What happens when a capacitor is connected to a battery?

When a capacitor is connected to a battery, the following process occurs:
1. Charging the Capacitor:
o Initially, when the capacitor is uncharged, it behaves like a short circuit and allows current to flow from the battery.
o As the current flows, the capacitor starts accumulating charge on its plates. The battery supplies the charge, causing one plate of the capacitor to become positively charged and the other negatively charged.
2. Potential Difference Across the Capacitor:
o As charge builds up on the plates, the potential difference (voltage) across the plates of the capacitor increases.
o The capacitor continues to charge until the voltage across its plates equals the voltage of the battery. At this point, the current flow decreases and eventually stops.
3. Capacitor Fully Charged:
o Once the voltage across the capacitor is equal to the battery voltage, the capacitor is said to be fully charged.
o No more current flows through the circuit, and the capacitor holds the charge. The battery no longer needs to supply current.
4. Energy Stored in the Capacitor:
o The energy stored in the capacitor is given by the formula: E=12CV2E = \frac{1}{2} C V^2 where:
 EE is the energy stored in the capacitor,
 CC is the capacitance of the capacitor,
 VV is the voltage across the capacitor (which is equal to the battery voltage).
5. Steady-State Condition:
o In the steady state, once the capacitor is fully charged, it acts like an open circuit, and no more current flows. The battery maintains a constant potential difference across the capacitor.
Final Answer:
When a capacitor is connected to a battery, it charges up, storing energy in the form of an electric field between its plates. Once the capacitor is fully charged, the current flow stops, and the capacitor holds the charge at a voltage equal to the battery's voltage.