Moving Coil Galvanometer

Q: What is a moving coil galvanometer?

An instrument that measures small currents by converting them to angular deflection of a coil in a magnetic field. Torque NBIA balances restoring torque kφ, giving deflection proportional to current.

Q: Why is the magnetic field in a galvanometer made radial?

A radial field ensures B lies in the plane of the coil regardless of rotation, making torque NBIA independent of coil angle. This gives a linear scale.

Q: What is the current sensitivity of a galvanometer?

S_I = φ/I = NAB/k. Increase by more turns N, larger area A, stronger B, or finer suspension (smaller k).

Q: What is voltage sensitivity and how does it differ from current sensitivity?

S_V = φ/V = NAB/(kR_g) = S_I/R_g. Increasing N raises S_I and R_g in step, so S_V is unchanged. Raising S_V requires larger A, B, or smaller k.

Q: How is a galvanometer converted into an ammeter?

Add a low-resistance shunt in parallel: S = I_g R_g/(I - I_g). Most current bypasses the galvanometer, keeping the ammeter low-resistance.

Q: How is a galvanometer converted into a voltmeter?

Add a high-resistance multiplier in series: R = V/I_g - R_g. Series resistance limits current, keeping the voltmeter high-resistance.

Q: Why should an ammeter have low resistance and a voltmeter high resistance?

Ammeter is in series; low resistance avoids reducing the measured current. Voltmeter is in parallel; high resistance avoids drawing significant current from the circuit.

Q: What is the figure of merit of a galvanometer?

F = I/φ = k/(NAB), reciprocal of current sensitivity. Smaller F means a more sensitive galvanometer.

Q: Can a galvanometer read alternating current?

Not directly. AC deflection reverses each half-cycle; the coil cannot follow 50 Hz oscillations and shows zero average. AC meters use rectification or a different principle.

PhysicsMagnetic Effects of Current and MagnetismFor NEET aspirants

The moving coil galvanometer (MCG) is a sensitive instrument that detects and measures small electric currents by converting the current into a mechanical deflection of a coil suspended in a magnetic field. When current $I$ flows through the coil, it experiences a torque $τ = N I A B$ (see Concept 261) which is balanced by the restoring torque of a spring. At equilibrium, deflection $ϕ$ is proportional to current: $ϕ = (\frac{N A B}{k}) I$ . This linear response is the foundation of every analog ammeter and voltmeter. Adding a low-resistance shunt in parallel converts a galvanometer to an ammeter; adding a high-resistance multiplier in series converts it to a voltmeter. Sensitivity and conversion are directly asked in JEE Main and NEET.

Key Formulas - Quick Reference

Deflection equation: $N I A B = k ϕ ⟹ I = \frac{k}{N A B} ϕ$
Current sensitivity: $S_{I} = \frac{ϕ}{I} = \frac{N A B}{k}$ (rad/A or div/A)
Voltage sensitivity: $S_{V} = \frac{ϕ}{V} = \frac{N A B}{k R _{g}}$ (rad/V), where $R_{g}$ = coil resistance
Relation: $S_{V} = \frac{S _{I}}{R _{g}}$
Ammeter conversion (galvanometer of range $I_{g}$ , full scale) to read up to $I$ : shunt $S = \frac{I _{g} R _{g}}{I - I _{g}}$ in parallel
Voltmeter conversion (to read up to $V$ ): multiplier $R = \frac{V}{I _{g}} - R_{g}$ in series
Ideal ammeter: zero resistance; Ideal voltmeter: infinite resistance

1. Construction

A moving coil galvanometer consists of:

A rectangular coil of $N$ turns of fine insulated wire wound on a light aluminium/non-magnetic frame.
The coil is suspended between the poles of a strong horseshoe magnet by a fine phosphor-bronze wire (which also carries current in and provides the restoring torque).
A soft iron core sits inside the coil (without touching), making the field radial - so field lines always lie in the plane of the coil.
The pole pieces are shaped cylindrically concave so that the field $B$ is always parallel to the plane of the coil, regardless of the coil's angular position.
A light mirror on the suspension reflects a light beam onto a scale, producing amplified deflection (lamp-and-scale reading).

Figure 1: The pole faces and the soft iron core share a common axis, so every field line in the air gap runs along a radius. The coil hangs from a phosphor bronze fibre of torsional constant

k

; current enters through the suspension and leaves through the hair spring, which also supplies the restoring torque

k ϕ

2. Working: Deriving the Deflection Equation

When current $I$ flows through the coil (area $A$ , $N$ turns, in field $B$ ), the deflecting torque is:

$τ_{def} = N B I A sin θ$

Because the field is radial (thanks to the cylindrical pole pieces and iron core), $B$ always lies in the plane of the coil, so $θ = 90°$ always and:

$τ_{def} = N B I A$ (independent of coil angle)

The twisted phosphor-bronze suspension provides a restoring torque proportional to angular deflection $ϕ$ :

$τ_{rest} = k ϕ$

where $k$ is the torsional constant (N·m per radian). At equilibrium:

N B I A = k ϕ ⟹ I = \frac{k}{N A B} ϕ or ϕ = \frac{N A B}{k} I

Since $ϕ \propto I$ , the scale can be marked linearly in units of current.

