Moving coil galvanometer and its current sensitivity
A coil in a radial magnetic field turns until the spring's torque balances NIAB, so the deflection φ ∝ I. Current sensitivity is φ/I = NAB/k.
Parts, and how to draw the diagram
- A coil of many turns of fine insulated wire on a light frame, free to turn about a fixed vertical axis. Draw it as a rectangle between the poles.
- A strong permanent magnet with concave (curved) pole pieces. Draw N on one side and S on the other, each cut as a curve facing the coil.
- A soft iron cylinder (core) inside the coil. Draw it as a circle at the centre.
- The concave poles and the core make the field radial. Draw the field lines along radii: from N, across the gap, into the core, and out again to S.
- A spring (or a fine suspension wire) fixed to the coil. It gives a restoring torque.
- A pointer fixed to the coil, moving over a scale. Label every part.
How it works
- 1A current I flows through the coil.
- 2The coil sits in a magnetic field B and feels a torque NIAB sin θ.
- 3In a radial field, the plane of the coil always lies along the field lines, so sin θ = 1 at every position. The torque is NIAB.
- 4The coil turns. The spring twists and gives a restoring torque kφ, where φ is the angle turned and k is the torsional constant of the spring.
- 5★The coil stops when the two torques balance: kφ = NIAB.
- 6★So, φ = (NAB/k) I. The deflection is proportional to the current, and the scale is linear (evenly marked).
★ key step
Current sensitivity vs voltage sensitivity
Figure of merit is the current needed for a deflection of one division. It is the inverse of the current sensitivity. The lab manual writes it as k; do not mix it up with the spring's torsional constant.
Activity: resistance of a galvanometer by half-deflection, and its figure of merit
You need a galvanometer, a cell, a high resistance box R (up to 10 kΩ), a low resistance box S (the shunt), two keys and connecting wires.
- 1Join the cell E, key K₁, the high resistance box R and the galvanometer G in series. Connect the box S across G through key K₂.
- 2Keep K₂ open. Take out a large R (say 5000 Ω), close K₁ and adjust R to get an even deflection θ, say 30 divisions.
- 3Close K₂. Adjust S until the deflection falls to exactly θ/2. Note R, θ and S.
- 4Repeat for 3 or 4 sets. For each, find G = RS/(R − S). When R is much larger than S, G ≈ S.
- 5Figure of merit (current per division): k = E/[(R + G)θ], using the readings taken with K₂ open.
- 6Result: write the mean G in ohms and the mean figure of merit in amperes per division.
Worked example: half-deflection readings
In a half-deflection experiment, E = 1.5 V. With K₂ open and R = 4900 Ω, the deflection is 30 divisions. With K₂ closed, the deflection falls to 15 divisions when S = 98 Ω. Find the resistance G of the galvanometer and its figure of merit.
- Formula: G = RS/(R − S).
- G = (4900 × 98)/(4900 − 98) Ω = 480200/4802 Ω = 100 Ω.
- Formula for the figure of merit: k = E/[(R + G)θ].
- k = 1.5/[(4900 + 100) × 30] A per division = 1.5/150000 A per division.
- k = 1.0 × 10⁻⁵ A per division, that is 10 μA per division.
G = 100 Ω; figure of merit = 1.0 × 10⁻⁵ A per division
Worked example: current sensitivity
A galvanometer coil has 50 turns of area 4.0 × 10⁻⁴ m² in a radial field of 0.25 T. The spring's torsional constant is 5.0 × 10⁻⁷ N m per radian. Find (a) its current sensitivity and (b) the deflection for a current of 20 μA.
- (a) Current sensitivity = NAB/k.
- = (50 × 4.0 × 10⁻⁴ × 0.25)/(5.0 × 10⁻⁷) rad/A = (5.0 × 10⁻³)/(5.0 × 10⁻⁷) rad/A.
- = 1.0 × 10⁴ rad/A.
- (b) φ = (current sensitivity) × I = 1.0 × 10⁴ × 20 × 10⁻⁶ rad = 0.20 rad.
- In degrees: 0.20 × 57.3° ≈ 11°.
(a) 1.0 × 10⁴ rad per ampere; (b) 0.20 rad, about 11°
The needle meters on older voltage stabilisers, battery chargers and many school lab ammeters are moving coil instruments. Digital meters have replaced many of them, but the same coil-in-a-field idea runs every electric motor.
3 marks: “State the principle of a moving coil galvanometer. Why is a radial magnetic field used, and what is the role of the soft iron core?” Principle: a current-carrying coil in a magnetic field feels a torque. A radial field keeps the plane of the coil along the field at every position, so τ = NIAB and φ ∝ I (linear scale). The soft iron core makes the field radial and stronger, which raises the sensitivity.
2 marks: “Define the current sensitivity of a galvanometer. Does doubling the number of turns double its voltage sensitivity? Explain.” Current sensitivity = φ/I = NAB/k. No: voltage sensitivity NAB/(kR_G) stays the same, because the coil's resistance also doubles.
5 marks: “With a labelled diagram, explain the working of a moving coil galvanometer. Derive the relation between deflection and current. Why can it not be used directly to measure a current of a few amperes?” Diagram: coil, concave poles, soft iron core, radial field, spring, pointer and scale. Deflecting torque NIAB in a radial field; restoring torque kφ; kφ = NIAB gives φ = (NAB/k)I. It gives full-scale deflection for microamperes or milliamperes, so a large current would damage it; its own resistance would also change the circuit current. It needs a shunt.
A radial field keeps sin θ = 1, so φ = (NAB/k) I: the twist grows in step with the current.