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Download Effects of measuring voltage with a multimeter Emmett
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Effects of measuring voltage with a multimeter Emmett Ientilucci Most people do not consider the effects a multimeter or digital multimeter (DMM) has in an electrical circuit. For example, consider the circuit below: R1 V R2 Rm The above schematic would be the actual schematic if you were trying to measure the voltage across R2. When measuring voltage with a DMM, the meter acts as a resistor in parallel with the device you are trying to measure. As long as the meters resistance is substantially larger than the resistance of the device you are trying to measure, the error in the measured voltage will be minimal. The idea is to have the meters resistance be as large as possible (compared to the device you are measuring). In this way, the meters resistance will not drastically alter the value of R2, the resistor in question. Example, if R2 was 1 kΩ and Rm was 20 MΩ, the equivalent resistance would still be about 1 kΩ. The voltage reading given by the meter would be for a 1 kΩ resistor. However, if R2 was 15 MΩ and Rm was 20 MΩ, the equivalent resistance would now be 8.5 MΩ, not 15 MΩ! The voltage reading given by the meter would be for an 8.5 MΩ resistor not the 15 MΩ that is actually in the circuit! Here is an example, V total = 5v R1 = 10 kΩ R2 = 15 MΩ Rm = 22 MΩ (typically) Q: What is the voltage across R2? First lets calculate the voltage across R2 with the meter out of the circuit. This is simply 2 resistors (R1, R2) in series. V2 = I2 R2 What is I2? I2 = I1 = I total What is I total? I total = Vtotal R total R total = R1 + R2 V2 = V total R2 R1 + R2 V2 = V total R2 R1 + R2 What is R total? Now put it all together or This is commonly called a voltage divider Plug in the numbers V2 = (5v) [ 10MΩ / (100kΩ + 10MΩ) ] V2 = 4.95 v Ok, now put the meter in the circuit and have it measure this result. The meter should display a reading of 4.95v, right? Not really...... Now there are 3 resistors to consider. V2 = I2 R2 I2 = Itotal What is I2? Rm R2 + Rm ... division of current or " current divider" What is I total? Vtotal R total I total = What is R total? We must consider Rm R total = R1 + Req V2 = Req = Rm Vtotal R2 R1 + Req R2 + Rm V 2 = Vtotal 1 .....since R2 and Rm are in parallel 1 + 1 R2 Rm The quanity Rm R2 is simply Req R2 + Rm Req R1 + Req Now plug in the numbers............. Re q = 1 1 1 10 MΩ + 22 MΩ V 2 = 5v = 6.97 MΩ (not 10 MΩ anymore!) 6.97 MΩ 100 kΩ + 6.97 MΩ V 2 = 4.92 v This should have been 4.95 v but the meters resistance in parallel with R2 induced a 30 mv difference. This is because the value of R2 was close to Rm, the meters input impedance. This is sometime referred to as “loading” down the circuit. In other words, the meter loaded down the circuit in test. This difference may not seem like much.....but it is worth considering when measuring devices that have an input resistance close to the input impedance of the meter.