Final answer:
The value of 'n' for converting a galvanometer to an ammeter is derived from the shunt resistor formula, considering the galvanometer's full scale deflection and the desired total current range for the ammeter.
Step-by-step explanation:
To find the value of n in the resistance 2n/2492 that allows a galvanometer to function as an ammeter with a full scale deflection of 0-1.5A, we must use the concept of shunt resistance. A galvanometer can be converted into an ammeter by connecting it in parallel with a known resistor (shunt), which allows for a larger current to be measured. The galvanometer gives full scale deflection with 0.006A, and it becomes a voltmeter with a 4990 ohm resistor for a 0-30V range. Since the galvanometer has a full scale deflection at 0.006A, the shunt resistor used to turn it into an ammeter must allow 1.5A to pass through the parallel combination of the galvanometer and the shunt, while only allowing 0.006A through the galvanometer itself.
The formula for finding the shunt resistor (Rs) is given by Rs = (Ig x Rg) / (I - Ig), where Ig is the current through the galvanometer for full scale deflection, Rg is the resistance of the galvanometer, and I is the total current. We are looking for Rs in the form 2n/2492 ohms. We will equate this formula with the given expression for Rs and solve for n.