Answer:
a. q = qm/√2 b. qm/√(2LC)
Explanation:
a. Charge on the capacitor
Let U₁ = energy in inductor and U₂ = energy in capacitor and U = total energy in circuit.
So, U₁ + U₂ = U.
Since the energy is shared equally between the capacitor and inductor, U₁= U₂,so
2U₂ = U
and U₂ = U/2
Now U₂ = q²/2C where q is the charge on the capacitor with capacitance C and
U = (qm)²/2C where qm is the maximum charge on the capacitor.
Since U₂ = U/2,
Substituting the values for U₂ and U, we have
q²/2C = [(qm)²/2C]/2
q² = (qm)²/2
taking square-root of both sides, we have
q = qm/√2
b. The current in the inductor
Since the energy in the capacitor equals the energy in the inductor,
1/2LI² = 1/2q²/C where L is the inductance of the inductor and I the current through it.
I² = q²/LC
taking square-root of both sides, we have
I = q/√LC
substituting the value of q from above, we have
I = qm/√2 ÷ √LC
I = qm/√(2LC)
