meter goes into the circuit	In series with the part	In parallel, across the part Mirror images: swap both connections when you swap meters.
Resistance of the finished meter	$\dfrac{SG}{S + G}$ , less than S	$G + R$ , large
Ideal resistance	Zero	Infinite
Range made n times larger	Shunt $\dfrac{G}{n - 1}$	Add $(n - 1)$ times the meter's resistance in series
For G = 100 Ω and Ig = 1 mA	1 A range: S ≈ 0.1 Ω	10 V range: R = 9900 Ω

A small resistance in parallel for current; a large resistance in series for voltage.

Watch out for (9)

More turns also mean more resistance
→ Moving coil galvanometer: deflection and sensitivity
Figure of merit is the inverse of sensitivity
→ Moving coil galvanometer: deflection and sensitivity
Current and voltage sensitivity differ by R
→ Moving coil galvanometer: deflection and sensitivity
The shunt carries I − Ig, not I
→ Converting a galvanometer into an ammeter with a shunt
A shunt goes in parallel
→ Converting a galvanometer into an ammeter with a shunt
The ammeter's resistance is less than the shunt
→ Converting a galvanometer into an ammeter with a shunt
Subtract the galvanometer's own resistance
→ Converting a galvanometer into a voltmeter, compared with an ammeter
Raising a voltmeter's range uses the meter's resistance
→ Converting a galvanometer into a voltmeter, compared with an ammeter
A voltmeter in series reads almost the whole supply
→ Converting a galvanometer into a voltmeter, compared with an ammeter

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