Why Does a Capacitor’s Voltage Become Constant When Connected to a Power Supply?

In basic circuit analysis, we often state a simple conclusion:

When a capacitor is connected to a DC power supply, its voltage eventually becomes equal to the supply voltage and then remains constant.

This statement is correct—but the reasoning behind it is often skipped.
To truly understand why this happens, we need to look at what a capacitor actually does, both physically and electrically.

1. A Capacitor Stores Charge — Not Voltage

At its core, a capacitor consists of two conductive plates separated by an insulating material (dielectric).

When the capacitor is not connected to a power source:

• Both plates are electrically neutral

• There is no electric field between them

• The voltage across the capacitor is zero

Once the capacitor is connected to a DC power supply:

• The power supply pushes electrons onto one plate

• Electrons are pulled away from the other plate

• Equal and opposite charges accumulate on the two plates

This separation of charge creates an electric field, and that electric field is what we measure as voltage.

📌 Key point:
A capacitor does not generate voltage by itself.
The voltage appears as a result of charge being forced onto its plates by the external power source.

📷 Figure 1 (Suggested)

Title: Structure of a Capacitor
Description:
Two parallel plates separated by a dielectric, with no charge applied (uncharged state).

2. Why the Capacitor Voltage Rises Toward the Supply Voltage

The relationship between charge and voltage in a capacitor is:

Where:

• VVV is the capacitor voltage

• QQQ is the stored charge

• CCC is the capacitance

At the moment the capacitor is first connected:

• The capacitor voltage is low

• The voltage difference between the power supply and the capacitor is large

• Current flows, charging the capacitor

As charging continues:

• More charge accumulates on the plates

• The capacitor voltage increases

• The voltage difference driving the current becomes smaller

This process continues smoothly until the capacitor voltage reaches the power supply voltage.

📷 Figure 2 (Suggested)

Title: Capacitor Charging Process
Description:
A capacitor connected to a DC source, showing current flow decreasing over time as voltage increases.

3. Why the Voltage Becomes Constant

The crucial moment occurs when:

The capacitor voltage equals the supply voltage.

At this point:

• There is no voltage difference across the circuit

• Without a voltage difference, there is no current

• Without current, no additional charge can move onto the capacitor

As a result:

• The charge on the capacitor remains unchanged

• The electric field remains unchanged

• The voltage remains constant

From a circuit perspective, a fully charged capacitor under DC conditions behaves like an open circuit.

📷 Figure 3 (Suggested)

Title: DC Steady-State Equivalent
Description:
Capacitor represented as an open circuit once fully charged.

4. Is the Voltage Truly Constant in Real Circuits?

In theory, the voltage can remain constant indefinitely.
In practice, several real-world factors affect this behavior:

1. Leakage Current
   No dielectric is perfectly insulating. Small leakage currents slowly discharge the capacitor.

2. External Loads
   If a load is connected in parallel, it draws charge and reduces the voltage.

3. Power Supply Variations
   Ripple, noise, or transient changes in the supply appear directly on the capacitor voltage.

This is why capacitor selection—capacitance value, voltage rating, dielectric type, and lifetime—is critical in power electronics and industrial applications.

📷 Figure 4 (Suggested)

Title: Real Capacitor with Leakage and Load
Description:
Equivalent circuit including leakage resistance and load, showing gradual voltage decay.

5. An Engineer’s Intuition

A practical way to think about it:

• The power supply moves charge

• The capacitor stores charge

• As charge accumulates, it becomes harder for the supply to push more charge

• Once the capacitor voltage matches the supply voltage, the “push” disappears

That is why the capacitor voltage settles and appears constant.