10 min readPathway sheet2 or 3-mark numericals on the shunt and the series resistance, circuit diagrams, and the conversion practical; also a NEET favourite

Converting a galvanometer into an ammeter and a voltmeter

A low shunt in parallel makes an ammeter; a high resistance in series makes a voltmeter. Ideal ammeter: zero resistance; ideal voltmeter: infinite resistance.

Shunt for an ammeterS = I_g G/(I − I_g), joined in parallel with G

Series resistance for a voltmeterR = V/I_g − G, joined in series with G

Ideal metersIdeal ammeter: zero resistance. Ideal voltmeter: infinite resistance.

Range raised n timesAmmeter: S = G/(n − 1). Voltmeter: R = (n − 1)G.

Why a galvanometer cannot be used directly

A galvanometer is very sensitive. It gives full-scale deflection for a small current I_g, often a few microamperes to a few milliamperes. A larger current would damage it. It also has its own resistance G. Put in series, it would change the current it is meant to measure. Put across a resistor, it would draw current and change the voltage. So we add a resistance to it: a low shunt in parallel for an ammeter, or a high resistance in series for a voltmeter. A shunt is a small resistance joined in parallel that carries most of the current.

Derivation: galvanometer to ammeter (range 0 to I)

1
The galvanometer has resistance G and full-scale current I_g.
2
Join a small resistance S, the shunt, in parallel with G.
3
At full scale, I_g flows through G and (I − I_g) flows through S.
4
Both are across the same potential difference: I_g G = (I − I_g)S.
5★
So, S = I_g G/(I − I_g).
6
Resistance of the ammeter: R_A = GS/(G + S), smaller even than S. An ideal ammeter has zero resistance.

★ key step

Derivation: galvanometer to voltmeter (range 0 to V)

1
Join a large resistance R in series with G.
2
At full scale, the current I_g flows when the voltage across the combination is V.
3
V = I_g(G + R).
4★
So, R = V/I_g − G.
5
Resistance of the voltmeter: R_V = G + R = V/I_g, which is very large. An ideal voltmeter has infinite resistance.

★ key step

Ammeter vs voltmeter

AmmeterGalvanometer + low shunt in parallel. Very low resistance. Joined in series, so it hardly changes the current it measures.

VoltmeterGalvanometer + high resistance in series. Very high resistance. Joined in parallel across two points, so it draws almost no current.

Activity: convert a galvanometer into a voltmeter or an ammeter of a desired range

Use a galvanometer whose resistance G and figure of merit k are known, for example from the half-deflection activity.

1
Count the divisions N on one side of the scale. Full-scale current I_g = k × N, where k is the figure of merit.
2
Voltmeter of range V₀: work out R = V₀/I_g − G. Take this resistance from a high resistance box and join it in series with G.
3
Join your voltmeter in parallel with a standard voltmeter across a rheostat connected to a battery. Change the rheostat and compare the two readings.
4
Ammeter of range I₀: work out S = I_g G/(I₀ − I_g). Use a short length of wire or a low resistance box as the shunt, joined in parallel with G.
5
Join your ammeter in series with a standard ammeter, a battery and a rheostat. Compare the readings for a few currents.
6
Observation: the readings agree within small errors. Result: the galvanometer has been converted into a voltmeter (or an ammeter) of the required range.

Worked example: both conversions

Problem

A galvanometer of resistance 50 Ω gives full-scale deflection for 2.0 mA. Convert it into (a) an ammeter of range 0 to 2.0 A and (b) a voltmeter of range 0 to 10 V.

Working

Given: G = 50 Ω, I_g = 2.0 × 10⁻³ A.
(a) S = I_g G/(I − I_g) = (2.0 × 10⁻³ × 50)/(2.0 − 0.002) Ω.
S = 0.10/1.998 Ω ≈ 0.050 Ω, joined in parallel with G.
(b) R = V/I_g − G = 10/(2.0 × 10⁻³) Ω − 50 Ω.
R = 5000 − 50 = 4950 Ω, joined in series with G.

Answer

(a) a shunt of about 0.050 Ω in parallel; (b) 4950 Ω in series

In real life

An analogue multimeter, the kind an electrician carries in many Indian homes, has a single moving coil galvanometer inside. Turning its dial switches in a shunt for current ranges or a series resistor for voltage ranges.

Exam angle

3 marks: “A galvanometer of resistance 20 Ω gives full-scale deflection for 5 mA. How will you convert it into (a) an ammeter of range 0 to 1 A and (b) a voltmeter of range 0 to 5 V?” (a) S = I_g G/(I − I_g) = (0.005 × 20)/0.995 ≈ 0.10 Ω, in parallel. (b) R = V/I_g − G = 5/0.005 − 20 = 980 Ω, in series.

2 marks: “Why is an ammeter joined in series and a voltmeter in parallel? What are their ideal resistances?” An ammeter must carry the whole current without changing it: series, ideal resistance zero. A voltmeter must measure the potential difference without drawing current: parallel, ideal resistance infinite.

2 marks: “A voltmeter has resistance R_V and range V. How can its range be doubled?” The full-scale current I_g stays the same, so the total resistance must double: join an extra resistance equal to R_V in series.

Remember it

Ammeter: a little side road (low shunt in parallel). Voltmeter: a long toll road (high resistance in series).