A tangent galvanometer is connected directly to an ideal battery. If the number of turns in the coil is doubled, the deflection will

Options

A. increase
B. decrease
C. remain unchanged
D. either increase or decrease

Answer

To solve the problem regarding the effect of doubling the number of turns in a tangent galvanometer on the deflection, we can follow these steps:

### Step 1: Understand the relationship in a tangent galvanometer
A tangent galvanometer operates based on the principle that the magnetic field produced by the coil of wire is proportional to the current flowing through it and the number of turns in the coil. The relationship can be expressed as:

\[ I = k \tan(\theta) \]

where:
- \( I \) is the current through the coil,
- \( k \) is a constant that depends on the galvanometer's construction,
- \( \theta \) is the angle of deflection.

### Step 2: Analyze the effect of doubling the number of turns
When the number of turns in the coil is doubled, we need to consider how this affects the current and the magnetic field produced. The magnetic field \( B \) at the center of the coil can be expressed as:

\[ B = \frac{\mu_0 n I}{2r} \]

where:
- \( \mu_0 \) is the permeability of free space,
- \( n \) is the number of turns,
- \( I \) is the current,
- \( r \) is the radius of the coil.

If we double the number of turns (\( n \rightarrow 2n \)), the magnetic field becomes:

\[ B' = \frac{\mu_0 (2n) I}{2r} = \frac{\mu_0 n I}{r} = 2B \]

### Step 3: Determine the effect on deflection
However, the current \( I \) is supplied by an ideal battery, which means it remains constant regardless of the number of turns in the coil. Therefore, the magnetic field strength increases, but since the current does not change, the angle of deflection \( \theta \) is determined by the balance of the magnetic field and the earth's magnetic field.

The relationship \( I = k \tan(\theta) \) indicates that the deflection angle \( \theta \) depends on the current \( I \), which remains unchanged. Thus, the deflection angle \( \theta \) will also remain unchanged.

### Conclusion
Therefore, if the number of turns in the coil is doubled, the deflection will remain unchanged.

**Final Answer: C remains unchanged.**

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