3. Sensitivity

3.1 Current sensitivity

The current sensitivity is deflection per unit current:

S_{I} = \frac{ϕ}{I} = \frac{N A B}{k}

To increase $S_{I}$ : increase $N$ , $A$ , $B$ , or decrease $k$ (use a finer suspension).

3.2 Voltage sensitivity

If a voltage $V$ is applied across the galvanometer of coil resistance $R_{g}$ , current is $I = V / R_{g}$ , so:

S_{V} = \frac{ϕ}{V} = \frac{N A B}{k R _{g}} = \frac{S _{I}}{R _{g}}

Increasing $S_{I}$ does not automatically increase $S_{V}$ : if we increase

N

, both

S_{I}

and

R_{g}

(which is proportional to wire length

\propto N

) go up in the same ratio, and

S_{V}

stays the same. Increasing

S_{V}

requires increasing

A

B

, or decreasing

k

- i.e., changing something besides the number of turns.

4. Conversion of Galvanometer

4.1 Galvanometer to Ammeter (shunt in parallel)

An ammeter must (a) measure current up to $I ≫ I_{g}$ (where $I_{g}$ is the full-scale current of the galvanometer), and (b) have very low resistance so as not to disturb the circuit.

Connect a low-resistance shunt $S$ in parallel with the galvanometer. When total current $I$ enters the parallel combination, $I_{g}$ passes through the galvanometer and $(I - I_{g})$ through the shunt. Equal voltage across both:

$I_{g} R_{g} = (I - I_{g}) S ⟹ S = \frac{I _{g} R _{g}}{I - I _{g}}$

Figure 2: The shunt carries almost all of the current, so the galvanometer never exceeds its full-scale current

I_{g}

and the combined resistance stays small. Equating the branch voltages gives

S = \frac{I _{g} R _{g}}{I - I _{g}}

Effective resistance of the ammeter: $R_{A} = \frac{R _{g} S}{R _{g} + S}$ , which is small (dominated by $S$ since $S ≪ R_{g}$ ).

4.2 Galvanometer to Voltmeter (multiplier in series)

A voltmeter must (a) measure voltage up to $V ≫ I_{g} R_{g}$ , and (b) have very high resistance so as not to draw current from the circuit.

Connect a high resistance $R$ (multiplier) in series with the galvanometer. Full-scale voltage $V$ drives current $I_{g}$ through the series combination:

$V = I_{g} (R_{g} + R) ⟹ R = \frac{V}{I _{g}} - R_{g}$

Figure 3: The large series resistance limits the current to

I_{g}

even for a large applied voltage, and it makes the meter's own resistance

R_{V} = R_{g} + R

high so it barely loads the circuit. Rearranging gives

R = \frac{V}{I _{g}} - R_{g}

Effective resistance $R_{V} = R_{g} + R$ , which is large.

Solved Example 1

A galvanometer of resistance

50 Ω

shows full-scale deflection at

2 mA

. How can it be converted into (a) an ammeter reading up to

2 A

, and (b) a voltmeter reading up to

10 V

Solution:

(a) Ammeter: Shunt $S = \frac{I _{g} R _{g}}{I - I _{g}} = \frac{0.002 \times 50}{2 - 0.002} \approx \frac{0.1}{1.998} \approx 0.05 Ω$ in parallel.

(b) Voltmeter: Multiplier $R = \frac{V}{I _{g}} - R_{g} = \frac{10}{0.002} - 50 = 5000 - 50 = 4950 Ω$ in series.

Solved Example 2

A galvanometer has

100

turns, area

2 cm^{2}

, and sits in a radial field of

0.5 T

. Torsional constant is

1 0^{- 8} N\cdotm per degree

. Find the current sensitivity.

Solution:

$S_{I} = \frac{N A B}{k} = \frac{100 \times 2 \times 1 0 ^{- 4} \times 0.5}{1 0 ^{- 8}} = \frac{0.01}{1 0 ^{- 8}} = 1 0^{6} degree/A = 1 degree/ μ A$ .

A very sensitive galvanometer indeed - $1 μ A$ deflects the pointer by $1°$ .

