The value of current at half power points is -

A. `sqrt(2)I_(m)`
B. `I_(m)//sqrt(2)`
C. `I_(m)//2`
D. `2I_(m)`

Options

A. `sqrt(2)I_(m)`
B. `I_(m)//sqrt(2)`
C. `I_(m)//2`
D. `2I_(m)`

Answer

To find the value of current at half power points, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Half Power Points**:
- The half power points are the frequencies at which the power is half of the maximum power at resonance.

2. **Define Power at Resonance**:
- At resonance, the current is maximum, denoted as \( I_m \). The power at resonance \( P \) can be expressed as:
\[ P = I_m^2 \cdot R \]
where \( R \) is the resistance.

3. **Determine Half Power**:
- The half power point means that the power at these points (let's call them points B and C) is:
\[ P_B = P_C = \frac{P}{2} = \frac{I_m^2 \cdot R}{2} \]

4. **Express Power at Half Power Points**:
- The power at points B and C can also be expressed as:
\[ P_B = I^2 \cdot R \]
where \( I \) is the current at half power points.

5. **Set Up the Equation**:
- Since the power at B (or C) is half of the maximum power:
\[ I^2 \cdot R = \frac{I_m^2 \cdot R}{2} \]

6. **Cancel Resistance**:
- We can cancel \( R \) from both sides (assuming \( R \neq 0 \)):
\[ I^2 = \frac{I_m^2}{2} \]

7. **Solve for Current \( I \)**:
- Taking the square root of both sides gives:
\[ I = \frac{I_m}{\sqrt{2}} \]

8. **Conclusion**:
- Therefore, the value of current at half power points is:
\[ I = \frac{I_m}{\sqrt{2}} \]
- The correct answer is option B: \( \frac{I_m}{\sqrt{2}} \).