Ammeter Shunt Resistance and Connection Explained

This question involves analyzing an assertion and a reason concerning the shunt resistor used in an ammeter.

Analysis of Assertion (A): Shunt Resistance is Low

An ammeter measures electric current. To measure currents exceeding the capacity of its internal galvanometer, a low-resistance resistor known as a shunt is connected in parallel with the galvanometer. The primary function of the shunt is to bypass the major portion of the total current, allowing only a small, measurable fraction to pass through the sensitive galvanometer mechanism.

In a parallel circuit configuration, current divides inversely proportional to the resistance in each branch. The voltage drop across parallel components is identical. Thus, if the shunt resistance ($R_{shunt}$) and the galvanometer resistance ($R_{gal}$) are in parallel, the voltage drop is the same:

$$ V = I_{shunt} \times R_{shunt} = I_{gal} \times R_{gal} $$

For the shunt to divert most of the current (i.e., $I_{shunt} \gg I_{gal}$), the shunt's resistance must be considerably less than the galvanometer's resistance ($R_{shunt} \ll R_{gal}$). This setup ensures the galvanometer receives only a fraction of the total current, extending the ammeter's measurement range safely and accurately.

Therefore, Assertion (A) is factually true.

Analysis of Reason (R): Shunt Connection Method

The shunt resistor is specifically designed and connected in parallel with the galvanometer. This arrangement is crucial for its function of diverting excess current.

Connecting the shunt in series with the ammeter would increase the overall resistance of the ammeter. This added resistance would impede the flow of current in the main circuit, leading to inaccurate readings of the actual circuit current. An ammeter ideally should have negligible resistance to avoid disturbing the circuit it is measuring. A series connection would counteract the purpose of extending the current range via shunting.

Therefore, Reason (R) is false.

Final Conclusion

Based on the analysis, Assertion (A) is true, and Reason (R) is false. This corresponds to the option stating 'A is true, R is false'.