(A) : If a galvanometer is converted into an ammeter and a milliammeter then the shunt resistance of ammeter is lower than that of milliammeter.
(R) : In Ammeter the current through shunt is less than that of galvonameter as compared to the case of milliammeter.

Options

A. Both 'A' and 'R' are true and 'R' is the correct explanation of 'A'.
B. Both 'A' and 'R' are true and 'R' is not the correct explanation of 'A'
C. 'A' is true and 'R' is false
D. 'A' is false and 'R' is false

Answer

To solve the question, we need to analyze the assertion (A) and the reason (R) given:

**Assertion (A)**: If a galvanometer is converted into an ammeter and a milliammeter, then the shunt resistance of the ammeter is lower than that of the milliammeter.

**Reason (R)**: In an ammeter, the current through the shunt is less than that of the galvanometer as compared to the case of the milliammeter.

### Step-by-Step Solution:

1. **Understanding the Concept of Shunt Resistor**:
- A galvanometer can be converted into an ammeter or a milliammeter by connecting a shunt resistor in parallel with it. The shunt allows most of the current to bypass the galvanometer, protecting it from high currents.

2. **Current Measurement**:
- An ammeter is designed to measure larger currents, while a milliammeter measures smaller currents (in milliamperes). Therefore, the range of an ammeter is greater than that of a milliammeter.

3. **Shunt Resistance Relation**:
- The shunt resistance (S) is inversely proportional to the range of current to be measured. This means that if we want to measure higher currents (as in an ammeter), we need a lower shunt resistance. Conversely, for measuring lower currents (as in a milliammeter), we need a higher shunt resistance.

4. **Mathematical Relation**:
- When we derive the relationship for the current through the galvanometer (Ig) and the total current (I), we find:
\[ I = \frac{I_g \cdot G}{S + G} \]
where G is the galvanometer's resistance. From this equation, we can see that as the current (I) increases (for an ammeter), the shunt resistance (S) must decrease.

5. **Analyzing the Assertion**:
- Since the ammeter measures higher currents, it requires a lower shunt resistance compared to the milliammeter, which is consistent with the assertion (A).

6. **Analyzing the Reason**:
- The reason (R) states that in an ammeter, the current through the shunt is less than that of the galvanometer. This is incorrect because, in an ammeter, the current through the shunt is actually more than that through the galvanometer due to the lower shunt resistance.

7. **Conclusion**:
- The assertion (A) is true, while the reason (R) is false. Therefore, the correct answer is that the assertion is true and the reason is false.

### Final Answer:
- Assertion (A) is true, and Reason (R) is false.