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Overview

🌳 Concept tree

Lesson 3→Analog Measuring Instruments – Galvanometer, Ammeter, Voltmeter and Ohmmeter

├── Use

├── Construction

├── Action

├── Why the parts are used (typical reasons)

├── Sensitivity

├── The ammeter (shunt)

├── The voltmeter (multiplier)

├── Comparison of ammeter and voltmeter

├── The ohmmeter

├── Using the galvanometer to measure current
emf and resistance

├── Analogue and digital instruments

├── Typical "give reasons" for this chapter

└── Summary of formulas

Lesson 3: Analog Measuring Instruments – Galvanometer, Ammeter, Voltmeter and Ohmmeter · 1 / 15

Use

Detects very weak currents, measures their intensity and determines their direction (polarity).
It works on the torque on a current-carrying coil in a magnetic field.

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Construction

A rectangular coil of many turns of thin insulated copper wire, wound on a light aluminium frame.
The frame is mounted on a soft-iron cylinder (core) between the poles of a strong permanent horseshoe magnet; the pole pieces are concave (curved) so that the field in the gap is radial.
The coil is pivoted on jewel (agate) bearings and carries a pointer moving over a scale (zero at the centre in a centre-zero instrument).
Two spiral (hair) springs, above and below, provide the restoring torque and also act as current leads to the coil.

Lesson 3: Analog Measuring Instruments – Galvanometer, Ammeter, Voltmeter and Ohmmeter · 3 / 15

Action

The current in the coil gives a couple τ = BIAN. The coil turns until this torque is balanced by the opposite torque of the twisted springs, which is proportional to the angle of deflection (τ_spring = c θ, where c is the torsion constant of the springs).
The radial field and soft-iron core keep the plane of the coil always parallel to the field lines, so the sides always cut the field at 90° and B is the same magnitude at every angle. Then the deflecting torque BIAN is independent of the angle, and the balanced angle θ is proportional to the current → the scale is uniform.
Reversing the current reverses the deflection.

At balance→B I A N = c θ, so θ = (B A N / c) I. The factor BAN/c is the sensitivity.

Lesson 3: Analog Measuring Instruments – Galvanometer, Ammeter, Voltmeter and Ohmmeter · 4 / 15

Why the parts are used (typical reasons)

Comparison aspect	Main idea	Keywords
Soft-iron core	concentrates the flux strengthens the field in the gap and with the concave poles makes the field radial	concentratesfluxstrengthensfield
Spiral springs	give a restoring torque proportional to the angle (so equilibrium is reached) and carry the current to the coil without hindering its rotation. They also bring the pointer back to zero when the current stops	giverestoringtorqueproportional
Light aluminium frame	low inertia and damps the oscillations by eddy currents so the pointer settles quickly	inertiadampsoscillationseddy
Concave pole pieces	make the field radial so the scale is uniform	makefieldradialscale
Many turns of thin wire and a strong magnet	large torque for a small current (high sensitivity)	largetorquesmallcurrent
Permanent magnet (not an electromagnet)	the field must be constant and independent of any current	fieldmustconstantindependent

Lesson 3: Analog Measuring Instruments – Galvanometer, Ammeter, Voltmeter and Ohmmeter · 5 / 15

Sensitivity

The sensitivity of a galvanometer is the deflection (in degrees or scale divisions) produced per unit current through the coil, e.g.
degree/μA.
It increases with a large number of turns, a larger coil area and a stronger field, and with a weaker control spring (smaller c).
Example 7a. A galvanometer deflects by 40° when the current is 20 μA. Sensitivity = 40/20 = 2 degree/μA. Because the deflection is proportional to the current, a current of 35 μA gives 70°, and a deflection of 25° indicates a current of 12.5 μA.

✍️ Worked examples

Example 7b — changing the turns.→If the number of turns of this coil is doubled (all else unchanged), the sensitivity doubles to 4 degree/μA.

