Basic Meters Reading: Physics, 8 Edition Custom Edition J.D. ...

Physics 155.3: Introduction to Electricity and Magnetism

Basic Meters

Reading: Physics, 8th Edition Custom Edition J.D. Cutnell & K.W. Johnson Chapter 20.11, Pages 622-624 Assignment: N/A

Physics 155.3: Introduction to Electricity and Magnetism Table of Contents 1

Basic Meters ......................................................................................................... 3 D’Arsonval Meter Movement ................................................................................ 3 Voltmeter .............................................................................................................. 5 Ammeter ............................................................................................................... 7

List of Figures Figure 1: Voltmeter and Ammeter in Circuit .................................................................... 3 Figure 2: D’Arsonval Movement ...................................................................................... 4 Figure 3: Ammeter Shunt Resistance.............................................................................. 7 List of Examples Example 1: Voltmeter Series Resistor ............................................................................. 6 Example 2: Ammeter Shunt Resistance .......................................................................... 8 Example 3: Meter Loading .............................................................................................. 9

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1

Basic Meters You have seen to voltmeters and ammeters in previous material. See below. It is now time to analyze them.

Figure 1: Voltmeter and Ammeter in Circuit In order to do this operating characteristics of the devices must be considered. The most important characteristic of both meters is that they should not interfere with the circuit. It is an unfortunate by-product of taking a measurement of either voltage or current that the fact that you are taking a measurement changes the value of what you are trying to measure. The best we can do is to minimize the error in our measurement. Why this is important and why it is a concern will be discussed in the following sections. D’Arsonval Meter Movement The D’Arsonval permanent magnet moving coil (PMMC) meter movement (or galvanometer) is a traditional meter movement mechanism. A simplified diagram is shown on the next page. Note that the needle deflects only one way (i.e., there is a positive and negative terminal associated with the meter movement). (R. Bolton - 2012)

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Figure 2: D’Arsonval Movement Most traditional dc instruments use meters based on some form of the D’Arsonval meter movement. A change in current causes a proportional change in the force acting on the coil in the magnetic field between the poles. Professor Pywell will address the operation of this type of meter movement in his lectures on magnetic circuits. Note that since the movement consists of a multi-turn coil of wire the basic movement has some internal resistance. A typical value is 50Ω. As well the basic movement has some maximum value of current that can pass through the wires in the coil (since they are relatively small in cross sectional area and would “blow” if too much current was used). A typical value of galvanometer current is 1mA or less (50µA is very common). Subject to these restrictions, the D’Arsonval movement has a long history and has only recently been replaced with modern digital meters (not actually meter movements but semiconductor electronic devices). (R. Bolton - 2012)

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Voltmeter A voltmeter is used to measure voltage. As such it is a two terminal device (since it must measure potential difference between two different points). Recall that voltage is measured across a circuit component. As such, a voltmeter is placed in parallel with the component(s) it is measuring the voltage across. Since it is placed in parallel an ideal voltmeter would draw no current through it (i.e., it would have infinite resistance). Since this is impossible, it must draw some current, but we would like to minimize the amount. To do this, a real voltmeter would have a high resistance (recall the current divider rule). This is accomplished by adding a series resistor inside the voltmeter to increase the internal resistance. A by-product of this is that through the appropriate choice of series resistance, a voltmeter can be made to measure different ranges of voltage (i.e., 1mV, 10mV, 100mV, 1V, 10V, etc.). The value of the series resistance can be calculated using the Voltage Divider Rule (VDR). Note that in the case of a voltmeter current flowing through the PMMC causes a deflection of the needle. All that is necessary is to “calibrate” the scale so that it reads voltage instead of current.

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Example 1: Voltmeter Series Resistor Determine the value of the series resistor in a voltmeter having a 1mA galvanometer movement and 50Ω internal resistance such that it will be capable of measuring 5 volts. Solution: The 1mA maximum current is intended to be reached when the voltage the voltmeter is measuring is 5V.

