From galvanometer to ammeter, voltmeter and ohmmeter
الأسبوع 7 · الفصل الثاني (٤): تحويل الجلفانومتر إلى أميتر (مجزئ التيار) وإلى فولتميتر (مضاعف الجهد)، والأوميتر وتدريجه غير المنتظم، والأجهزة التناظرية والرقمية · 3 دروس
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From galvanometer to ammeter: the shunt
Physics Sec 3 Term 1, Chapter 2: pp. 46–51
GoalFind the shunt resistance that turns a galvanometer into an ammeter of a chosen range.
New words
full-scale current (Ig) · the current that turns the galvanometer pointer to the end of its scale; it is only a few mA or lessshunt (Rs) · a very small resistor connected in parallel with the galvanometer to carry most of the currentammeter · a galvanometer with a shunt, connected in series to measure a current; its own resistance is very small
Explanation
A galvanometer alone can carry only a tiny current Ig, with a resistance Rg. To measure larger currents, a shunt Rs is connected in parallel with it and the pair is connected in series in the circuit. Of the current I that enters the pair, Ig goes through the coil and I − Ig goes through the shunt. The two branches are in parallel, so they have the same potential difference: IgRg = (I − Ig)Rs, which gives Rs = IgRg ÷ (I − Ig). The larger the range I, the smaller the shunt. The resistance of the whole ammeter is Rg and Rs in parallel, which equals IgRg ÷ I: very small, so putting the ammeter in the circuit hardly changes the current.
Worked examples
Rg = 60 Ω, Ig = 1.5 mA, wanted range 0.3 A. Rs = IgRg ÷ (I − Ig) = 0.0015 × 60 ÷ (0.3 − 0.0015) = 0.09 ÷ 0.2985 = 0.302 Ω. The ammeter’s own resistance is IgRg ÷ I = 0.09 ÷ 0.3 = 0.3 Ω.
The same galvanometer for a range of 5 A: Rs = 0.09 ÷ (5 − 0.0015) = 0.09 ÷ 4.9985 = 0.018 Ω. A larger range needs a smaller shunt.
A galvanometer with Rg = 20 Ω and Ig = 2.5 mA has a shunt Rs = 0.5 Ω. At full scale the shunt carries I − Ig = Ig × Rg ÷ Rs = 0.0025 × 20 ÷ 0.5 = 0.1 A, so the range is I = 0.1 + 0.0025 = 0.1025 A (102.5 mA).
Class activity
Paper practice, no real meter. Draw a circuit with a cell, a resistor and an ammeter in series. Mark the place where a shunt would be connected and write above the two branches which of them carries almost all of the current at full scale.
Practice
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A galvanometer has Rg = 80 Ω and Ig = 0.5 mA. Find the shunt that gives a range of 1 A.