Lesson 3: Analog Measuring Instruments – Galvanometer, Ammeter, Voltmeter and Ohmmeter · 6 / 15

The ammeter (shunt)

An ammeter measures current directly and is connected in series in the circuit.
A galvanometer coil can carry only a very small current I_g (full-scale deflection, FSD).
To measure a larger current I the instrument is converted a very small resistance, the shunt Rs, is connected in parallel with the galvanometer coil (resistance Rg).
Reasoning the main current I divides into Ig through the coil and Is through the shunt, so Is = I − Ig. The shunt and the coil have the same potential difference (they are in parallel):

Ig Rg = (I − Ig) Rs

Rs = Ig Rg / (I − Ig)

Notes:

The shunt is small, so the combined resistance of the ammeter R_g R_s/(R_g + R_s) is very small, which does not change the current in the circuit when connected in series. In fact this resistance equals I_g R_g / I.
Most of the current passes through the shunt; only a fraction I_g/I passes through the coil.
A larger measuring range needs a smaller shunt. To extend the range n times (I = n I_g): R_s = R_g / (n − 1).
The scale is recalibrated so that full scale reads I, not I_g.
The pointer in a DC ammeter deflects in one direction, so the positive terminal of the ammeter must be joined to the side nearer the positive pole of the source.

Example 7. A galvanometer of resistance 4 Ω gives FSD at 10 mA. To read up to 2 A:
R_s = 0.010 × 4 / (2 − 0.010) = 0.04/1.99 = 0.0201 Ω.
Example 7c. A galvanometer has R_g = 60 Ω and FSD current 1.5 mA. To convert it into an ammeter of range 0.3 A:
R_s = 0.0015 × 60 / (0.3 − 0.0015) = 0.09 / 0.2985 = 0.3015 Ω.
Total resistance of the ammeter = 60 × 0.3015 / 60.3015 = 0.300 Ω (= I_g R_g / I = 0.09/0.3 ✔).
Example 7d — range ×10. A galvanometer of 36 Ω is to read ten times its FSD current: R_s = 36 / (10 − 1) = 4 Ω in parallel. Check: when the main current is 10 I_g, 9 I_g goes through 4 Ω giving 36 I_g, and I_g goes through 36 Ω giving 36 I_g ✔.

Lesson 3: Analog Measuring Instruments – Galvanometer, Ammeter, Voltmeter and Ohmmeter · 7 / 15

The voltmeter (multiplier)

A voltmeter measures potential difference and is connected in parallel across the part of the circuit concerned.
The voltage across a galvanometer coil at FSD is tiny (Vg = Ig Rg), so the bare galvanometer could only measure very small voltages.
To measure larger voltages a large resistance, the multiplier Rm, is connected in series with the coil.
At FSD the instrument must carry I_g when the voltage across the whole instrument is V:
V = I_g R_g + I_g R_m → R_m = V / I_g − R_g (equivalently R_m = (V − V_g)/I_g)
Notes:

The total resistance of the voltmeter (R_g + R_m) is very large, so it draws a negligible current and does not change the voltage being measured.
The positive terminal of the voltmeter is connected to the point of higher potential; if the voltage is reversed, the connections must be reversed.
The multiplier makes the resistance large, so most of the measured voltage is across the multiplier and only a tiny voltage (I_g R_g) is across the coil.
Example 8. Galvanometer: R_g = 20 Ω, I_g = 5 mA. To read up to 30 V:
R_m = 30/0.005 − 20 = 6000 − 20 = 5980 Ω in series.
Example 8a. R_g = 40 Ω, I_g = 1 mA, desired range 12 V: R_m = 12/0.001 − 40 = 11 960 Ω. Total resistance of the voltmeter = 12 000 Ω. For a 3 V range the multiplier would be 3000 − 40 = 2960 Ω.

Example 8b.→What is the effect of the voltmeter resistance? A voltmeter of 12 000 Ω is connected across a 4000 Ω resistor in a circuit. The combination 4000 × 12 000 / 16 000 = 3000 Ω, so the voltmeter lowers the resistance between the two points by 25%, which is why a voltmeter’s resistance must be as large as possible compared with the resistance across which it is placed.

