We all have heard that a capacitor block DC and passes AC. But what is the reason behind this behavior of a capacitor?

A **capacitor blocks DC in a steady state only**. **When a capacitor gets charged fully** and the voltage across it becomes equal and opposite to the DC input voltage,** no more current can flow through it. **This is when we say the capacitor is blocking DC.

Whereas **in the case of input AC supply, the voltage drops, become zero, and reverses**. This happens multiple times in a second depending upon the frequency of the supply. Due to this, a c**apacitor never reaches the steady state as it keeps charging and discharging in both directions**. And thus we say it is passing the AC.

**Note:** Only capacitor with no polarity passes AC. For example, Tantalum and electrolytic are polarized capacitors i.e, cannot be used in reverse polarity. Hence, they can’t pass AC.

For a more detailed and mathematical answer keep reading.

## How does a capacitor work in DC?

A **capacitor at the beginning will have no net charge and no voltage.** The two plates of the capacitor are separated by a dielectric insulator, so there is no way a charge can flow from one plate to the other.

### Charging of a Capacitor and how it blocks DC

**When it is connected to a DC source, a battery,** the electrons flow from the battery to the connected capacitor plate. **The negative charge or electrons get accumulated on this plate.**

This net negative charge cannot cross the dielectric but can induce or polarize it. To put it simply, this negative charge repels the electrons from the other plate which then becomes positively charged. Right now the circuit is in a transient state.

This keeps happening until no more electrons can be accumulated on the lower plate and the capacitor is fully charged equal and opposite to the battery voltage. **Now no more current can flow through the circuit and this state is called a steady state. That’s when we say the capacitor is blocking DC.**

**Without a resistor, charging of the capacitor happens so quickly, it seems like DC was blocked from the beginning.**

Note that the opposite charges on the plates are attracted to each other but cannot cross the insulator dielectric. This creates an electric field inside the capacitor from the positive to the negative plate.

**What’s the net charge on the capacitor now?**

As ambiguous as it may sound, it is still zero. Since both plates have equal and opposite charges the overall net charge is zero.

## How does a capacitor work in AC?

Now replace the battery with an AC voltage source in the example. The charging process of the capacitor will be the same.

But now the input voltage is not steady, it periodically changes. So as soon as the capacitor gets fully charged to the peak voltage, the input voltage drops. This causes the capacitor to discharge in opposite direction and current flows through the circuit.

When the input voltage becomes zero again, the capacitor is fully discharged. But the input voltage is now reversed and climbs up. So capacitor charges again, though in opposite direction this time.

See the current does not get the time to settle and keeps changing and keeps flowing through the circuit. Hence the capacitor cannot block AC.

## Capacitor block DC but passes AC: Mathematical approach

The reactance of the capacitor is given by the formula, X_{C} = 1/2πfC. Where X_{C} is the reactance, f is the frequency and C is the capacitance value.

**The reactance of capacitor during DC**

Since f = 0 in the case of a DC supply. X_{C} = 1/0 = infinity. The reactance is infinite hence no current passes through the circuit. That’s how a capacitor blocks DC.

**The reactance of capacitor during AC**

Since f has some value in an AC supply(a, let’s say). X_{C} = 1/a = some value. The reactance has some value, hence current passes through the circuit. That’s how a capacitor passes AC.

nice explanation

Glad to be of help