An LC circuit oscillating at natural frequency conssts of an inductor of inductance 30 m H and a capacitor of capacitance 60`muF `. The maximum value of instantaneous charge on capacitor in the circuit is 200 `mu C ` . If I is the current in the circuit then answer the following :
(i) What is the value of `(dI)/(dt)` when charge is 150 `mu`C?
(ii) Calculate the value of I when charge is 200 `muC` .
(iii) Find the maximum value of I.
(iv) For what value of q I is half of its maximum value ?

Explanation

To solve the problem step-by-step, let's break it down into the parts as requested.

### Given Data:
- Inductance \( L = 30 \, \text{mH} = 30 \times 10^{-3} \, \text{H} \)
- Capacitance \( C = 60 \, \mu\text{F} = 60 \times 10^{-6} \, \text{F} \)
- Maximum charge on the capacitor \( Q_0 = 200 \, \mu\text{C} = 200 \times 10^{-6} \, \text{C} \)

### Natural Frequency Calculation:
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