Answer:
The maximum charge on the capacitor in the LC circuit is Q = I0 * sqrt(C0 * L0).
Step-by-step explanation:
To calculate the maximum charge on the capacitor in an LC circuit, we can use the formula for the charge on a capacitor:
Q = C0 * V
Where:
Q = Maximum charge on the capacitor
C0 = Capacitance of the capacitor
V = Maximum voltage across the capacitor
In an LC circuit, the maximum voltage across the capacitor occurs when the maximum current flows through the inductor. At this point, all the energy is stored in the magnetic field of the inductor, and there is no energy stored in the electric field of the capacitor. The energy oscillates between the inductor and the capacitor as the LC circuit oscillates.
The maximum current, I0, in an LC circuit is given by:
I0 = V / sqrt(L0 / C0)
Where:
I0 = Maximum current in the LC circuit
V = Maximum voltage across the capacitor
L0 = Inductance of the inductor
C0 = Capacitance of the capacitor
Rearranging the formula for V:
V = I0 * sqrt(L0 / C0)
Now, we can calculate the maximum charge on the capacitor, Q:
Q = C0 * V
Q = C0 * (I0 * sqrt(L0 / C0))
Simplifying:
Q = I0 * sqrt(C0 * L0)
Therefore, the maximum charge on the capacitor in the LC circuit is Q = I0 * sqrt(C0 * L0).