A galvanometer needle deflects full scale for a 60.0-\mu A current
The correct answer and explanation is:
To convert a galvanometer into an ammeter that can measure larger currents, a shunt resistor is typically added in parallel with the galvanometer. The shunt resistor bypasses some of the current to prevent the needle from deflecting too much.
Explanation:
- Galvanometer Sensitivity: A galvanometer is an instrument that can detect small currents. The sensitivity of a galvanometer is determined by the amount of current required to deflect the needle to full scale. In this case, the full-scale deflection happens when the current is 60.0 μA.
- Shunt Resistor Concept: The shunt resistor is designed to carry the majority of the current, ensuring that only a small fraction flows through the galvanometer. By doing this, the galvanometer measures a much smaller current than the total current being passed through the system. The purpose is to prevent the galvanometer from being damaged by larger currents while still allowing it to function as a measurement device.
- Current Division: When a current flows through a parallel combination of the galvanometer and the shunt resistor, the total current divides between them. The ratio of the currents is determined by the resistances of the galvanometer and the shunt. Since the galvanometer is designed to deflect fully for a current of 60.0 μA, it will only measure that amount of current in the circuit, and the rest will flow through the shunt.
- Calculation of Shunt Resistor: To convert the galvanometer to an ammeter capable of measuring larger currents, one would calculate the value of the shunt resistor needed. Suppose the total current to be measured is I_total. The current through the galvanometer (I_g) should be 60.0 μA at full-scale deflection. The shunt resistance R_s is calculated using Ohm’s law, with the relation between the current, voltage, and resistance.
- Final Outcome: By adding an appropriately calculated shunt resistor, the galvanometer can be used as an ammeter to measure currents much larger than 60.0 μA without exceeding its maximum deflection capacity.
Thus, the current division principle and the addition of a shunt resistor enable a galvanometer to measure larger currents by diverting most of the current away from the sensitive part of the instrument.