Capacitive Reactance
In a DC circuit, a fully charged capacitor blocks all current — once the capacitor plates are charged to the supply voltage, no more electrons can flow. In an AC circuit, the situation is completely different. Because the voltage is constantly changing direction, the capacitor is perpetually charging and discharging, so current flows continuously. But the capacitor still opposes that AC current in a way that depends on frequency. This opposition is called capacitive reactance, and it is one of the two fundamental reactive quantities (the other being inductive reactance) that govern the behavior of radio circuits.
Capacitive reactance is inversely proportional to frequency. At low frequencies a capacitor presents high opposition to AC; at high frequencies the opposition is small. This is why capacitors are used to block low frequencies and pass high frequencies.
View LargerWhy Capacitors Pass AC But Block DC
A capacitor consists of two conducting plates separated by an insulating material (the dielectric). Electrons cannot physically cross the gap — the insulator prevents that. Yet in an AC circuit, current flows as if the capacitor were not there. How?
The answer lies in the charging and discharging process. When AC voltage is applied, it alternately pushes electrons toward one plate and then pulls them back, then pushes them toward the other plate and pulls them back, over and over in step with the AC frequency. Electrons flow in and out of each plate continuously. Although no electrons actually cross from one plate to the other, a back-and-forth current flows in the external circuit as if current were passing straight through.
For DC, the capacitor charges up to the supply voltage and then current stops — the electric field in the dielectric exactly opposes any further charge movement. For AC, the voltage is never steady long enough for the capacitor to fully charge; before it reaches the DC steady state, the voltage has reversed and the capacitor starts discharging in the other direction. The higher the frequency, the less time there is for the capacitor to charge up between reversals, and the less opposition it presents to the current.
This behavior — where the opposition to current decreases as frequency increases — is the defining characteristic of capacitive reactance, and it is the opposite of what resistors do (constant opposition regardless of frequency) and opposite of what inductors do (increasing opposition with frequency).
The Capacitive Reactance Formula
Capacitive reactance is given the symbol XC (the subscript C for capacitor) and is measured in ohms, exactly like resistance. The formula is:
XC = 1 / (2πfC)
where:
XC = capacitive reactance in ohms (Ω)
f = frequency in hertz (Hz)
C = capacitance in farads (F)
2π ≈ 6.2832
Every variable in this formula does exactly what physical intuition predicts:
- Larger capacitance → lower reactance. A larger capacitor stores more charge per volt, so less voltage is needed to push a given amount of charge — meaning less opposition to current.
- Higher frequency → lower reactance. At higher frequencies, the voltage changes so rapidly that the capacitor never has time to resist the current. The plates charge and discharge faster, current flows more easily.
- Lower frequency → higher reactance. At low frequencies the capacitor has more time to charge up and oppose further current flow. At DC (f = 0), the formula gives XC = infinity — perfectly blocking DC, as expected.
A 100 µF electrolytic capacitor is used as a bypass capacitor in an audio amplifier. What is its reactance at 1 kHz (the middle of the audio band)?
XC = 1 / (2π × 1000 × 100 × 10-6)
XC = 1 / (2 × 3.14159 × 0.1)
XC = 1 / 0.6283 = 1.59 Ω
At 1 kHz, this capacitor presents only 1.59 ohms of reactance — effectively a short circuit compared to the typical hundreds of ohms in the signal path. It does its job of bypassing audio signals to ground.
A 0.01 µF (10 nF) coupling capacitor is used between stages in an HF receiver working at 14 MHz. What is its reactance?
XC = 1 / (2π × 14 × 106 × 10 × 10-9)
XC = 1 / (2 × 3.14159 × 14 × 106 × 10-8)
XC = 1 / (2 × 3.14159 × 0.14)
XC = 1 / 0.8796 = 1.14 Ω
At 14 MHz the 10 nF capacitor has only 1.14 ohms of reactance — low enough to pass RF signals with negligible loss while still blocking any DC bias voltage between stages.
How much reactance does that same 10 nF capacitor present at 60 Hz (line frequency)?
XC = 1 / (2π × 60 × 10 × 10-9)
XC = 1 / (3.7699 × 10-6) = 265,258 Ω ≈ 265 kΩ
At 60 Hz, this same capacitor presents 265,000 ohms of opposition — effectively blocking the low-frequency hum entirely, even though it passes 14 MHz signals freely. This enormous difference in reactance across frequency is the foundation of filter design.
