An inductor of inductance 2.0 mH is connected across a charged capacitor of capacitance 5.0 µF and the resulting LC circuit is set oscillating at its natural frequency. Let Q denote the instantaneous charge on the capacitor and I the current in the circuit. It is found that the maximum value of Q is 200 µC.
1. When Q = 100 µC, what is the value of |dI/dt|?
2. When Q = 200 µC, what is the value of I?
3. Find the maximum value of I.
4 When I is equal to one-half its maximum value, what is the value of |Q|?
Nuclei of a radioactive element A are being produced at a constant rate α. The element has a decay constant λ. At time t = 0, there are N0 nuclei of the element.
5. Calculate the number N of nuclei of A at time t.
6. If α = 2N0λ, calculate the number of nuclei of A after one half life of A, and also the limiting value of N as t → ∞.
Source 1998 JEE