If in a moving coil galvanometer, a current I produces a deflection `theta`, then

Answer

To derive the relationship between the current \( I \) and the deflection \( \theta \) in a moving coil galvanometer, we can follow these steps:

### Step 1: Understanding the Concept
In a moving coil galvanometer, the deflection \( \theta \) produced by a current \( I \) is related to the sensitivity of the galvanometer. Sensitivity is defined as the amount of deflection per unit current.

### Step 2: Define Sensitivity
Let’s denote the sensitivity of the galvanometer as \( S \). The sensitivity can be expressed as:
\[ S = \frac{\theta}{I} \]
where \( \theta \) is the deflection in radians and \( I \) is the current.

### Step 3: Rearranging the Equation
From the definition of sensitivity, we can rearrange the equation to express current \( I \) in terms of deflection \( \theta \):
\[ I = \frac{\theta}{S} \]

### Step 4: Conclusion
This shows that the current \( I \) is directly proportional to the deflection \( \theta \):
\[ I \propto \theta \]
Thus, we can conclude that:
\[ I = k \cdot \theta \]
where \( k \) is a constant that depends on the sensitivity of the galvanometer.

### Step 5: Units of Measurement
It is important to note that for this relationship to hold, \( \theta \) should be measured in radians. If \( \theta \) is measured in degrees, the relationship would need to include a conversion factor.

### Final Relation
Therefore, the final relationship can be summarized as:
\[ I = k \cdot \theta \quad \text{(where } \theta \text{ is in radians)} \]