5. Why the Radial Field Matters

Without the soft iron core and curved pole pieces, the field would be nearly uniform and horizontal. Then $τ = N B I A sin θ$ , where $θ$ is the angle between coil normal and $B$ . As the coil rotates, $sin θ$ changes, making the scale non-linear.

With the radial field, $B$ is always parallel to the coil plane, so $sin θ = 1$ always, and $τ = N B I A$ is constant. This gives:

Figure 4: Viewed from above, the coil is a line and its two sides carry current into (

\otimes

) and out of (

⊙

) the page. With a radial field the field arrow at each side always lies along that line, so

θ = 90°

and

τ = N B I A

whatever the deflection. With a uniform field the torque would shrink as

cos ϕ

and the scale would be non-linear.

Linear scale (deflection $\propto$ current directly).
Maximum torque for any angular position - so full range is usable.

Figure 5: The practical payoff of the radial field. Equal current steps give equal angular steps, so the dial can simply be marked off in equal divisions and read directly as current.

Common Mistakes to Avoid

Watch out

Confusing shunt and multiplier: shunt (low $R$ , in parallel) makes an ammeter; multiplier (high $R$ , in series) makes a voltmeter. Reversing them destroys the meter.
Using ammeter formula for voltmeter conversion or vice versa.
Thinking increasing $N$ increases voltage sensitivity: $R_{g}$ grows in step with $N$ , so $S_{V}$ is unaffected.
Ignoring the radial-field trick: the linear scale is a direct consequence; if the problem shows a uniform field, the torque is $N B I A sin θ$ , not $N B I A$ .
Using degrees where radians are needed (or vice versa) in the sensitivity expression - be consistent.
Assuming an ammeter and voltmeter have zero and infinite resistance: these are ideals. Real meters have a small (ammeter) or large (voltmeter) but finite resistance that can affect the circuit.

Frequently Asked Questions

Q1. What is a moving coil galvanometer?

The MCG is an instrument that measures small electric currents by converting them into an angular deflection of a coil suspended in a magnetic field. Torque $N B I A$ on the coil is balanced by a spring restoring torque $k ϕ$ , giving deflection $ϕ = (N A B / k) I$ , directly proportional to current.

Q2. Why is the magnetic field in a galvanometer made radial?

A radial field (produced by cylindrical pole pieces and a soft iron core inside the coil) ensures $B$ is always in the plane of the coil regardless of its rotation. This makes torque $N B I A$ constant (not $N B I A sin θ$ ), giving a linear scale and full-range readability.

Q3. What is the current sensitivity of a galvanometer?

Current sensitivity $S_{I} = ϕ / I = N A B / k$ - deflection per unit current. Increase by using more turns $N$ , larger area $A$ , stronger field $B$ , or finer suspension (smaller $k$ ).

Q4. What is voltage sensitivity and how does it differ from current sensitivity?

Voltage sensitivity $S_{V} = ϕ / V = N A B / (k R_{g}) = S_{I} / R_{g}$ . Increasing $N$ raises both $S_{I}$ and $R_{g}$ proportionally, so $S_{V}$ is unchanged. To raise $S_{V}$ you must increase $A$ or $B$ , or decrease $k$ .

Q5. How is a galvanometer converted into an ammeter?

Connect a low-resistance shunt $S$ in parallel: $S = \frac{I _{g} R _{g}}{I - I _{g}}$ , where $I_{g}$ is the full-scale current of the galvanometer and $I$ is the desired ammeter range. Most of the current bypasses the galvanometer through the shunt, so the ammeter has small effective resistance.

Q6. How is a galvanometer converted into a voltmeter?

Connect a high resistance $R$ (multiplier) in series: $R = V / I_{g} - R_{g}$ , where $V$ is the desired voltmeter range. The series resistance limits current, making the voltmeter high-resistance so it does not disturb the circuit.

Q7. Why should an ammeter have low resistance and a voltmeter high resistance?

An ammeter is connected in series, so its resistance adds to the circuit. Low resistance ensures the current being measured is not significantly reduced. A voltmeter is connected in parallel with the component being measured; high resistance ensures negligible current is drawn from the circuit, so the voltage reading is accurate.

Q8. What is the figure of merit of a galvanometer?

Figure of merit is the reciprocal of current sensitivity: $F = I / ϕ = k / (N A B)$ - current per unit deflection. A galvanometer with a smaller figure of merit is more sensitive.

Q9. Can a galvanometer read alternating current?

Not directly. The deflection reverses each half-cycle, and for AC of standard frequency ( $50$ Hz), the coil cannot follow the rapid oscillations. It shows zero average deflection. AC ammeters use rectification (converting AC to DC first) or a different physical principle (moving iron, hot wire).

Previous year questions on Moving Coil Galvanometer

2 questions from past papers, each with a step-by-step solution.

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