Capacitive reactance

As a capacitor charges, an impressed voltage builds across the plates and opposes the applied voltage. That opposition limits current, much as counter-EMF limits current in an inductor. Because the effect comes from capacitance, it is called capacitive reactance, measured in ohms.

XC = 1 / (2πfC)

• XC in ohms
• f in hertz
• C in farads
• π ≈ 3.1416

A 35 µF capacitor on a 120 V, 60 Hz line:

C = 35 × 10⁻⁶ F

XC = 1 / (2 × 3.1416 × 60 × 35×10⁻⁶) ≈ 75.8 Ω

I = E / XC = 120 / 75.8 ≈ 1.58 A

Same ideas as Ohm’s law, with XC in place of R — but remember the phase: current still leads voltage by 90° in a pure C circuit. You cannot treat watts as E × I the way you do for resistors.

If you measure voltage and current into a capacitor (and assume nearly pure capacitive behavior):

XC = E / I

C = 1 / (2πf XC)

Example: 480 V, 60 Hz, 2.6 A → XC ≈ 184.6 Ω → C ≈ 14.4 µF.

That is how a clamp meter plus voltage reading can estimate capacitance on a dedicated capacitive load when a bridge is not handy — with judgment about other circuit paths.

At 60 Hz a given motor-run capacitor draws a certain current. On a VFD output with high-frequency components, capacitive cables and filters can draw surprising current. At DC, f = 0, XC is infinite — open after the transient.

Real capacitors have some losses (ESR, dielectric loss). Q relates energy stored to energy lost per cycle. High-Q capacitors waste less as heat. In power PF banks and resonant circuits, losses matter for heating and efficiency. For many motor-run checks, µF and voltage rating dominate the day-to-day test.

Series capacitors: total C falls → XC of the combination rises.

Parallel capacitors: total C rises → XC falls.

Once you have CT, compute one XC for the equivalent capacitor at that frequency.

Inductive reactance rises with frequency: XL = 2πfL. Capacitive reactance falls with frequency. That opposite behavior is why RLC circuits can resonate — the topic of the next course.

Flip the formula when you know current:

XC = E/I → C = 1/(2πf XC)

A dedicated capacitor draws 4.0 A from 480 V at 60 Hz:

XC = 120 Ω → C ≈ 22.1 µF

If the nameplate says 25 µF, either the can has drifted low, frequency content is not pure 60 Hz, or another path shares the feeder.

Both limit current magnitude, but:

• R converts energy to heat continuously
• XC stores and returns energy each cycle
• Phase shift exists only for XC (and XL)

Saying “it has 75 ohms” is incomplete until you say resistive or reactive.

Compute CT first, then one XC. Do not average the individual XC values as if they were resistors of mixed types without converting through C. Parallel equal capacitors: CT = nC → XC_eq = XC/n. Series equal capacitors: CT = C/n → XC_eq = n×XC.

Situation. A PF correction bank is sized for 60 Hz. After a process change, a large VFD load adds harmonics. Capacitor-bank fuses start blowing even though “kVAR should match.”

What happened. Harmonic frequencies lower XC (XC ∝ 1/f). Capacitors draw more current than the 60 Hz design assumed. Fuses open; cans overheat.

Applied lesson. XC depends on frequency content, not only nameplate hertz. Harmonic-rich sites need reactors/filters or harmonic-rated banks — not just more µF.