Reactance of Capacitors and Inductors – AC Opposition

In DC circuits, capacitors and inductors are fairly boring:

• Capacitors behave like open circuits
• Inductors behave like short circuits

note

In AC circuits, things change dramatically. Capacitors and inductors oppose current flow, similar to resistors — but this opposition depends on frequency.

This frequency-dependent opposition is called reactance.

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Capacitive Reactance (Xc)

Capacitors resist changes in voltage.
In AC circuits, this shows up as opposition to current called capacitive reactance (Xc).

important

Capacitors oppose low frequencies strongly and allow high frequencies easily.

• At DC (0 Hz): reactance is infinite → blocks current
• At high frequency: reactance approaches zero → behaves like a short

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Capacitive Reactance Formula

$X_c = \frac{1}{2\pi f C}$

Where:

• Xc = capacitive reactance (Ohms)

• f = frequency (Hz)

• C = capacitance (Farads)

• π ≈ 3.14159

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Example: 1 µF Capacitor

• At 1 kHz:

  • Xc ≈ 159 Ω

• At 10 kHz:

  • Xc ≈ 16 Ω

• At 100 Hz:

  • Xc ≈ 1590 Ω

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Inductive Reactance (XL)

Inductors resist changes in current.
In AC circuits, this produces inductive reactance (XL).

• At DC (0 Hz): reactance is near zero

• At high frequency: reactance becomes very large

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Inductive Reactance Formula

$XL=2\pi fLX_L = 2\pi f L$

Where:

• XL = inductive reactance (Ohms)

• f = frequency (Hz)

• L = inductance (Henries)

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Example: 100 mH Inductor

• At 1 kHz:

  • XL ≈ 628 Ω

• At 10 kHz:

  • XL ≈ 6280 Ω

• At 100 Hz:

  • XL ≈ 63 Ω

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Capacitor vs Inductor Reactance

Property	Capacitor	Inductor
Reactance symbol	Xc	XL
Formula	$1 / (2\pi fC)$	$2πfL$
DC behavior	Blocks current	Passes current
High-frequency behavior	Passes current	Blocks current
Reactance vs frequency	Decreases	Increases

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Why Reactance Matters

Applications:

• High-pass filters → capacitors block low frequencies

• Low-pass filters → inductors block high frequencies

• AC coupling → capacitors remove DC offsets

• Power supplies → inductors smooth current ripple

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Reactance vs Resistance

Resistance	Reactance
Dissipates energy as heat	Stores energy temporarily
Independent of frequency	Depends on frequency
Converts energy	Returns energy to the circuit
Exists in DC and AC	Exists only in AC

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Key Takeaway

Reactance explains why frequency matters in AC circuits.
Capacitors oppose low frequencies, inductors oppose high frequencies — and together they enable filtering, signal shaping, and efficient power conversion.