Lesson 3: Analog Measuring Instruments – Galvanometer, Ammeter, Voltmeter and Ohmmeter · 8 / 15

Comparison of ammeter and voltmeter

Comparison aspect	Ammeter	Voltmeter
Measures	current	potential difference
Connected	in series	in parallel
Added resistor	small shunt in parallel with the coil	large multiplier in series with the coil
Total resistance	very small	very large
Effect on circuit if ideal	none (does not change the current)	none (draws no current)

Lesson 3: Analog Measuring Instruments – Galvanometer, Ammeter, Voltmeter and Ohmmeter · 9 / 15

The ohmmeter

An ohmmeter measures an unknown resistance directly.
Measuring a resistance by Ohm’s law needs both an ammeter and a voltmeter (R = V / I).
If the voltage is fixed and known, we can drop the voltmeter and mark the galvanometer scale in ohms instead of amperes.
It is a micro-ammeter (galvanometer) in series with a fixed resistance, a variable resistance (adjusted for zero) and a cell of constant emf (about 1.5 V), with two terminals between which the unknown resistance R_x is connected.

Comparison aspect	Main idea	Keywords
Zero adjustment	with the terminals touching (R_x = 0, short circuit), the variable resistor is adjusted so that the pointer gives full-scale deflection: R_total = V_B / I_g.	terminalstouchingshortcircuit
•	With R_x inserted the current is I = V_B/(R_total + R_x), which is smaller, so the deflection is smaller and the scale is calibrated directly in ohms.	insertedcurrentRtotalsmaller
Features of the scale	zero ohms is at the full-scale end (the right) and infinite resistance at the left (open circuit) — opposite to the current scale it is non-linear (the readings are spread out at the zero end and crowded at the high-resistance end)	zeroohmsfullright
•	If R_x = R_total the current is half of FSD; if R_x = 2 R_total it is one-third FSD, etc. In general, I / I_g = R_total / (R_total + R_x).	Rtotalcurrenthalfthird
Reasons	the cell must have a constant emf (otherwise the calibration is wrong) the fixed resistor protects the meter and sets the calibration the variable resistor is needed to bring the pointer exactly to the zero mark when the cell ages	cellmustconstantotherwise

Comparison aspect	Main idea	Keywords
Example 9.	An ohmmeter has a 1.5 V cell and a total internal resistance of 3000 Ω at FSD (500 μA). With an unknown resistor of 3000 Ω: I = 1.5/6000 = 250 μA = half of FSD. With 9000 Ω: I = 1.5/12000 = 125 μA = quarter of FSD	ohmmetercelltotalinternal
Example 9a — a calibration table.	An ohmmeter has a 1.5 V cell and FSD current 1 mA, so its total internal resistance is 1.5/0.001 = 1500 Ω. For different R_x:	ohmmetercellcurrenttotal

R_x	total resistance	current	fraction of FSD
0	1500 Ω	1.0 mA	1
500 Ω	2000 Ω	0.75 mA	3/4
1500 Ω	3000 Ω	0.5 mA	1/2
4500 Ω	6000 Ω	0.25 mA	1/4
13 500 Ω	15 000 Ω	0.1 mA	1/10
The unequal steps (from 0 to 500 Ω is a quarter of the scale while from 4500 to 13 500 Ω is only 15% of it) show why the ohmmeter scale is non-linear

Example 9b — design.→A milliammeter of resistance 20 Ω has FSD 10 mA. It is used as an ohmmeter with a 1.5 V cell of internal resistance 1 Ω. For FSD the total resistance must be 1.5/0.010 = 150 Ω, so the standard resistor needed (including the variable one) is 150 − 20 − 1 = 129 Ω. A reading of 6 mA means the total resistance is 1.5/0.006 = 250 Ω, so R_x = 250 − 150 = 100 Ω. With R_x = 600 Ω the current is 1.5/750 = 2 mA.

