Capacitance, Capacitive Reactance, and RC Circuits

What Is Capacitance?

A capacitor stores electrical energy in an electric field between two conducting plates separated by an insulating material called a dielectric. Capacitance (C) is the measure of how much charge a capacitor can store per volt applied across it. The unit is the farad (F), though practical capacitors are rated in microfarads (µF), nanofarads (nF), or picofarads (pF).

Two broad families appear in this lab. Electrolytic capacitors use a chemical oxide layer as the dielectric and achieve large capacitance in a small package; they are polarized, meaning the positive lead must always connect to the higher potential — reverse polarity can rupture the component or cause it to vent hazardous material. Film capacitors use a plastic film dielectric and are non-polarized; they tolerate AC without concern for polarity.

Capacitive Reactance (X_C)

In a DC circuit, a fully charged capacitor blocks current entirely. In an AC circuit, the capacitor charges and discharges with every cycle, so current does flow — but it is opposed by capacitive reactance (X_C). The formula is:

X_C = 1 / (2πfC)

where f is frequency in hertz and C is capacitance in farads. X_C is measured in ohms.

Two relationships follow directly from the formula:

• Higher frequency → lower X_C. The capacitor cycles faster, so it impedes current less.
• Larger capacitance → lower X_C. More stored charge means the voltage builds more slowly, again reducing opposition.

This is the opposite of inductive reactance (X_L = 2πfL), which rises with frequency. Remembering that contrast will serve you on credentialing exams.

Current Leads Voltage in a Capacitor

In a purely capacitive AC circuit, current reaches its peak 90 degrees before voltage reaches its peak. The phrase "ELI the ICE man" is a classic memory aid: in a Capacitor (ICE), I (current) comes before E (voltage). On a phasor diagram, the current phasor is drawn 90° ahead of (leading) the voltage phasor across the capacitor.

Physically, the current must flow first to build up charge on the plates; only after charge accumulates does the voltage appear. Think of filling a bucket — water (current) flows in before the bucket (voltage) is full.

The RC Time Constant (τ)

When a DC voltage is applied to a series RC circuit through a switch (or the rising edge of a square wave), the capacitor does not charge instantly. The voltage across C rises exponentially:

v_C(t) = V_S × (1 − e^(−t/τ))

The time constant τ (tau) is:

τ = R × C

where R is in ohms and C is in farads; τ is in seconds.

At exactly one time constant, the capacitor has charged to approximately 63.2% of the source voltage. After five time constants (5τ) the capacitor is considered fully charged (>99%). On the oscilloscope, you will identify the moment the waveform reaches 63% of its final value and read the elapsed time — that is your measured τ.

Lab Safety — Read Before Touching Any Capacitor

Electrolytic capacitors can store dangerous charge even after power is removed. Before handling any electrolytic:

1. Remove the power source.

2. Discharge the capacitor through a resistor of appropriate value (your instructor will specify). Never short the leads directly — the sudden discharge can damage the component and create a spark.

3. Verify with your DMM that the voltage across the capacitor is at or near zero before making contact.

4. Observe polarity markings. The negative lead is marked with a stripe and a minus sign. Connect it to the lower-potential point.

Wear safety glasses whenever energizing any circuit on the bench. Keep the function generator amplitude within the voltage rating of the capacitors in use. If a capacitor becomes warm, smells, or bulges, de-energize immediately, tell the instructor, and do not handle it.

Apply lockout/tagout (LOTO) discipline: whenever you need to reconfigure wiring, disconnect the power source first, verify the circuit is de-energized, then make your changes.

Connecting It All in the AC RC Circuit

When a sine-wave source drives a series RC circuit, the total opposition to current is impedance (Z):

Z = √(R² + X_C²)

Voltage divides between R and C. Because X_C and R are 90° out of phase with each other, you cannot simply add the voltages — you must use the Pythagorean relationship:

V_S² = V_R² + V_C²

You can recover X_C from measurements using Ohm's law for AC: X_C = V_C / I, where I = V_R / R (current is common in a series circuit and in phase with V_R).

When you sketch the phasor diagram in your lab log, place the current phasor I along the reference (horizontal) axis, draw V_R in phase with I, draw V_C pointing downward (−90° from I), and draw V_S as their phasor sum. Label all four phasors with measured values.