Instuments based on tangent law are most accurate when the defiection is

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. Any angle

Answer

To solve the question regarding the accuracy of instruments based on the tangent law, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Tangent Law**: The tangent law states that the tangent of the angle of deflection (θ) in a galvanometer is proportional to the ratio of the vertical magnetic field (Bv) to the horizontal magnetic field (Bh). This can be expressed as:
\[ \tan \theta = \frac{B_v}{B_h} \]

2. **Identify Conditions for Accuracy**: For the instrument to provide the most accurate readings, the vertical and horizontal magnetic fields should be equal. This means:
\[ B_v = B_h \]

3. **Set Up the Equation**: If \( B_v = B_h \), then we can substitute this into our tangent law equation:
\[ \tan \theta = \frac{B_h}{B_h} = 1 \]

4. **Find the Angle**: The angle θ for which the tangent is equal to 1 is:
\[ \tan \theta = 1 \implies \theta = 45^\circ \]

5. **Conclusion**: Therefore, the deflection is most accurate when the angle of deflection is:
\[ \theta = 45^\circ \]

### Final Answer:
The instruments based on tangent law are most accurate when the deflection is **45 degrees**.

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