Fundamentals and Practice of Electrical Measurements
3.1 The Electrical Parameters: Current, Voltage, and Resistance In all electrical measurements, current and voltage measuring instruments with
two terminals are employed. The object being measured similarly has two termi-
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nals which either correspond to both measurement connections (e.g., object and reference electrode) or the two ends of an open circuit. Every measuring instru- ment and every object to be measured is a two-terminal network, which is de- scribed by the characteristic I(U).
In principle, when a measurement is made, the characteristic curves of the mea- suring instrument and those of the object being measured should intersect so that the coordinates of the intersection give the measured values. Figure 3-2 shows an I(U) characteristic curve of the object being measured and the curves of two different measuring instruments, 1 and 2. The measured objects are in general two-terminal networks with a short-circuit current, 70 at U = 0 and an electromagnetic force U0 at 7 = 0. Such two-terminal networks are also called active two-terminal networks.
Measuring instruments, on the other hand, are generally passive networks whose
Fig. 3-1 Computer-aided data storage system for monitoring the cathodic protection of a long-distance pipeline.
Table 3-2 Survey of measuring instruments for corrosion protection measurements
Measuring Input resistance/
instrument Type Range voltage drop 1. Electronic dc and ac 100 mV - 1000 V 10 MQ
multimeter dc and ac 10 /fA - 10 A
2. Sensitive dc and ac 1 mV - 1000 V 1 MQ/V; max 10 MQ multimeter dc and ac 1 /xA - 3 A 1 - 500 mV electronic (potential,
pipe current)
3. Amplifier- dc 1 /iA - 1000 V 1 MQ - 100 MQ voltmeter
4. Recording dc 10 mV - 500 mV 1 MQ - 25 MQ potentiometer (potential)
5. Multichannel dc and ac 1 mV - 10 mV 1 MQ - 10 MQ recorder potential
dc and ac (potential)
6. Resistance Resistances 0 - 999 kQ 1 kQ measuring (soil
instrument resistance, dc and ac grounding (potential) resistance)
7. Computerized dc -5 V + 5 V 40 MQ measuring (potential)
instrument for intensive measurement
Table 3-2 Survey of measuring instruments for corrosion protection measurements (continued)
Scale Power
length Weight Dimensions demand Current
Response (mm) (kg) (mm) (W) supply Remarks
— 101 0.45 146x118x44 0.004 9-V flat Resistance cell battery measurement and mains l.OQ-20^
instrument
0.8 110 1.5 205x128x100 0.015 V cells Built-in filter for ac
0.3 2 x 3 5 3.0 205x160x170 2.0 4 x 9-V 1-V output for batteries or recorder, zero in 220 V center of scale 0.5 100 3.5 260x205x105 0.45 Unicell or 2 amplifiers,
6-V and X-Y recorder mains
instrument
0.5 250 7.5 435x350x150 12 220-V or 2 recorders 12-V
accumu- lator
— LCD- 1 185x70x170 2.1 6-V cells 108 Hz ± 4%
indicator automatic adjustment
— LCD- 3.6 420x300x100 — NiCd 6-V Damping indicator cells 16 2/3 Hz: 40 dB
50 Hz: 45 dB
characteristic curves are straight lines through the origin. They are defined clearly by the internal resistance of the instrument. In Fig. 3-2, the internal resistance of instru- ment 1 is cot a and that of instrument 2, cot ft. The measuring instrument should, if possible, be static with a rapid response, i.e., with a nonstationary pair of values (£/,/). In addition, the stationary characteristic curve of the measuring instrument should be reached in a very short time. In contrast, two-terminal networks with capacities and inductances as well as electrochemical two-terminal networks are not static, but dynamic. Besides the measured values ([/1? 7j) and (t/2,/2), there are nonstationary states of the measured object where the measured values all lie on lines 1 or 2. That makes it clear that measuring instruments with a static stationary characteristic curve are needed.
In measuring voltage, instrument 1 reads U{ instead of U0. The error in measure- ment becomes smaller with decreasing measured current /, and corresponding de- creasing a, i.e., with increasing internal resistance. Voltmeters must be as high resistance as possible. The usual moving coil voltmeters have internal resistances of about 10 kQ per volt (^ =0.1 mA) and are not suitable for measuring potential.
High-resistance instruments with about 1 MQ per volt (I{ = 1 /lA) are usual in prac- tice. Stationary potentials can be measured with them; their response times are, however, somewhat long (>1 s). For potential measurements, analog-reading elec- tronic amplifier-voltmeters with resistances of 107to 1012 Q are generally used. The response times are <1 s, with electronic displays <1 ms.
In measuring current with instrument 2, a reading of 72 instead of 70 is obtained.
Here the error is smaller with decreasing measured voltage U2 and correspondingly increasing ft, i.e., decreasing internal resistance. That means that in measuring cur- rent, the instrument must have as low an internal resistance as possible in order not to increase the total resistance of the circuit and thereby alter the measured values. The usual moving coil instruments have internal resistances of 100 Q per mA"1
Fig. 3-2 Current and voltage measurement in a current-voltage diagram (explana- tion in the text).
(U2 = 0.1 V) and are suitable for current measurement. For smaller currents, sensi- tive instruments with 5 kQ per /xAr1 (U2 = 5 rnV) are used. Small currents are usu- ally measured by the voltage drop across a fixed resistance (calibrated shunt) using an electronic amplifier-voltmeter. This method has the advantage that the circuit does not have to be interrupted to measure the current.
Resistance is measured either indirectly by separate current and voltage mea- surements or directly by comparison in a bridge. In both cases it involves two mea- surements. The instruments for measuring the current and voltage U2 have to be chosen so as to make the deviation from U and /in Fig. 3-2 as small as possible.
In contrast to simple current and potential measurements, polarization measure- ments (i.e., current-potential curves) demand active systems with active external circuits with variable characteristic curves (see Fig. 2-3). These external circuits should be as static as possible so that all nonstationary values lie on the known curve, which is known as the resistance straight line of the external circuit. External circuits for electrochemical protection have steep straight lines in the /(£/) diagram (i.e., low internal resistance) because the potential can be well controlled independent of the current. The usual dc sources with high internal resistance are less suitable because changes in current requirements cause correspondingly large changes in voltage.
For certain systems (e.g., groups II and IV in Section 2.4) only low-resistance pro- tective rectifiers can be used (see Chapter 21).