Lesson 3: Analog Measuring Instruments – Galvanometer, Ammeter, Voltmeter and Ohmmeter · 10 / 15

Using the galvanometer to measure current, emf and resistance

Comparison aspect	Main idea	Keywords
Current	convert it into an ammeter by a shunt and connect it in series	convertammetershuntconnect
emf (or potential difference)	convert it into a voltmeter by a multiplier and connect it in parallel across the source. For the emf the source must be on open circuit (no current flowing) with a voltmeter of very high resistance	convertvoltmetermultiplierconnect
Resistance	convert it into an ohmmeter or use an ammeter and a voltmeter together to find R = V/I	convertohmmeterammetervoltmeter

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Analogue and digital instruments

Analogue (pointer) meters use a pointer on a scale; a multimeter can be switched to measure current, voltage and resistance.
Digital multimeters show the value as numerals on an LCD (liquid-crystal display) without a pointer.
An ohmmeter, which measures resistance, has a non-linear graduated scale.
Full deflection of the pointer corresponds to zero resistance (a short circuit), and the pointer moves back as the resistance increases.
For example, the same instrument reads 200 µA when the measured resistance is 3750 Ω, and 100 µA when it is 11250 Ω.
Because the readings are not evenly spaced, the marks on the right side of the scale are further apart than the marks on the left.

Digital multimeters do not use a pointer.
They show the value as numerals on a small liquid-crystal display (LCD), which makes the reading easier to take.

Lesson 3: Analog Measuring Instruments – Galvanometer, Ammeter, Voltmeter and Ohmmeter · 12 / 15

Typical "give reasons" for this chapter

A soft-iron cylinder is fixed inside the coil of the galvanometer: to strengthen the field and make it radial.
The coil is attached to a pair of spiral springs to supply a restoring torque proportional to the angle and to lead the current to the coil.
A high resistance is connected in series with the galvanometer when it is used as a voltmeter: to limit the current to I_g at FSD and to make the voltmeter draw negligible current.
An ammeter is connected in series and a voltmeter in parallel: so that the ammeter carries the whole current of the branch and the voltmeter sees the same voltage as the element.
A constant resistor is placed inside the ohmmeter to protect the meter and fix the calibration.
The cell of an ohmmeter must have a constant emf a changing emf would make the calibration wrong.
The scale of the ohmmeter is not linear and runs in the opposite sense to that of the ammeter: because I = V_B/(R_total + R_x) is not proportional to R_x, and larger resistance gives smaller current.

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Summary of formulas

Quantity	Formula
Flux density	B = Φ/A (tesla = Wb/m² = N/A·m)
Straight wire	B = μI/(2πd)
Circular coil (centre)	B = μNI/(2r)
Solenoid (axis)	B = μNI/L = μnI
Force on a wire	F = BIL sin θ
Force between parallel wires	F = μ I₁ I₂ L / (2π d)
Torque on coil	τ = BIAN sin θ (θ from field to normal)
Magnetic moment	m = NIA
Ammeter shunt	R_s = I_g R_g / (I − I_g)
Voltmeter multiplier	R_m = V/I_g − R_g
Ohmmeter at FSD	R_total = V_B / I_g

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Lesson 3: Analog Measuring Instruments – Galvanometer, Ammeter, Voltmeter and Ohmmeter · 14 / 15

Part 15

📖

🔍 In-Depth Explanations, Deductions & Multi-Book Insights:

Physics Thanaweya Amma (2026/2027)

Lesson 3 – Analog Measuring Instruments – Galvanometer, Ammeter, Voltmeter and Ohmmeter
The Moving Coil Galvanometer detects weak DC currents based on magnetic torque.
By connecting appropriate precision resistors, it converts into a DC Ammeter (using a small parallel shunt resistor Rs), a DC Voltmeter (using a large series multiplier Rm), or an Ohmmeter.

