Two galvanometers A and B require 3 mA and 6 mA respectively, to produce the same deflection of 10 divisions. Then,

Options

A. A is more sensitive than B
B. B is more sensitive than A
C. A and B are equally sensitive
D. sensitiveness of B is twice that of A

Answer

To determine which galvanometer, A or B, is more sensitive, we can follow these steps:

### Step 1: Understand Sensitivity
Sensitivity of a galvanometer is defined as the amount of current required to produce a certain deflection. It is inversely proportional to the maximum current that can be passed through the galvanometer for a given deflection.

### Step 2: Identify Given Values
From the problem, we know:
- Galvanometer A requires 3 mA to produce a deflection of 10 divisions.
- Galvanometer B requires 6 mA to produce the same deflection of 10 divisions.

### Step 3: Write the Sensitivity Relationship
Let the sensitivity of galvanometer A be \( S_A \) and that of galvanometer B be \( S_B \). According to the definition of sensitivity:
\[ S_A \propto \frac{1}{I_A} \quad \text{and} \quad S_B \propto \frac{1}{I_B} \]
where \( I_A \) and \( I_B \) are the currents required for the same deflection.

### Step 4: Calculate the Sensitivity Ratio
We can express the ratio of sensitivities as:
\[ \frac{S_A}{S_B} = \frac{I_B}{I_A} \]
Substituting the values we have:
\[ \frac{S_A}{S_B} = \frac{6 \, \text{mA}}{3 \, \text{mA}} = 2 \]

### Step 5: Interpret the Result
This means:
\[ S_A = 2 \times S_B \]
This indicates that galvanometer A is more sensitive than galvanometer B.

### Conclusion
Thus, galvanometer A is the more sensitive galvanometer.

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