Current and Voltage Measurements. Current measurement
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- Everett Neal
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1 Current and oltage easurements Current measurement ccording to current continuity (i.e. charge conservation) law, the current can be measured in any portion of a single loop circuit. B Circuit Element
2 Contact-less methods B ny current produces a magnetic field. agnetic field rotates the indicator (like a compass needle) ssues: Not very accurate. Low-sensitive only applicable to high-current circuits
3 Current measurement device mmeter agneto-electric ammeter The ammeter uses the magnetic field created by the current to deflect the needle. The coil attached to the needle increases the magnetic field of the current.
4 Current measurement device - mmeter The magnetic field of the coil is proportional to the electric current The deflection angle is proportional to the magnetic field Hence, the deflection angle is proportional to the current The maximum current that can be measured depends on the full scale deflection (f.s.d) of the ammeter
5 Current measurement device - mmeter mmeter On a circuit diagrams, an ammeter is shown as an in a circle.
6 Series resistance method most commonly used in all modern instruments 1. Break the circuit (or a branch) mmeter 2. nsert an ammeter B Circuit Element X 3. The current through the ammeter is measured by the needle deflection angle. 4. The current through the resistor or any circuit component X is the same as that through the ammeter 5. Electronic instruments are used to display or transmit the results
7 Distortions introduced by easurement B mmeter The resistor is shown by rectangle here to emphasize that the method can be applied to NY circuit component, not to resistors only. The ammeter inserted in the circuit changes the actual current in it. Let the resistance of the Element X be The actual circuit current is = B / fter insertion of the ammeter, the total circuit resistance changes and so does the current.
8 eminder: Series electric circuit B For the resistor 1: 1 = 1 / 1 ; For the resistor 2: 2 = 2 / 2 ; From the current continuity: 1 = 2 = ; 1 = 1 ; 2 = (1) 2 From the energy conservation: B = ; (2) From (1) and (2): B = = ( ) (3) Solve (3) for the current B = Find 1 and 2 from (1) = = B 1 1 = B = B
9 Distortions introduced by current measurement Let the ammeter resistance (the resistance of the coil) be B mmeter Circuit Element The actual circuit current is The measured current, = B B + = < The measured current is less than the actual current in the circuit
10 Problem 1 B mmeter Circuit Element The resistor 2 kohm is connected to a 9 battery. The mmeter connected in series with the resistor indicates the current 4 m flowing through the circuit. What is the actual current in the original circuit (without the ammeter) in m? 0 of Timed response
11 Problem 2 B mmeter Circuit Element The resistor 2 kohm is connected to a 9 battery. The mmeter connected in series with the resistor indicates the current 4 m flowing through the circuit. What is the mmeter internal resistance in Ohms? 0 of Timed response
12 Problem 3 B mmeter Circuit Element resistor is connected to a 9 battery. The mmeter connected in series with the resistor indicates the current 4.5 m in the circuit. The mmeter internal resistance is 100 Ohm. What is the actual current in the circuit (without the ammeter) in m? 0 of Timed response
13 Distortions introduced by current measurement B Circuit Element The actual / measured current ratio B B + = + = + = 1 / = = 1 mmeter The actual circuit current is The measured current The relative measurement error B = B < + =
14 equirements for accurate current measurements B mmeter For accurate measurements, The ETE resistance must be << Circuit Element Example What is the relative current measurement error if the ammeter resistance = 0.001? =0.001= 0.1%
15 oltage measurements 2 B To measure the voltage, we need to probe the voltage between two nodes in the circuit. arious types of analog and digital electronics instruments are capable of amplifying or attenuating the input signals. Since voltage measurement does not need any intrusion it does not seem to make distortions NOT TUE!
16 2 oltage measurements B oltmeter When the voltage is applied to the input of any instrument, there is a current flowing into the input. ccording to the charge conservation law, this current reduces the current through the test element. Therefore, the voltage changes, too.
17 oltage measurements ssume the voltmeter internal resistance. S The total resistance with the voltmeter connected, EQ + = < The voltage measured by the voltmeter, = S * EQ The actual voltage, = S * >
18 Problem 4 S esistor 1k is connected to a 10 m current source. The voltmeter connected in in parallel with the resistor indicates the voltage 9.5 What is the actual voltage across the resistor (with no voltmeter connected) in? 0 of Timed response
19 Problem 5 S esistor 1k is connected to a current source. The voltmeter with internal resistance 10k connected in in parallel with the resistor indicates the voltage 9.09 What is the actual voltage across the resistor (with no voltmeter connected) in? 0 of Timed response
20 oltage measurements S The actual voltage: The measured voltage: = = S EQ S = S + ( ) S + + = = = 1+ S The error introduced by the measurement: = = 1; =
21 oltage measurements = 1= E2 n order to achieve less than 0.1% error in measurements, what values of is needed? B oltmeter < 0.1% = 0.001; > The OLTETE resistance must be >> On a circuit diagram, a voltmeter is shown as an in a circle.
22 oltmeter and ammeter comparison mmeter oltmeter The ammeter resistance must be much lower than the resistance of the circuit to be measured The voltmeter resistance must be much higher than the resistance of the circuit to be measured mmeter connected to a large series resistor can be used as a voltmeter mmeter oltmeter
23 Summary For accurate current measurements, the resistance of the current meter (connected in series with the circuit element under testing), must be much smaller than that of the tested element. For accurate voltage measurements, the resistance of the voltmeter (connected in parallel with the circuit element under testing), must be much greater than that of the tested element. The current and voltage measurement errors (relative) are given by: 1 = = 1=
24 Smart voltmeter circuit zero current consumption
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