Voltmeter Design
DC Electric Circuits
Suppose I were about to measure an unknown voltage with a manualrange voltmeter. This particular voltmeter has several different voltage measurement ranges to choose from:
 500 volts
 250 volts
 100 volts
 50 volts
 25 volts
 10 volts
 5 volts
What range would be best to begin with, when first measuring this unknown voltage with the meter? Explain your answer.
An important step in building any analog voltmeter or ammeter is to accurately determine the coil resistance of the meter movement. In electrical metrology, it is often easier to obtain extremely precise (“standard”) resistance values than it is to obtain equally precise voltage or current measurements. One technique that may be used to determine the coil resistance of a meter movement without need to accurately measure voltage or current is as follows.
First, connect a decade box type of variable resistance in series with a regulated DC power supply, then to the meter movement to be tested. Adjust the decade box’s resistance so that the meter movement moves to some precise point on its scale, preferably the fullscale (100%) mark. Record the decade box’s resistance setting as R_{1}:

Then, connect a known resistance in parallel with the meter movement’s terminals. This resistance will be known as R_{s}, the shunt resistance. The meter movement deflection will decrease when you do this. Readjust the decade box’s resistance until the meter movement deflection returns to its former place. Record the decade box’s resistance setting as R_{2}:

The meter movement’s coil resistance (R_{coil}) may be calculated following this formula:

Your task is to show where this formula comes from, deriving it from Ohm’s Law and whatever other equations you may be familiar with for circuit analysis.
Hint: in both cases (decade box set to R_{1} and set to R_{2}), the voltage across the meter movement’s coil resistance is the same, the current through the meter movement is the same, and the power supply voltage is the same.
Don’t just sit there! Build something!! 
Learning to mathematically analyze circuits requires much study and practice. Typically, students practice by working through lots of sample problems and checking their answers against those provided by the textbook or the instructor. While this is good, there is a much better way.
You will learn much more by actually building and analyzing real circuits, letting your test equipment provide the “answers” instead of a book or another person. For successful circuitbuilding exercises, follow these steps:
 Carefully measure and record all component values prior to circuit construction.
 Draw the schematic diagram for the circuit to be analyzed.
 Carefully build this circuit on a breadboard or other convenient medium.
 Check the accuracy of the circuit’s construction, following each wire to each connection point, and verifying these elements onebyone on the diagram.
 Mathematically analyze the circuit, solving for all values of voltage, current, etc.
 Carefully measure those quantities, to verify the accuracy of your analysis.
 If there are any substantial errors (greater than a few percent), carefully check your circuit’s construction against the diagram, then carefully recalculate the values and remeasure.
Avoid very high and very low resistor values, to avoid measurement errors caused by meter “loading”. I recommend resistors between 1 kΩ and 100 kΩ, unless, of course, the purpose of the circuit is to illustrate the effects of meter loading!
One way you can save time and reduce the possibility of error is to begin with a very simple circuit and incrementally add components to increase its complexity after each analysis, rather than building a whole new circuit for each practice problem. Another timesaving technique is to reuse the same components in a variety of different circuit configurations. This way, you won’t have to measure any component’s value more than once.
We know that connecting a sensitive meter movement directly across the terminals of a substantial voltage source (such as a battery) is a Bad Thing. So, I want you to determine what other component(s) must be connected to the meter movement to limit the current through its coil, so that connecting the circuit to a 6volt battery results in the meter’s needle moving exactly to the fullscale position:

Determine the different range values of this multirange voltmeter:

All components on the printed circuit board are “surfacemount,” soldered onto the top surfaces of the copper traces. The switch (SW1) schematic diagram is shown to the immediate right of the circuit board, with resistor values shown below the circuit board.
Suppose you tried to measure the voltage at all three test points with an analog voltmeter having a sensitivity rating of 20 kΩ per volt, set on the 10 volt scale. How much voltage would it indicate at each test point? How much voltage should it ideally indicate at each test point?

Test point Ideal voltage Meter indication
TP1
TP2
TP3
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