What happens when a capacitor is connected to a DC/AC source?

This is a fundamental concept in electronics. The behavior of a capacitor is completely different when connected to a DC source versus an AC source.

Here’s a detailed breakdown of what happens in each case.

1. Connecting a Capacitor to a DC Source (like a Battery)

When you first connect a capacitor to a DC voltage source, a very specific sequence of events occurs.

What Happens:

1. Initial Rush of Current (Charging Phase):

   • At the exact moment of connection (t = 0), the capacitor acts like a short circuit. The voltage across its plates is zero.

   • Because there's a voltage difference between the source and the capacitor, electrons rush from the negative terminal of the source onto one plate of the capacitor.

   • Simultaneously, electrons are pulled from the opposite plate toward the positive terminal of the source. This creates a net positive charge on that plate.

   • This movement of electrons is an electric current, which is very high initially.

2. Build-up of Charge and Voltage:

   • As charge (electrons) builds up on the plates, they start to repel any new electrons trying to join them.

   • The voltage across the capacitor's plates (V_c) begins to rise, opposing the voltage of the source (V_s).

3. The Steady State (Fully Charged):

   • When the voltage across the capacitor (V_c) becomes equal to the source voltage (V_s), the pushing force from the source and the opposing force from the capacitor are balanced.

   • At this point, the current stops completely.

   • The capacitor now has a fixed amount of charge (Q) stored on its plates, given by the formula: Q = C × V, where C is the capacitance.

   • In this state, the capacitor behaves like an open circuit. It blocks any further DC current.

Key Takeaway for DC:

A capacitor blocks steady-state DC current. It allows a brief current only during the charging period until it becomes fully charged.

Analogy: Imagine blowing up a balloon. The air you blow in is the current. At first, it's easy (high current). As the balloon fills, it gets harder to blow more air in (current decreases). When the pressure inside equals the pressure from your lungs, no more air flows (zero current), and the balloon is fully charged.

2. Connecting a Capacitor to an AC Source (like a Wall Outlet)

An AC (Alternating Current) source constantly changes its voltage and polarity. This prevents the capacitor from ever reaching a steady state, leading to completely different behavior.

What Happens:

1. Continuous Charging and Discharging:

   • When the AC voltage increases, the capacitor charges.

   • When the AC voltage decreases, the capacitor discharges.

   • When the AC voltage reverses polarity, the capacitor charges in the opposite direction (the roles of its plates swap).

2. Continuous Current Flow:

   • Because the source voltage is constantly changing, the capacitor is constantly trying to "catch up" by charging and discharging. This continuous movement of charge onto and off of the plates results in a continuous current flowing through the circuit.

   • It appears as if the AC current is "passing through" the capacitor, even though no individual electron physically crosses the gap between the plates.

3. Capacitive Reactance (X₀):

   • The capacitor doesn't behave like a simple resistor. It offers a different kind of opposition to AC current called capacitive reactance (X_c).

   • The formula for capacitive reactance is: X₀ = 1 / (2πfC)

     • f is the frequency of the AC source (in Hertz, Hz).

     • C is the capacitance (in Farads, F).

   • Key observations from the formula:

     • Higher Frequency (f) means Lower Reactance (X_c). Capacitors allow high-frequency signals to pass more easily.

     • Lower Frequency (f) means Higher Reactance (X_c). Capacitors resist low-frequency signals.

     • DC is a frequency of 0 Hz. If you put f=0 into the formula, X_c becomes infinite. This confirms that a capacitor blocks DC.

Key Takeaway for AC:

A capacitor allows AC current to pass, but it opposes it with an amount (reactance) that depends on the frequency. It acts as a frequency-dependent resistor.

Summary Table

Practical Applications Based on This Behavior

• DC Blocking / AC Coupling: A capacitor is used to remove the DC component of a signal, allowing only the AC part to pass. This is crucial in amplifier stages.

• Power Supply Filtering: Large capacitors are used in power supplies to smooth out the rectified AC, reducing ripple and providing a more stable DC voltage.

• Timing Circuits: The predictable charging time (via a resistor) is used to create delays and generate waveforms in circuits like oscillators.

• Filters: Capacitors are used with resistors to create filters that selectively pass or block certain frequencies (e.g., bass/treble controls in audio systems, noise filtering).