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Ammeter An ammeter is used to measure current. As such it is a two terminal device (since it must have an input and an output). Recall that current is measured through a circuit component. As such an ammeter is placed in series with the component(s) it is measuring the current through. Since it is placed in series an ideal ammeter would have no voltage across it (i.e., it would have zero resistance). Since this is impossible, it must have some voltage across it, but we would like to minimize the amount. To do this, a real ammeter would have a low resistance (recall the voltage divider rule). This is accomplished by adding a parallel resistor (the shunt resistor) across the meter mechanism inside the ammeter to decrease the internal resistance. A by-product of this is that through the appropriate choice of shunt resistance, an ammeter can be made to measure different ranges of current (i.e., 1mA, 10mA, 100mA, 1A, 10A, etc.). The value of the shunt resistance can be calculated using the Current Divider Rule (CDR).

Figure 3: Ammeter Shunt Resistance.

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Example 2: Ammeter Shunt Resistance Determine the value of the shunt resistor in an ammeter having a 1mA galvanometer movement and 50Ω internal resistance such that it will be capable of measuring 100 mA. Solution: The 1mA maximum current is intended to be reached when the current the ammeter is measuring is 100mA.

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Example 3: Meter Loading Consider the circuit below (used previously). It is known that 20mA of current flows counter-clockwise in the circuit. 35V a

110Ω 50V

90Ω 30V

20mA

200Ω b

c

7V

What will our 5V voltmeter read if it is placed so as to measure the voltage from point b to point c (i.e., Vbc)? The true voltage is 4.00V (i.e., 20mA·200Ω). Why is the voltage positive?? What will our 100mA ammeter read if it is placed so as to measure the current through point b? Assume the voltmeter has been removed. Solution: Voltmeter: 35V a

110Ω

90Ω

50V

30V 200Ω b

7V

c +

V

-

The effective resistance of the voltmeter is 5000Ω (i.e., 50Ω in series with 4950Ω). Placing this in parallel (R. Bolton - 2012)

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with the 200Ω resistor will change the total resistance in the circuit. The 200Ω resistor now looks like:

R200 =

200Ω ⋅ 5000Ω = 192.3Ω (200Ω + 5000Ω )

The total series resistance is now

Rseries = 110Ω + 90Ω + 192.3Ω = 392.3Ω Therefore the current is now

8V = 20.39mA 392.3Ω The voltmeter current (through the coil) is (CDR) I=

 200Ω  I c = 20.39ma   = 784.2 µA 5200 Ω   Therefore the voltmeter reads (recall 1mA of current in the coil is calibrated for 5V on the scale)

 784.2 µA  Vbc = 5V   = 3.92V mA 1   Recall the true voltage was 4.00V.

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Ammeter: 35V a

110Ω

90Ω

50V

30V +

7V

A

-

200Ω

b

c

The effective resistance of the ammeter is 0.50Ω (i.e., 50Ω in parallel with 0.505Ω). Placing this in series with the 200Ω resistor at point b changes the total resistance in the circuit. The total series resistance is now

Rseries = 110Ω + 90Ω + 200Ω + 0.50Ω = 400.5Ω Therefore the current is now

− 8V = −19.98mA 400.5Ω The ammeter current (through the coil) is (CDR) I=

 0.505Ω  I c = −19.98mA  = −199.7 µA  50.505Ω  Therefore the ammeter reads (recall 1mA of current in the coil is calibrated for 100mA on the scale)

 − 199.73µA  I b = 100mA  = −19.97mA 1mA   Recall the true current was -20.0mA.

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Note that both the voltmeter and ammeter have to be connected in the correct way (i.e., correct polarity) since the needle connected to the moving coil can only deflect one way. The voltmeter was connected with its positive terminal at point b and its negative terminal at point c. This measures Vbc. This will measure a positive voltage. The ammeter was connected with its positive terminal towards the 7V battery on the left and its negative terminal towards the 200Ω resistor on the right. This will measure a positive current.

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