6 For the LORD giveth wisdom: out of his mouth cometh knowledge and understanding.

7 He layeth up sound wisdom for the righteous: he is a buckler to them that walk uprightly.

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Introduction

Welcome back to The Amazing Capacitor series!

In Part 1, we learned what a capacitor is, how it stores energy in an electric field, and what affects its capacitance.

Now it’s time to answer one of the most important questions in electronics:

How does a capacitor charge?

In this lesson we’ll explore:

• RC charging circuits
• The RC time constant (τ)
• Why capacitor voltage rises slowly
• Why current decreases over time
• Kirchhoff’s Voltage Law
• Ohm’s Law
• Real breadboard demonstrations
• An introduction to capacitor discharging

By the end of this lesson, you’ll understand both the mathematics and the physics behind capacitor charging.

Check out the Video!

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Reviewing the Capacitor

A capacitor consists of two conductive plates separated by an insulating material called a dielectric.

When a DC voltage is applied:

• Electrons accumulate on one plate.
• Electrons leave the opposite plate.
• An electric field develops between the plates.
• Energy is stored in that electric field.

The relationship is

C = Q / V

where

• C = Capacitance (Farads)
• Q = Charge (Coulombs)
• V = Voltage (Volts)

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What Determines Capacitance?

Three things affect capacitance:

Plate Area

Larger plates store more charge.

Larger plate area = Higher capacitance

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Plate Spacing

Moving the plates closer together increases capacitance.

Smaller spacing = Higher capacitance

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Dielectric Material

Different dielectric materials store electric fields more effectively.

Higher dielectric constant = Higher capacitance.

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RC Charging Circuits

Our circuit consists of

• 5 V power supply
• 100 kΩ resistor
• 100 μF capacitor
• Switch

The resistor controls how quickly the capacitor charges.

Without the resistor, the capacitor would charge almost instantly.

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The RC Time Constant

The charging speed is determined by

τ = RC

where

• τ = Time Constant
• R = Resistance
• C = Capacitance

For our circuit

100,000 Ω × 100 μF

= 10 seconds

This means

One Time Constant (1τ) = 10 seconds

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Why 63.2%?

One of the most interesting facts about RC circuits is that after one time constant, the capacitor reaches

63.2%

of its final voltage.

For a 5 V supply

VC

= 5 × (1 − e⁻¹)

= 3.16 V

No matter what resistor or capacitor values you use, one time constant always corresponds to 63.2% of the final voltage.

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The Charging Equation

The voltage across the capacitor is

VC(t) = VDC(1 − e^(−t/RC))

where

• VDC = Supply voltage
• t = Time
• R = Resistance
• C = Capacitance

This equation describes the exponential charging curve.

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What is “e”?

The symbol e is a mathematical constant equal to approximately

2.71828…

Like π,

• it never terminates,
• and it never repeats.

Unlike π, which naturally appears in circles,

e naturally appears whenever something grows or decays continuously, such as capacitor charging.

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Kirchhoff’s Voltage Law

As the capacitor charges,

the supply voltage is always shared between

• the resistor
• the capacitor.

Kirchhoff’s Voltage Law states

VDC = VR1 + VC1

This relationship is true at every instant during charging.

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What Happens During Charging?

Immediately after the switch closes

• Capacitor voltage = 0 V
• Resistor voltage = 5 V
• Current is maximum

As time passes

• Capacitor voltage increases
• Resistor voltage decreases
• Current decreases

Eventually

• Capacitor voltage approaches 5 V
• Resistor voltage approaches 0 V
• Current approaches 0 A

The capacitor now behaves like an open circuit to DC.

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Current During Charging

Using Ohm’s Law

I = VR1 / R1

As resistor voltage decreases,

current also decreases.

Current is highest the instant the switch closes and gradually falls to zero.

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Breadboard Demonstration

In the lab we verify the theory using

• 5 V power supply
• 100 kΩ resistor
• 100 μF capacitor
• Digital multimeter
• Stopwatch

Measurements show the capacitor reaches approximately

2.98 V after 10 seconds

which is very close to the calculated value of

3.16 V

Small differences are expected because of component tolerances and manual timing.

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Capacitor Discharging

After charging,

the capacitor becomes the source of energy.

When power is removed,

the capacitor discharges through the resistor.

During discharge

• capacitor voltage decreases
• resistor voltage appears across the resistor
• current flows in the opposite direction
• all values gradually decay back to zero.

We’ll explore capacitor discharging in greater detail in the next lesson.

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Key Takeaways

✔ A resistor controls charging speed.

✔ The RC time constant is

τ = RC

✔ After one time constant,

the capacitor reaches 63.2% of its final voltage.

✔ Kirchhoff’s Voltage Law is true at every instant.

✔ As capacitor voltage rises,

resistor voltage and current decrease.

✔ After charging,

a capacitor behaves like an open circuit to DC.

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Conclusion

Capacitors may seem mysterious at first, but once you understand the RC time constant and the charging equation, their behavior becomes very predictable.

By combining Ohm’s Law, Kirchhoff’s Voltage Law, and the exponential charging equation, you can accurately predict how any RC charging circuit will behave.

In the next lesson, we’ll take a deeper look at capacitor discharging, compare the charging and discharging curves, and continue building our understanding of one of electronics’ most important components.

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