Moving coil galvanometer and its conversion into an ammeter and a voltmeter
In a galvanometer NBIA = kα, so the deflection is proportional to the current. A low shunt in parallel makes an ammeter; a high series resistance makes a voltmeter.
Parts of a moving coil galvanometer, and how to draw it
- A galvanometer detects small currents. Its principle: a current-carrying coil in a magnetic field feels a torque.
- Coil: many turns of fine insulated wire on a light non-magnetic frame, free to turn on two pivots. Draw it as a rectangle between the poles.
- Magnet: a strong horseshoe magnet with curved (concave) pole pieces, N on one side and S on the other.
- Soft iron core: a cylinder inside the coil. With the curved poles, it makes the field radial: the field lines run along radii, so the plane of the coil always lies along them. It also makes the field stronger.
- Springs: fixed to the coil. They give a restoring torque and carry the current in and out.
- Pointer and scale: a light pointer on the coil moves over a scale. Label every part.
How it works
- 1A current I flows through the coil, which sits in a field B.
- 2The coil feels a torque NBIA sin θ. In a radial field, sin θ = 1 in every position, so the torque is NBIA.
- 3The coil turns and twists the springs. They give a restoring torque kα, where α is the angle turned and k is the restoring torque per unit twist.
- 4The coil stops when the two torques balance: NBIA = kα.
- 5★So, I = (k/NBA)α, and α ∝ I. The scale is evenly marked. k/NBA is called the galvanometer constant.
- 6Current sensitivity α/I = NBA/k rises with more turns, a larger coil, a stronger field and weaker springs (made of phosphor bronze or quartz). A good galvanometer can detect about 0.1 μA.
★ key step
Derivations: shunt for an ammeter, series resistance for a voltmeter
The galvanometer has a resistance G and gives full-scale deflection for a current I_g. I_g = (number of divisions on the scale) × (figure of merit, the current per division).
- 1Ammeter (range 0 to I): join a small resistance S, called a shunt, in parallel with the galvanometer.
- 2At full scale, I_g flows through G and (I − I_g) through S. Both have the same potential difference across them.
- 3★I_gG = (I − I_g)S, so S = I_gG/(I − I_g).
- 4The ammeter's resistance is GS/(G + S), smaller even than S. An ideal ammeter has zero resistance. It is joined in series.
- 5Voltmeter (range 0 to V): join a large resistance R in series with the galvanometer. At full scale, I_g(G + R) = V.
- 6★So, R = V/I_g − G. The voltmeter's resistance, G + R, is very large; an ideal voltmeter has infinite resistance. It is joined in parallel.
★ key step
Ammeter vs voltmeter
Order of resistance: ammeter < galvanometer < voltmeter.
Activity: galvanometer resistance by half deflection, then a 0 to 3 V voltmeter
You need a cell, a galvanometer, a 5000 Ω resistance box R, a small resistance box S, two keys, a rheostat and a standard voltmeter.
- 1Join the cell, key K, box R and the galvanometer G in series. Join box S across G through a second key K₂.
- 2With K₂ open, take out a large R and close K. Adjust R to get an even deflection θ, more than 70% of full scale.
- 3★Close K₂. Adjust S until the deflection falls to θ/2. Half the current now goes through S, so G = S (R is so large that the total current hardly changes).
- 4Repeat for 3 or 4 values of R. Take the mean of G.
- 5Find the full-scale current: I_g = [E/(R + G)] × (n/θ). Here E is the cell's emf and n is the number of divisions on the scale.
- 6★Work out R_s = 3 V/I_g − G. Take this resistance out of a high resistance box and join it in series with G. You now have a 0 to 3 V voltmeter.
- 7Join your voltmeter and a standard voltmeter in parallel across part of a rheostat connected to the cell. Compare their readings in steps of 0.5 V.
- 8Result: record G, I_g and R_s. The two meters should agree closely.
★ key step
Worked example: making an ammeter and a voltmeter
A galvanometer has a resistance of 40 Ω and 30 divisions on its scale. Its figure of merit is 1.0 × 10⁻⁴ A per division. Convert it into (a) an ammeter of range 0 to 3 A and (b) a voltmeter of range 0 to 3 V.
- Full-scale current: I_g = 30 × 1.0 × 10⁻⁴ A = 3.0 × 10⁻³ A.
- (a) S = I_gG/(I − I_g) = (3.0 × 10⁻³ × 40)/(3 − 0.003) Ω = 0.12/2.997 Ω.
- S ≈ 0.040 Ω, joined in parallel with the galvanometer.
- (b) R = V/I_g − G = 3/(3.0 × 10⁻³) Ω − 40 Ω = 1000 Ω − 40 Ω = 960 Ω.
- Join 960 Ω in series. The voltmeter's total resistance is then 1000 Ω.
(a) a shunt of about 0.040 Ω in parallel; (b) 960 Ω in series
The analogue multimeter an electrician uses to check household wiring is a galvanometer with switchable shunts and series resistances. The needle meter on a battery charger works the same way.
2 marks: “Why is a radial magnetic field used in a moving coil galvanometer?” In a radial field the plane of the coil always lies along the field, so sin θ = 1 and the torque NBIA does not depend on the coil's position. Then α ∝ I and the scale is evenly marked.
2 marks: “A galvanometer of resistance 50 Ω gives full-scale deflection for 2.0 mA. How will you convert it into an ammeter of range 0 to 5 A?” S = I_gG/(I − I_g) = (2.0 × 10⁻³ × 50)/(5 − 0.002) Ω ≈ 0.020 Ω, joined in parallel.
3 marks: “A galvanometer of resistance 100 Ω gives full-scale deflection for 1.0 mA. Find the resistance needed to make a voltmeter of range 0 to 10 V, say how it is joined, and give the voltmeter's resistance.” R = V/I_g − G = 10/0.001 − 100 = 9900 Ω, joined in series; the voltmeter's resistance is 10 000 Ω.
Ammeter: Low resistance in Parallel. Voltmeter: High resistance in Series. The ammeter goes in series in the circuit; the voltmeter goes across.