In a moving coil galvanometer, the deflection of the coil `theta` is related to the electric current i by the relation

Options

A. `i prop tan theta`
B. `i prop theta`
C. `i prop ( theta)^2`
D. `i prop (sqrt theta)`

Explanation

To solve the problem regarding the relationship between the deflection of the coil (θ) and the electric current (I) in a moving coil galvanometer, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Galvanometer**:
A moving coil galvanometer is an instrument used to measure small electric currents. It consists of a coil of wire that is suspended in a magnetic field. When an electric current passes through the coil, it experiences a torque due to the magnetic field, which causes it to rotate and produce a deflection (θ) on a scale.

2. **Deflection and Current Relationship**:
The deflection of the coil (θ) is directly related to the electric current (I) flowing through it. This relationship can be expressed mathematically as:
\[ I \propto \theta \]
This means that the current (I) is directly proportional to the angle of deflection (θ).

3. **Linear Proportionality**:
The linear relationship indicates that if the current increases, the deflection will also increase proportionally. This is crucial for the sensitivity of the galvanometer, as it allows for accurate measurements of small currents.

4. **Conclusion**:
Therefore, we can conclude that in a moving coil galvanometer, the deflection (θ) is linearly proportional to the electric current (I). The relationship can be summarized as:
\[ I = k \cdot \theta \]
where \( k \) is a constant of proportionality that depends on the design of the galvanometer.