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.
Best Answer
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.