When a current of 1A passes through a tangent galvanometer, angle of defection is deg 60. When current is reduced to 0.5A, then the new angle of deflection will be

Options

A. `deg30`
B. `deg45`
C. `deg60`
D. `deg15`

Answer

To solve the problem, we need to understand the relationship between the current passing through the tangent galvanometer and the angle of deflection. The angle of deflection (θ) is directly proportional to the current (I) passing through the galvanometer.

### Step-by-Step Solution:

1. **Understanding the Proportionality**:
The angle of deflection (θ) is directly proportional to the current (I). This can be expressed mathematically as:
\[ \theta \propto I \]
This means if the current changes, the angle of deflection will change in the same ratio.

2. **Setting Up the Ratios**:
Let’s denote:
- \( \theta_1 = 60^\circ \) (angle of deflection when current \( I_1 = 1A \))
- \( \theta_2 \) = angle of deflection when current \( I_2 = 0.5A \)

From the proportionality, we can write:
\[ \frac{\theta_1}{\theta_2} = \frac{I_1}{I_2} \]

3. **Substituting Known Values**:
Substitute the known values into the equation:
\[ \frac{60^\circ}{\theta_2} = \frac{1A}{0.5A} \]
Simplifying the right side gives:
\[ \frac{60^\circ}{\theta_2} = 2 \]

4. **Cross-Multiplying to Solve for \( \theta_2 \)**:
Cross-multiply to find \( \theta_2 \):
\[ 60^\circ = 2 \cdot \theta_2 \]
Now, divide both sides by 2:
\[ \theta_2 = \frac{60^\circ}{2} = 30^\circ \]

5. **Conclusion**:
Therefore, when the current is reduced to 0.5A, the new angle of deflection will be:
\[ \theta_2 = 30^\circ \]

### Final Answer:
The new angle of deflection when the current is reduced to 0.5A is \( \boxed{30^\circ} \).