In a tangent galvanometer, when a current of `10mA` is passed, the deflection is `31^@`. By what percentage, the current has to be increased, so at to produce a deflection of `42^@`?

Explanation

To solve the problem, we need to determine the percentage increase in current required to change the deflection in a tangent galvanometer from \(31^\circ\) to \(42^\circ\).

### Step-by-Step Solution:

1. **Understand the relationship between current and deflection**:
In a tangent galvanometer, the current \(I\) is proportional to the tangent of the angle of deflection \(\theta\):
\[
I \propto \tan(\theta)
...