A multimeter instrument is one which is adapted for measuring both current and voltage. It has a shunt R as shown, and a series of voltage multipliers R as shown, and a series of voltage multiplier R’. The shunt is connected permanently across the coil, and the resistances in R’ are adjusted to give the desired full-scale voltages with the shunt in position. A switch or plug enables the various full-scale values of current or voltage to be chosen in the multimeter, but the user does the mental arithmetic. The instrument shown in the figure is reading 1.7 volts; if it were on the 10-volt range, it would be reading 6.4.
The terminals of a meter, multimeter or otherwise, are usually marked + and -; the pointer is deflected to the right when current passes through the meter from + to -.
A multimeter is generally deployed in the measurement of resistance as well as current and voltage. An extra position on the switch, marked ‘R’ or ohms’, puts a fry cell C and a variable resistor R” in series with the moving coil. Before the instrument is used to measure a resistance, its terminals, TT are short-circuited, and R” is adjusted until the pointer is fully deflected. As shown in the figure, it is then opposite the zero on the ohms scale. The short-circuit is next removed, and the unknown resistance Rx is connected across the terminals. The current falls, and the pointer moves to the left, indicating on the ohms scale the value of Rx. The ohms scale is calibrated by the makers with known resistances. The multimeter has become a very useful instrument in electronic workshops and laboratories for students and electricians.
Use of Voltmeter and Ammeter
A moving – coil voltmeter is a current – operated instrument. It can be used to measure potential differences only because the current which it draws is proportional to the potential difference applied to it, from Ohm’s law. Since its action depends on Ohm’s law, a moving-coil voltmeter cannot be used in any experiment to demonstrate that law; that is why, when describing such an experiment, we specified measuring instruments whose readings are not dependent on Ohm’s law.
Having established Ohm’s law, however, we can use moving-coil voltmeters freely; they are both more sensitive and more accurate than other forms of voltmeters. The current which they take does, however, sometimes complicate their use. To see how it may do so, let us suppose that we wish to measure a resistance R of about 100 ohms. We connect it in series with a cell, a milliammeter, and a variable resistance; across it we place the voltmeter. We adjust the current until the voltmeter reads, say, V1 = 1 Volt; let us suppose that the milliammeter then reads I = 12 mA. The value of the resistance then appears to be
But the milliammeter reading includes the current drawn by the volt-meter. If that is 2 mA, then the current through the resisitor, I’, is only 10 mA and its resistance is actually
The current drawn by the voltmeter has made the resistance appear 17 percent lower than its true value.
In an attempt to avoid this error, we might connect the voltmeter across both the resistor and the milliammeter. But its reading would then include the potential difference across the milliammeter. Let us suppose that this is 0.05 volt when the current through the milliammeter is 10 mA. Then the potential difference V’ across the resistor would be 1 volt, and the voltmeter would read 1.05 volt. The resistance would appear to be
Thus the voltage drop across the milliammeter would make the resistance appear 5 percent higher than its true value.
Errors of this kind are negligible only when the voltmeter current is much less than the current through the resistor, or when the voltage drop across the ammeter is much less than the potential difference across the resistor. If we were measuring a resistance of about 1 ohm, for example, the current I’ would be 1 amp, and I would be 1.002 amp. The error in measuring R would then be only 0.2 percentage less than the intrinsic error of the meter. But the circuit diagram for this setup would give the same error as before. It could do so because, as we saw when considering shunts, the shunt across the milliammeter would have been chosen to make the voltage drop still 0.05 volt. Thus, V1 would still be 1.05 volt when V’ was 1 volt, and the error would be 5 percent as before.
In low resistance circuits, therefore, the voltmeter should be connected accurately, so that its reading does not include the voltage drop across the ammeter. But in high – resistance circuits the voltmeter should be connected accurately, so that the ammeter does not carry its current.
Is a moving coil voltmeter is connected across a cell, it will not read its true e.m.f., because the current which it draws will set up a voltage drop across the initial resistance of the voltmeter is very high compared with the internal resistance. E.m.f. are thus compared by a potentiometer method, discussed shortly.
Figure of Merit of a Voltmeter
If a milliammeter of 1 mA f.s.d. (full scale deflection) is converted into a voltmeter, then if it is to have 1 volt f.s.d. its total resistance coil plus multiplier must be 1000 ohms. (One volt across its terminals will send through it a current of 1/1000 amp = 1 mA.) if it is to have 10 volts f.s.d., then its total resistance must be 10000 ohms; for 20 volts f.s.d., 20000 ohms, and so on. It will have a resistance of 1000 ohms for every volt of its full-scale deflection. Such a meter is said to have a figure of merit of 1000 ohms per volt. Similarly, a voltmeter which takes 10 mA, or 1/100 amp, for full-scale deflection has a figure of merit of 100 ohms per volt. The greater the figure of merit of a voltmeter, expressed in this way, the less will it disturb any circuit to which it is connected, and the less error will its current cause in any measurement made with it. On the other hand, the greater the figure of merit, the more delicate the moving system of the meter and the greater its intrinsic error. First-grade, and particularly ‘sub-standard’, meters therefore have medium or low figure of merit: from 500 to 66.7 ohms per volt.
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