Simple Nature - Light and Matter

Now if we are carrying out this measurement on a resistor that ispart of a larger circuit, we have changed the behavior of the circuitthrough our act of measuring. It is as though we had modifiedthe circuit by replacing the resistance R with the smaller equivalentresistance of R and R v in parallel. It is for this reason thatvoltmeters are built with the largest possible internal resistance.As a numerical example, if we use a voltmeter with an internalresistance of 1 MΩ to measure the voltage drop across a oneohmresistor, the equivalent resistance is 0.999999 Ω, which isnot different enough to make any difference. But if we tried to usethe same voltmeter to measure the voltage drop across a 2−MΩresistor, we would be reducing the resistance of that part of thecircuit by a factor of three, which would produce a drastic changein the behavior of the whole circuit.This is the reason why you can’t use a voltmeter to measure thevoltage difference between two different points in mid-air, or betweenthe ends of a piece of wood. This is by no means a stupid thing towant to do, since the world around us is not a constant-voltageenvironment, the most extreme example being when an electricalstorm is brewing. But it will not work with an ordinary voltmeterbecause the resistance of the air or the wood is many gigaohms. Theeffect of waving a pair of voltmeter probes around in the air is thatwe provide a reuniting path for the positive and negative chargesthat have been separated — through the voltmeter itself, which isa good conductor compared to the air. This reduces to zero thevoltage difference we were trying to measure.In general, a voltmeter that has been set up with an open circuit(or a very large resistance) between its probes is said to be “floating.”An old-fashioned analog voltmeter of the type described herewill read zero when left floating, the same as when it was sittingon the shelf. A floating digital voltmeter usually shows an errormessage.9.2.3 Series resistancesThe two basic circuit layouts are parallel and series, so a pair ofresistors in series, h/1, is another of the most basic circuits we canmake. By conservation of charge, all the current that flows throughone resistor must also flow through the other (as well as through thebattery):I 1 = I 2 .The only way the information about the two resistance values isgoing to be useful is if we can apply Ohm’s law, which will relate theresistance of each resistor to the current flowing through it and thevoltage difference across it. Figure h/2 shows the three constantvoltageareas. Voltage differences are more physically significantthan voltages, so we define symbols for the voltage differences acrossh / 1. A battery drives currentthrough two resistors in series. 2.There are three constant-voltageregions. 3. The three voltagedifferences are related. 4. Ifthe meter crab-walks around thecircuit without flipping over orcrossing its legs, the resultingvoltages have plus and minussigns that make them add up tozero.Section 9.2 Parallel and Series Circuits 537