The ohmmeter

An ohmmeter measures an unknown resistance directly. Measuring a resistance by Ohm's law needs both an ammeter and a voltmeter (R = V / I). If the voltage is fixed and known, we can drop the voltmeter and mark the galvanometer scale in ohms instead of amperes.

It is a micro-ammeter (galvanometer) in series with a fixed resistance, a variable resistance (adjusted for zero) and a cell of constant emf (about 1.5 V), with two terminals between which the unknown resistance R_x is connected.

• Zero adjustment: with the terminals touching (R_x = 0, short circuit), the variable resistor is adjusted so that the pointer gives full-scale deflection: R_total = V_B / I_g.
• With R_x inserted the current is I = V_B/(R_total + R_x), which is smaller, so the deflection is smaller and the scale is calibrated directly in ohms.
• Features of the scale: zero ohms is at the full-scale end (the right) and infinite resistance at the left (open circuit) — opposite to the current scale; it is non-linear (the readings are spread out at the zero end and crowded at the high-resistance end).
• If R_x = R_total the current is half of FSD; if R_x = 2 R_total it is one-third FSD, etc. In general, I / I_g = R_total / (R_total + R_x).
• Reasons: the cell must have a constant emf (otherwise the calibration is wrong); the fixed resistor protects the meter and sets the calibration; the variable resistor is needed to bring the pointer exactly to the zero mark when the cell ages.

Example 9. An ohmmeter has a 1.5 V cell and a total internal resistance of 3000 Ω at FSD (500 μA). With an unknown resistor of 3000 Ω: I = 1.5/6000 = 250 μA = half of FSD. With 9000 Ω: I = 1.5/12000 = 125 μA = quarter of FSD.

Example 9a — a calibration table. An ohmmeter has a 1.5 V cell and FSD current 1 mA, so its total internal resistance is 1.5/0.001 = 1500 Ω. For different R_x:

Example 9b — design. A milliammeter of resistance 20 Ω has FSD 10 mA. It is used as an ohmmeter with a 1.5 V cell of internal resistance 1 Ω. For FSD the total resistance must be 1.5/0.010 = 150 Ω, so the standard resistor needed (including the variable one) is 150 − 20 − 1 = 129 Ω. A reading of 6 mA means the total resistance is 1.5/0.006 = 250 Ω, so R_x = 250 − 150 = 100 Ω. With R_x = 600 Ω the current is 1.5/750 = 2 mA.