🌳 Hierarchy Classification & Concept Tree

Analog Electromagnetic Instruments

├── 1. Moving Coil Galvanometer (MCG)

Comparison aspect	Main idea	Keywords
│ ├── Components	Concave magnetic poles cylindrical soft iron core (produces radial magnetic field)	Concavemagneticpolescylindrical
│ ├── Equilibrium condition	Deflecting magnetic torque = Restoring torsion torque (τ_mag = τ_torsion)	DeflectingmagnetictorqueRestoring
│ └── Sensitivity	S = θ / I (Constant due to radial field uniform scale)	Constantradialfielduniform
•	├── 2. Direct Current Ammeter (Measures large currents)	DirectCurrentAmmeterMeasures
│ ├── Conversion	Small resistor (Shunt Rs) connected in PARALLEL with galvanometer	SmallresistorShuntconnected
│ └── Shunt formula	Rs = (Ig · Rg) / (I – Ig)
•	├── 3. Direct Current Voltmeter (Measures high potential differences)	DirectCurrentVoltmeterMeasures
│ ├── Conversion	Large resistor (Multiplier Rm) connected in SERIES with galvanometer	LargeresistorMultiplierconnected
│ └── Multiplier formula	Rm = (V – Vg) / Ig = (V – Ig · Rg) / Ig
•	└── 4. The Ohmmeter (Measures unknown resistance Rx)	OhmmeterMeasuresunknownresistance
├── Components	Galvanometer standard resistor Rc variable rheostat Rv battery (VB	Galvanometerstandardresistorvariable
├── Total internal resistance	Rinternal = Rg + Rc + Rv + r = VB / Ig	Rinternal
└── Scale non-uniformity	I is inversely proportional to total resistance (Rinternal + Rx)	inverselyproportionaltotalresistance

📋 Master Teacher's Blackboard & Exam Secrets

Comparison aspect	Main idea	Keywords
RULE 1	Concave poles + cylindrical iron core produce a RADIAL magnetic field ensuring the coil plane is always parallel to field lines making torque constant and the scale UNIFORM (θ ∝ I)	Concavepolescylindricaliron
RULE 2	The Ohmmeter scale is NON-UNIFORM and calibrated in reverse (0 Ω at full-scale current Ig ∞ Ω at zero current) because current is inversely proportional to (Rinternal + Rx) not Rx alone	OhmmeterscaleUNIFORMcalibrated
RULE 3	If current drops to 1/4 of full scale (Ig/4) total resistance is 4 Rinternal meaning unknown resistance Rx = 3 Rinternal	currentdropsfullscale
RULE 4	Smaller shunt resistance Rs decreases overall ammeter resistance and increases its measuring range but decreases its current sensitivity	Smallershuntresistancedecreases
📊 Comparative Analysis	Instrument Conversion Architecture Comparison	InstrumentConversionArchitectureComparison

Instrument	Modifying Resistor	Connection Mode	Primary Function	Ideal Meter Resistance
DC Ammeter	Shunt Resistor (Rs: Very small)	Parallel with Galvanometer	Increases current measuring range	Zero (R_ammeter → 0)
DC Voltmeter	Multiplier (Rm: Very large)	Series with Galvanometer	Increases voltage measuring range	Infinite (R_voltmeter → ∞)
Ohmmeter	Internal calibrated resistors	Series with internal battery	Measures unknown resistor Rx directly	Calibrated internally

Lesson 3: Analog Measuring Instruments – Galvanometer, Ammeter, Voltmeter and Ohmmeter · 15 / 15

Curriculum

Physics

Chapter 1 - Electric Current, Ohms Law and Kirchhoffs Laws

Chapter 2 - Magnetic Effects of Electric Current and Measuring Instruments

Chapter 3 - Electromagnetic Induction and AC Dynamo and Transformer

Chapter 4 - Alternating Current AC Circuits

Chapter 5 - Dual Nature of Wave and Particle

Chapter 6 - Atomic Spectra and X-Rays

Chapter 7 - Lasers and Principles

Chapter 8 - Modern Electronics and Semiconductors

More lessons

Lesson 3: Analog Measuring Instruments – Galvanometer, Ammeter, Voltmeter and Ohmmeter