IF the current is doubled, the deflection is also doubled in

Options

A. a tangent galvanometer
B. a moving coil galvanometer
C. Both (a) and (b)
D. None of the above

Answer

To solve the question, we need to analyze the relationship between current and deflection in both a tangent galvanometer and a moving coil galvanometer.

### Step-by-Step Solution:

1. **Understanding the Tangent Galvanometer:**
- The tangent galvanometer operates based on the principle that the magnetic field produced by a current-carrying coil is proportional to the tangent of the angle of deflection (θ) from the magnetic meridian.
- The relationship can be expressed as:
\[ I = k \tan(\theta) \]
- Where \( I \) is the current, \( k \) is a constant, and \( \theta \) is the angle of deflection.

2. **Analyzing the Effect of Doubling the Current:**
- If the current is doubled (i.e., \( I' = 2I \)), we can substitute this into the equation:
\[ 2I = k \tan(\theta') \]
- This implies:
\[ \tan(\theta') = 2 \tan(\theta) \]
- Using the tangent double angle identity, we know that:
\[ \tan(2\theta) \neq 2 \tan(\theta) \]
- Therefore, the deflection will not simply double; it will change according to the tangent function, leading to a deflection that is not equal to \( 2\theta \).

3. **Understanding the Moving Coil Galvanometer:**
- The moving coil galvanometer operates based on a different principle, where the current is directly proportional to the angle of deflection:
\[ I = \frac{k}{nAB} \theta \]
- Here, \( n \) is the number of turns, \( A \) is the area of the coil, and \( B \) is the magnetic field.
- In this case, if the current is doubled:
\[ 2I = \frac{k}{nAB} \theta' \]
- This implies:
\[ \theta' = 2\theta \]
- Thus, the deflection will indeed double when the current is doubled.

4. **Conclusion:**
- From the analysis, we find that when the current is doubled, the deflection is doubled in a moving coil galvanometer but not in a tangent galvanometer.
- Therefore, the correct answer to the question is **Option B: a moving coil galvanometer**.