The Laws of Circuit

D'Arsonval Movement and Voltmeter Sensitivity (and Internal Resistance)

What is the "sensitivity of voltmeter"? D'Arsonval movement (or just movement) is a current measuring device which can be utilized for Ammeter or Voltmeter. A movement is characterized by rated voltage (Vm)and rated current (Im). Either the rated voltage across or rated current through the movement fully deflects the meter scale. For example, if a movement is rated with 100mV and 1mA, then a voltage of 100mV across the movement would fully deflect the scale, while a voltage of 50mV across would only half deflect the scale. Similarly, a current amount of 1mA through the movement would fully deflect the scale, and half deflection with 0.5 mA. The movement also has resistance determined by the rated voltage and rated current. In 100mV and 1mA movement, the resistance of the movement is 100[mV]/1[mA]=100 ohm. Then, what is the sensitivity of voltmeter? Well, we have to discuss about voltmeter first to answer the question. Consider again the 100mV 1mA movement. The full deflection voltage is 100mV. Now if we want to increase the full scale voltage to 10V, for example, we have to add a resistor in series with the movement so that the additional resistor can take up the voltage 10 - 0.1 V.   Remember an 100mV 1mA movement cannot take up more than 100mV across itself and 1mA through itself.  In this 10V full scale voltmeter, 10V across the voltmeter would fully deflect the scale while, for example, 5V would half deflect it. The amount of the series resistance is given by the rest of the voltage (i.e., full scale voltage minus the rated voltage) over the rated current (that is: (10-0.1)/(0.001)=9900 ohm). Then, the 10V full scale voltmeter has a total resistance of 10,000 ohm (from 100 ohm(of movement itself) + 9900 ohm(of the series resistance)) . Now let's consider using this voltmeter to measure the voltage across a resistor in a circuit. The internal resistance of 10,000ohm of the voltmeter is actually added (in parallel actually) to the circuit, and the resistance of the object resistor now, when measured, is appeared to be changed to another value. This change is normally called a loading effect. To quickly find how much loading effect a voltmeter brings to a circuit, some voltmeter comes with a new rating called "voltmeter sensitivity". Voltmeter sensitivity is given by [ohm/V], in other words, sensitivity tells you about the internal resistance of a voltmeter with a full scale value. Let's go back to the original movement of 100mV 1mA. If we use this movement for a voltmeter, the internal resistance is the resistance of the movement (100ohm) and the full scale is 100mV (or 0.1V), therefore the sensitivity is 100/0.1 = 1000 [ohm/V]. If this movement is used for 10V full scale, then the internal resistance of the voltmeter is found by the product of Sensitivity and the Full Scale, 1000 (sensitivity)x10 (full scale)=10,000 ohm.  Consider this as "Keep the same sensitivity no matter what the full scale is."  In the 10V full scale, the sensitivity is 10000 ohm/10 V = 1000. In a nutshell, sensitivity of voltmeter is found by dividing the resistance [ohm]of a movement by the rated voltage [V] of the movement. Once you have this sensitivity, the internal resistance of a voltmeter with the movement is determined by multiplying the sensitivity by the full scale value.
Example 1: 100mV 2mA movement ---Sensitivity is 50[ohm]/0.1[V]=500 [ohm/V]. If this movement is used to build a 100V full scale voltmeter, the internal resistance of the voltmeter is: 500[ohm/V]x100[V]=50,000[ohm].
Example 2: 50mV 1mA movement ---Sensitivity is 50[ohm]/0.05[V]=1000[ohm/V]. If this movement is used to build a 100V full scale voltmeter, the internal resistance of the voltmeter is: 1000[ohm/V]x100[V]=100,000[ohm]

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