How XC Varies with Frequency
The inverse relationship between XC and frequency means that doubling the frequency halves the reactance, and halving the frequency doubles the reactance. This is a hyperbolic relationship — the graph of XC vs. frequency is a smooth curve that falls steeply at low frequencies and flattens out at high frequencies.
In practical terms, a "rule of thumb" widely used in RF design is that a bypass or decoupling capacitor should have a reactance of one-tenth (or less) of the impedance it is bypassing. If you need to bypass a 50-ohm RF line at 7 MHz, choose a capacitor whose reactance at 7 MHz is 5 ohms or less:
C ≥ 1 / (2π × f × XC) = 1 / (2π × 7 × 106 × 5) = 4.55 nF
So a 10 nF capacitor (the nearest standard value larger than 4.55 nF) would work adequately.
| Capacitor Value | XC at 60 Hz | XC at 1 kHz | XC at 7 MHz | XC at 144 MHz |
|---|---|---|---|---|
| 1 µF | 2,653 Ω | 159 Ω | 22.7 Ω | 1.1 Ω |
| 100 nF | 26,530 Ω | 1,592 Ω | 227 Ω | 11.0 Ω |
| 10 nF | 265,300 Ω | 15,920 Ω | 2,274 Ω | 110.5 Ω |
| 100 pF | 26.5 MΩ | 1.59 MΩ | 227 Ω | 11.0 Ω |
| 10 pF | 265 MΩ | 15.9 MΩ | 2,274 Ω | 110.5 Ω |
Study this table carefully. Note that a 100 pF capacitor has only 11 ohms of reactance at 144 MHz (2-meter amateur band) but over 26 megaohms at 60 Hz. This is why VHF circuits use small capacitors for bypassing and coupling — large electrolytics, which work well at audio frequencies, are often useless at VHF because their lead inductance (parasitic inductance of the leads and foil) resonates with the capacitance and creates complex impedance behavior.
Capacitive Reactance and Phase
Resistance and reactance both oppose current flow, but they do so in fundamentally different ways with respect to phase.
In a purely resistive circuit, voltage and current are in phase — they reach their peaks at exactly the same instant. In a purely capacitive circuit, the current leads the voltage by 90 degrees. This means the current reaches its peak one quarter of a cycle before the voltage. The mnemonic that helps remember this is "ICE": In a Capacitor, current (I) comes before voltage (E, the old symbol for EMF/voltage). The complementary mnemonic for inductors is "ELI": voltage (E) leads current (I) in an Inductor.
The phase difference exists because the capacitor's voltage depends on its accumulated charge, not its instantaneous current. The capacitor charges most rapidly when current is at its peak (maximum rate of charge delivery), and the voltage builds up more slowly over time. This 90-degree lead of current over voltage is a defining property of capacitive reactance.
Because capacitive reactance involves a 90-degree phase shift, it cannot be simply added to resistance the way two resistors are added. Reactance and resistance are perpendicular quantities — they are combined using the Pythagorean theorem (explained fully in the Impedance lesson, M07E).
Capacitive Reactance Calculator
Capacitive Reactance — XC = 1 / (2πfC)
Enter frequency and capacitance to calculate XC. Use the unit selectors to avoid having to convert manually.
Ham Radio Applications
Capacitive reactance governs the behavior of capacitors throughout your transceiver and antenna system. Understanding it lets you predict how a circuit will behave before you build it, and diagnose problems when something goes wrong.
Bypass Capacitors
Every DC supply line entering an RF stage in your transceiver has bypass capacitors on it. Their purpose is to provide a low-impedance path to ground for RF energy, preventing RF from riding on the DC supply lines and coupling between stages. The bypass capacitor must present a very low reactance at the operating frequency. A good bypass capacitor for 40-meter operation (7 MHz) would be 1 nF to 10 nF: at 7 MHz, a 10 nF capacitor has only 2.27 ohms reactance.
Coupling Capacitors
Coupling capacitors pass AC signals between stages while blocking DC bias voltages. They must have low reactance at the signal frequency (so they pass the signal with little loss) but effectively block DC (infinite reactance at f = 0). In audio circuits, coupling capacitors are typically 1–10 µF; in RF circuits they range from a few picofarads at microwave frequencies to a few nanofarads at HF.
