In a direct current (D.C.) circuit, a capacitor behaves differently compared to its behavior in an alternating current (A.C.) circuit due to the nature of the applied voltage. Let's explore how a capacitor behaves in a D.C. circuit and some important concepts related to its behavior:
1. Charging a Capacitor:
When a capacitor is connected to a D.C. voltage source (such as a battery), it begins to charge. Initially, the capacitor acts like a short circuit as it has no charge stored on its plates. As time passes, electrons accumulate on one plate of the capacitor, while an equal number of electrons are drawn away from the other plate and accumulate on the positive terminal of the voltage source.
2. Charging Process:
The charging process follows an exponential curve. As the charge on the plates increases, the voltage across the capacitor also increases. The rate of charging decreases as the voltage across the capacitor approaches the voltage of the source. The time it takes for a capacitor to charge to approximately 63.2% of the source voltage is known as the time constant (τ) and is given by the formula τ = RC, where R is the resistance in the circuit and C is the capacitance of the capacitor.
3. Steady State:
In a D.C. circuit, if sufficient time has passed, the capacitor will become fully charged, and the voltage across the capacitor plates will become equal to the voltage of the source. At this point, the current through the circuit becomes negligible because the capacitor acts as an open circuit to D.C. Current only flows initially during the charging process.
4. Energy Storage:
When a capacitor is fully charged, it stores electric potential energy in the electric field between its plates. The energy stored in a capacitor is given by the formula E = 0.5 * C * V^2, where C is the capacitance and V is the voltage across the capacitor.
5. Discharging a Capacitor:
If the D.C. voltage source is removed or disconnected, the charged capacitor will begin to discharge. The stored energy in the capacitor will be released as it supplies current to the circuit. The discharge process also follows an exponential decay curve, and the time constant for discharging is again given by τ = RC.
In summary, in a D.C. circuit, a capacitor initially acts as a short circuit and gradually charges up. Once fully charged, it prevents further current flow, acting as an open circuit. When the voltage source is removed, the capacitor discharges, releasing the stored energy. The behavior of a capacitor in a D.C. circuit is crucial for various applications, such as energy storage, filtering, and timing circuits.