☰ Contents · Physics

Ammeter, voltmeter and measuring a source

Lessons 39–40 · 2 lessons · N. Sh. Turdiyev, K. A. Tursunmetov, A. G. Ganiyev, K. T. Suyarov, J. E. Usarov, A. K. Avliyoqulov. Physics Grade 10, 1st edition. Niso Poligraf Publishing House, Tashkent, 2017
39

Extending the measuring range of an ammeter and a voltmeter

Textbook: pp. 145–146
GoalCalculate how to make an ammeter (with a shunt) and a voltmeter (with a series resistor) from a galvanometer and extend the measuring range.
New words
shunt · shuntseries (multiplier) resistor · qo‘shimcha qarshilikgalvanometer · galvanometrmeasuring range · o‘lchash chegarasi
Explanation

A galvanometer measures only a very small current or voltage: its permitted current is Ig, its resistance Rg, and its voltage limit Ug = Ig·Rg. To extend the current range n times (I = nIg) a small resistance – a shunt – is connected in parallel with it: the voltages are equal, Ig·Rg = (I – Ig)·r, so r = Rg/(n – 1). Then only 1/n of the total current passes through the galvanometer; the ammeter is connected in series in the circuit and its resistance is very small. To extend the voltage range n times (U = nUg) a series resistor is added: U = Ig(Rg + r), so r = Rg(n – 1). A voltmeter is connected in parallel with the part being measured and its resistance must be very large. Connecting an ammeter in parallel or a voltmeter in series spoils the circuit and may burn out the instrument. When the range is extended n times, the scale division value also grows n times.

Worked examples
Rg = 100 Ω, Ig = 1 mA; we need to measure up to 5 mA: n = 5, shunt r = Rg/(n – 1) = 100/4 = 25 Ω. If 0.6 mA flows through the galvanometer, the circuit current is 0.6·5 = 3 mA.
Rg = 50 Ω, Ig = 2 mA (Ug = 0.1 V). For a voltmeter up to 10 V, n = 100: r = Rg(n – 1) = 50·99 = 4950 Ω in series; total resistance 5000 Ω.
Class activity

Only by calculation: for given Rg and Ig compute the shunt and multiplier for a 1 A ammeter and a 5 V voltmeter and draw the circuit diagrams. Connect real instruments only with the teacher.

Practice
1
How is a shunt connected to an ammeter and how is its resistance found?
2
A galvanometer with Rg = 90 Ω needs its range extended 10 times. What is the shunt (Ω)?
3
A galvanometer with Rg = 200 Ω must have its voltage range extended 6 times. What series resistor (Ω) is needed?
4
Why must a voltmeter have a large resistance and an ammeter a small one?