A circuit contains a capacitor and inductance each with negligible res...
A circuit contains a capacitor and inductance each with negligible res...
Introduction:
In this circuit, we have a capacitor and an inductance connected in series with negligible resistance. The capacitor is initially charged, and the charging battery is disconnected. We need to determine how the charge on the capacitor will change over time.
Explanation:
When the charging battery is disconnected, the capacitor and inductor form a closed circuit. The capacitor stores energy in the form of electric field, while the inductor stores energy in the form of a magnetic field.
1. Energy Transfer:
Initially, the capacitor is fully charged, and it holds a certain amount of energy. As the circuit is closed, the capacitor starts discharging, and its energy is transferred to the inductor. The electric field across the capacitor decreases, and the magnetic field in the inductor increases.
2. Inductor Behavior:
According to Faraday's law of electromagnetic induction, a changing magnetic field induces an electromotive force (emf) in the inductor. This emf opposes the change in current through the inductor. As a result, the inductor resists any change in current and acts as a source of energy.
3. Charging and Discharging Currents:
Initially, when the capacitor starts discharging, the current flows through the inductor and decreases over time. This decreasing current induces a back emf in the inductor, which opposes the current's decrease. Consequently, the charge on the capacitor decreases exponentially rather than linearly.
4. Exponential Decay:
The rate of change of charge on the capacitor is proportional to the current flowing through the inductor. Since the current decreases exponentially, the rate of change of charge on the capacitor also decreases exponentially. This leads to an exponential decay in the charge on the capacitor over time.
Conclusion:
Therefore, the charge on the capacitor will decrease exponentially over time when the charging battery is disconnected in a circuit containing a capacitor and inductance with negligible resistance.