[johnconnor92]

The answer for R1 is 112.5 Ohm. Why?

[Stonebridge]

(Original post by johnconnor92)

The answer for R1 is 112.5 Ohm. Why?

Your method is incorrect.
The current through the galvo is indeed 0.2mA (200uA) but the current through the shunt resistors is the main circuit current to be measured (1mA for the connection at A) minus the current in the galvo.
That is, 0.8mA

You have made the same mistake in each of the 3 cases. Correct this and you should get the correct answer.

[johnconnor92]

(Original post by Stonebridge)
Your method is incorrect.
The current through the galvo is indeed 0.2mA (200uA) but the current through the shunt resistors is the main circuit current to be measured (1mA for the connection at A) minus the current in the galvo.
That is, 0.8mA

You have made the same mistake in each of the 3 cases. Correct this and you should get the correct answer.

I can't thank you enough! By the way, I don't really understand the purpose of the "to make a multi-range current meter" in the question. In all 3 situations the ammeter operates under 0.2mA situation instead being put in different currents to measure a different scale. So is this current meter which we're considering actually multi-range? What exactly is the multi-range meant to mean over here?

Thank you!

[Stonebridge]

Multi range means the same basic galvo mechanism (usually moving coil meter) can be used to measure different currents.
The galvo mechanism itelf is designed such that it is very sensitive. The pointer will move to full scale deflection for a current of 0.2mA. That can't be changed. It is dependent on the design.
If you want to place this meter in a circuit to measure a current up to, say, 10mA you have to use "shunt" resistors to divert the excess current leaving only 0.2mA in the movement.
The value of the shunt resistors is calculated as in the example above. The current in the meter movement is always 0.2mA and the current in the shunt is the current to be measured minus the current in the galvo. (In this case the shunt current is 9.8mA)
It then becomes a relatively simple circuit problem to calculate the value of the shunt required.
In this case it's a bit more complicated because the 3 resistors combination used needs to provide 3 different ranges (3 different shunt currents) depending on how they are connected. The connections turn out to be a mixture of series and parallel.
So yes, the meter mechanism always takes 0.2mA here, but the meter itself (mechanism plus shunt) takes any current you wish to measure depending on the internal shunt used.