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Hi,
Rm is meter internal resistance.
Rs is series resistor used for the test.
Vs is the voltage of the power supply used for the test.
Vm is voltage across the meter for the test.
I guess you need to know Rshunt, the resistance needed for the shunt.
For two parallel resistors, the total resistance RT is:
RT=R1*R2/(R1+R2)
and with R1=Rm and R2=Rshunt, we have:
RT=Rm*Rshunt/(Rm+Rshunt)
and the voltage across that resistance RT is simply:
v=i*RT
solving for RT now we get:
RT=v/i
and that's the total resistance you need. Since we know the resistance Rm from the test, we can calculate RT by solving the parallel resistance formula for Rshunt:
Rshunt=(Rm*RT)/(Rm-RT)
Now when the max current flows through the circuit the meter pointer will point to the max reading.
It is also customary to test this after you've calculated the shunt resistance and connected everything. Using a test current, see that the meter reads correctly using another current meter for the test or some other means of verifying the current such as with a known fixed resistance. You may then want to adjust Rshunt a little with another parallel or series resistance.
You also have to think about what happens to the shunt resistor as the current flows though it. If it heats up significantly you may have to increase the power handling ability of the resistance. The formula for power is:
P=R*i^2
or:
P=v*i
and for a shunt you should really use a resistor that can handle a lot more power than is needed, say 5 times or more. That helps to ensure it does not heat up much. If it heats up too much, it will skew the readings.
I had used a piece of chromium wire one time for a shunt. When that heats up the resistance changes. It worked ok though because I never had to go too high on the current. It was easy to adjust because I used a bolt and clip to allow sliding up and down the wire a little for adjustment so I could get it pretty accurate.
