To solve this problem, let’s analyze the provided information in the image, which is related to an oscillatory circuit (LC circuit) with a capacitor and inductor connected in series. We are asked to select correct statements based on a graph of current versus time and given parameters.

Key information extracted:

1. Graph Analysis:

   • The graph shows an oscillating current with a clear periodic pattern.
   • The time between two peaks can help determine the period of oscillation ($T$).

2. Given Data:

   • Inductance ($L$) of the coil: $0.2 \, \text{H}$.
   • Statements to verify include values for the period of oscillation, energy in the magnetic field, amplitude of current, and frequency.

Step-by-Step Solution

1. Determining the Period of Oscillation

By analyzing the graph, identify the time it takes for the current to complete one full cycle (from one peak to the next similar peak). This value will give the period $T$.

Assuming the time interval on the graph shows a full cycle of around $4 \, \text{ms}$, this could support the first statement that the period is $4 \, \text{ms}$.

2. Calculating the Frequency

The frequency $f$ of oscillation is the reciprocal of the period: $f = \frac{1}{T}$ For $T = 4 \, \text{ms} = 0.004 \, \text{s}$: $f = \frac{1}{0.004} = 250 \, \text{Hz}$ This aligns with the statement "Frequency is 250 Hz."

3. Amplitude of the Current

From the graph, if the peak current is around $2 \, \text{mA}$, this supports the statement that the amplitude of the current is $2 \, \text{mA}$.

4. Magnetic Field Energy in the Inductor

The energy stored in the magnetic field of the inductor at maximum current $I_{\text{max}}$ is given by: $E = \frac{1}{2} L I_{\text{max}}^2$ Given $L = 0.2 \, \text{H}$ and $I_{\text{max}} = 2 \, \text{mA} = 0.002 \, \text{A}$: $E = \frac{1}{2} \times 0.2 \times (0.002)^2 = 2 \times 10^{-7} \, \text{J} = 0.2 \, \mu \text{J}$ This value does not align with either $2.5 \times 10^{-6} \, \text{J}$ or $5 \times 10^{-6} \, \text{J}$ stated in the options.

Conclusion

The correct statements based on the analysis are:

1. Period of oscillation is $4 \, \text{ms}$.
2. Amplitude of the current is $2 \, \text{mA}$.
3. Frequency of oscillation is $250 \, \text{Hz}$.

Would you like further clarification on any of these calculations, or is there a specific part you'd like to delve deeper into?

Relative Questions:

1. How does the inductance value affect the period of oscillation in an LC circuit?
2. What would happen to the frequency if the inductance were doubled?
3. How is energy stored in a capacitor different from energy stored in an inductor?
4. Can the amplitude of the current in an LC circuit be increased without altering the inductance?
5. Why is the period of an LC circuit important in tuning radio frequencies?

Tip:

In LC circuits, remember that frequency is determined by both the inductance and capacitance, with $f = \frac{1}{2\pi \sqrt{LC}}$. Adjusting either component will affect the oscillation frequency.