31.11
Consider an LC circuit connecting a charged capacitor with an inductor. When the circuit is closed, the capacitor discharges through the inductor, transferring energy from the electric field to the magnetic field.
The current continues to flow towards the discharged capacitor as the inductor resists a change in current through it. This continued current charges the capacitor with opposite polarity, increasing the capacitor's electric field while decreasing the inductor's magnetic field.
The charged capacitor again discharges, converting electrical energy to magnetic energy. On re-charging the capacitor, energy flows back to the capacitor, and the initial state of the circuit is restored.
If there is no energy dissipation, the charges on the capacitor continue to change polarity indefinitely, called electrical oscillations.
Here, the charge on the capacitor and the current through the inductor varies sinusoidally with time.
Initially, when the charge on the capacitor is at maximum, the current in the inductor is zero. As time progresses, the charge becomes zero on the capacitor, and the current becomes maximum in the inductor. With time, the process reverses and repeats itself.
理想化的 LC 电路可以通过在电场和磁场之间转移电路中存储的能量而在没有任何电动势源的情况下振荡。 在这样的 LC 电路中,如果在开关闭合之前电容器包含电荷 q,则电路的所有能量最初存储在电容器的电场中 。 该能量由下式给出
当开关闭合时,电容器开始放电,在电路中产生电流。 电流反过来在电感器中产生…