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
3
The ohmmeter and the multimeter
Physics Sec 3 Term 1, Chapter 2: pp. 46–51
GoalExplain how an ohmmeter reads resistance, calculate its pointer positions and name the multimeter.
New words
ohmmeter · a galvanometer in series with a cell, a fixed and a variable resistor; the unknown resistance Rx joins the series circuit between the probesown resistance Ri of the ohmmeter · the total resistance inside the instrument, galvanometer plus the other resistors; Ri = E ÷ Igmultimeter · one instrument with a selector switch for current, voltage and resistance; analogue ones have a pointer, digital ones a display
Explanation
Before use, the two probes are touched together (Rx = 0) and the variable resistor is adjusted until the pointer reaches the end of the scale: Ig = E ÷ Ri, so Ri = E ÷ Ig. That end of the scale is therefore marked 0 Ω. When the probes are put across an unknown resistance Rx, the current falls to I = E ÷ (Ri + Rx), so the pointer stops short of the end. Half of full scale means Rx = Ri; one third means Rx = 2Ri; one quarter means Rx = 3Ri; no deflection means an open circuit, Rx very large. Equal steps of current are not equal steps of resistance, so the scale is not evenly spaced and the numbers are crowded together at the high-resistance end, opposite to a current scale. The resistance reading is made on a part that is out of every circuit and carries no current. A multimeter is described here only: its switch connects the galvanometer to shunts, to multipliers or to the ohmmeter cell.
Worked examples
An ohmmeter has a cell of E = 1.5 V and a galvanometer with Ig = 300 µA at full scale. Ri = E ÷ Ig = 1.5 ÷ (300 × 10⁻⁶) = 5000 Ω. The graph shows the current for several values of Rx.
With the same instrument: Rx = 2500 Ω gives I = 1.5 ÷ (5000 + 2500) = 200 µA, two thirds of full scale; Rx = 20 000 Ω gives I = 1.5 ÷ 25 000 = 60 µA, one fifth of full scale.
Pointer current (µA)
Rx = E ÷ I − Ri (Ω)
300
0
250
1 000
200
2 500
150
5 000
100
10 000
50
25 000
Reading the scale backwards: Rx = E ÷ I − Ri. The table shows how a scale marked in equal current steps gives unequal resistance steps.
Class activity
Paper practice. For an ohmmeter with E = 1.5 V and Ri = 5000 Ω, draw a half-circle scale and mark the places of 0 Ω, 5000 Ω, 10 000 Ω and 15 000 Ω using the currents 300, 150, 100 and 75 µA. Notice how the marks crowd together on one side. Never test a part that is connected to a supply.
Practice
1
An ohmmeter has E = 1.5 V and a full-scale current of 500 µA. Find Ri.
Ri = 1.5 ÷ (500 × 10⁻⁶) = 3000 Ω.
2
With this instrument, find the current for Rx = 3000 Ω and for Rx = 9000 Ω.
