Which of the following has higher resistance - milliammeter or ammeter? The question is the same as the heading - Which of the following has higher resistance - milliammeter or ammeter ?
Now my teacher's and my answers don't match.
It is assumed that the spring constant / torsional constant is same for both cases and all other physical constants except the resistance (and/or the specific resistance)  (flux, number of loops etc) of the ammeters are same. 
The two answers - 


*

*Milliammeter has lower resistance. Consider a wire carrying 10mA , if we attach an ammeter or a milliammeter  to it, the deflection of the ammeter will be much lower than the deflection of milliammeter. 


$\phi = (\frac{NAB}{k})\frac{V}{R}$
Since, milliammeter is more sensitive, the resistance is lower in milliammeter.


*

*For a constant voltage , the current through a milliammeter must be lower (in the order of milliamperes) but the current through a ammeter would be higher (in the order of amperes) thus the resistance in milliammeter will be higher.

 A: Answer #1 uses an invalid argument.  The conclusion that a milliammeter has lower resistance does not follow from the observed fact that the milliammeter has higher deflection.
Consider that some work must be done to deflect the needle.  Because of the assumption that the physical constants are the same, the work is equal for equal deflection.  Also remember that electrical power is I2R.  Since for the same deflection, the current is lower in the milliammeter, the effective resistance must be higher.
But this argument too is in error, because power != force of deflection.  Rather power is rate of work per time.  The relationship between force and current depends on magnetic field strength, and the connection between that and resistance is very tenuous.
Finally, your question says that the two meters are physically identical in every way.  While implies that the resistance is also identical.  You can't vary resistance by changing the gage of wire, for example, without also affecting the spring constant.
A: I don't have the facilities at hand to draw a circuit diagram, so I'll just describe it.  A conventional electromechanical current meter consists of these parts:


*

*M1 -- the meter movement itself (which we idealize as having zero internal resistance).

*R1 -- the innate resistance of the meter movement.  This is packaged inside the meter, but we can consider it to behave like a separate discrete resistor.

*R2 -- the external (to the meter movement) series resistor.  This is not absolutely necessary, but most designs have one.

*R3 -- the "shunt" resistor


M1, R1, and R2 are wired "in series".  And, for our purposes, we can consider R1 and R2 as a single resistor.  R3 is wired "in parallel" with the other three.
So assume that M1's needle registers full scale when 100ma is running through the meter -- this means that M1 is a "100ma movement".  Also assume that R1+R2 sums to 10 ohms.  This means that if we apply 1 volt to the meter (with R3 not present), 100ma will flow through the 10 ohms of resistance, and the meter will register full scale.
Now, suppose we want a meter that reads 10A full scale.  This means that when 10A is flowing through the meter assembly, 100ma must be flowing through the meter proper, while 9.9A flows through the "shunt" resistor.  The easy way to figure it is that 1V will produce a full scale reading on the meter, so we need a total resistance that will pass 10A at 1V.  Ie, the total resistance of the meter assembly must be 0.1 ohm, and 9.9A must flow through the shunt resistor at 1V.  So the shunt resistor would be (1.0 / 9.9) or 0.10101... ohms.
So, clearly the milliammeter has a higher resistance (100 ohm) than the ammeter (0.1 ohm).
A: Let us assume that the instrument design is the same as in http://en.wikipedia.org/wiki/Ammeter (the words  "spring constant / torsional constant",  "flux, number of loops" seem to imply that). Then, to get the same deflection for lower current you need more loops, therefore, the resistance of the milliammeter will be higher. It looks like the same conclusion is correct for designs with shunts, but the analysis is trickier.
A: The ideal current meter has 0 resistance, which means it drops 0 volts regardless of how much current you put thru it.  Real current meters have some resistance.  One measure of quality of a current meter is how low this resistance is, with lower being better since that disturbs the system being measured less.
At one level, your distinction between "ammeter" and "milliammeter" is meaningless.  They are both current meters, just reading out the measured value in different units.  This is like asking which is longer, a foot tape measure or a meter tape measure.
However, we can assume or guess from the labels that the milliammeter is intended to measure lower currents than the ammeter.  Since the electronics for amplifying and converting the small voltage across the sense resistor are the same at the same level of quality, the milliammeter will have a larger sense resistor.  This is needed to generate the same voltage at milliamp levels that the sense resistor in the ammeter does at ampere levels.
Again, there is no inherent rule that all current meters intended for milliamp-level currents have larger sense resistors than those intended for ampere-level currents, but that will generally be the case when the two meters have about the same level of technology and price.  There are also other ways of measuring current than measuring the voltage drop across a sense resistor, but that is by far the most common for a off the shelf "ammeter".