Antenna Tuning
The variable capacitor in an antenna tuner changes its capacitance to adjust its reactance at the operating frequency, canceling the reactive component of the antenna's impedance and presenting a resistive 50-ohm load to the transmitter. When you turn the capacitor dial on your antenna tuner, you are adjusting XC to achieve resonance — the same process as tuning a radio receiver to a station.
Filter Design
The cutoff frequency of a simple RC low-pass filter is the frequency at which XC equals R — in other words, where the capacitor's reactance equals the series resistance. Below that frequency the signal passes; above it the signal is attenuated. The filter lesson (M07K) covers this in detail, but the underlying mechanism is entirely governed by XC.
⚖ Experiment: Observing Capacitive Reactance with a Multimeter
This experiment demonstrates that a capacitor impedes AC current in a frequency-dependent way by observing the voltage drop across a resistor in series with a capacitor, with AC signals at different audio frequencies.
- Function generator or audio signal source (even a smartphone app works)
- True-RMS multimeter (or an oscilloscope)
- 22 µF electrolytic capacitor
- 1 kΩ resistor
- Breadboard and connecting wires
- Small audio amplifier or the phone's headphone jack as signal source
- Connect the 1 kΩ resistor in series with the 22 µF capacitor on the breadboard. Connect a signal source across the series combination. Observe the polarity marking on the electrolytic capacitor — for this AC experiment use a non-polarized capacitor if available, or limit signal amplitude to avoid reverse-biasing an electrolytic.
- Set the signal source to 100 Hz and a moderate output level. Measure the AC voltage across the resistor with your multimeter set to AC volts.
- Calculate the expected XC at 100 Hz: XC = 1 / (2π × 100 × 22 × 10-6) = 72.3 Ω. Since XC is much larger than R (1000 Ω) at this frequency, the capacitor dominates and you should see a smaller voltage across R.
- Increase the frequency to 1 kHz and measure again. XC at 1 kHz = 7.23 Ω — much smaller than R = 1000 Ω, so now the resistor drops most of the voltage.
- Record the resistor voltage at several frequencies: 100 Hz, 500 Hz, 1 kHz, 5 kHz, 10 kHz.
At low frequencies (100 Hz) the voltage across R is low because the capacitor's high reactance limits current through the series circuit. As frequency increases, XC decreases, more current flows, and the voltage across R rises toward the source voltage. Above about 1 kHz the resistor's voltage levels off as XC becomes negligible compared to R. This directly demonstrates that capacitive reactance decreases with increasing frequency — the core property of capacitive reactance.
Frequently Asked Questions
Does capacitive reactance dissipate power the way resistance does?
No. Reactance stores and returns energy — it does not convert electrical energy to heat. In a purely capacitive circuit (no resistance), current flows and voltage is present, but the average power delivered to the capacitor over a complete cycle is zero. During one quarter cycle the capacitor stores energy; during the next quarter it returns that energy to the source. This is why reactive circuits can have high voltages and currents without dissipating much power — the energy just sloshes back and forth between the source and the reactive element. Only resistance dissipates power as heat.
Why does a bypass capacitor need to be large (high capacitance) to work at audio frequencies but small at RF?
Because XC = 1/(2πfC), achieving low reactance requires either high frequency or high capacitance. At audio frequencies (1 kHz), to get XC below 10 ohms you need C > 16 µF — which requires a large electrolytic. At RF (7 MHz), the same 10-ohm target requires C > only 2.3 nF — a tiny ceramic or film capacitor. Large electrolytic capacitors have significant lead inductance that causes them to resonate at relatively low frequencies, making them ineffective at VHF and above. This is why RF circuits use multiple capacitors in parallel: a large electrolytic for audio bypass, a small ceramic (100 nF) for RF bypass, and sometimes an even smaller chip capacitor (100 pF) for UHF bypass.
What happens at the frequency where XC = R in a series RC circuit?
That frequency is the cutoff frequency (fc) of the RC filter. At fc, the signal is attenuated by 3 dB — it falls to 70.7% of its original amplitude. Below fc, the signal is relatively unattenuated (passes easily); above fc, the capacitor shunts more and more of the signal to ground. This is the operating principle of every RC filter in electronics. In a low-pass RC filter, signals below fc pass and signals above fc are progressively attenuated.
Test Your Knowledge
Answer the questions below to check your understanding. Every answer can be found in the lesson above.