What does I mean in the Capacitive Dropper Supply Current formula?

I is Available RMS current (A).

Capacitive Dropper Supply Current

Q: How do you calculate Capacitive Dropper Supply Current?

Use the formula I = 2π × f × C × Vrms = Vrms / Xc. A capacitive dropper (X-rated capacitor) supplies a small DC current from the mains by using the capacitor’s reactance to limit current without dissipating heat. Enter the values you know in the calculator above and it solves for the remaining variable.

Q: What is the formula for Capacitive Dropper Supply Current?

The Capacitive Dropper Supply Current formula is I = 2π × f × C × Vrms = Vrms / Xc, where I—Available RMS current (A); f—Line frequency (Hz); C—Dropper capacitor (F); Vrms—Line RMS voltage (V).

I = 2π · f · C · Vrms

Quick answer

This calculator solves I = 2π × f × C × Vrms = Vrms / Xc for Supply Current. With Line Frequency 1 kHz, Dropper Capacitor 100 µF, Line Voltage 12 V, the result is 7.54 A. It solves in 4 directions, so you can enter the values you have and get the one you need.

Calculator

Line Frequency

Dropper Capacitor

Line Voltage

Supply Current (mA)

—

Formula

I = 2π × f × C × Vrms = Vrms / Xc

Description

A capacitive dropper (X-rated capacitor) supplies a small DC current from the mains by using the capacitor’s reactance to limit current without dissipating heat. The available current equals the line voltage divided by the capacitor’s reactance. It is a cheap, transformerless way to power low-current loads such as LED night-lights and timer ICs—but the circuit is not isolated from the mains and is dangerous to touch.

Variables

I — Available RMS current (A)
f — Line frequency (Hz)
C — Dropper capacitor (F)
Vrms — Line RMS voltage (V)

Practical Notes

Use an X2-rated capacitor and a bleeder resistor. The output is NOT mains-isolated—never use where a user can contact the low-voltage side. Roughly 1 µF gives ~70 mA at 230 V/50 Hz.

Symbols and units

Symbol	Meaning	Default unit	Accepted units
I	Supply Current	mA	pA, nA, µA, mA, A, kA
f	Line Frequency	Hz	Hz, kHz, MHz, GHz
C	Dropper Capacitor	µF	pF, nF, µF, mF, F
Vrms	Line Voltage	V	pV, nV, µV, mV, V, kV

Step by step

1. What you know: Line Frequency 1 kHz, Dropper Capacitor 100 µF, Line Voltage 12 V
2. The relation: I = 2π × f × C × Vrms = Vrms / Xc
3. Substitute: f = 1 kHz, C = 100 µF, Vrms = 12 V
4. Result: Supply Current = 7.54 A

Related quantities from the same inputs

P = V × I = 90.48 W

Worked examples

Minimum range

Given: Line Frequency 5 Hz, Dropper Capacitor 100 nF, Line Voltage 0.33 V

Result: Supply Current = 1.037 µA

Low range

Given: Line Frequency 50 Hz, Dropper Capacitor 1 µF, Line Voltage 3.3 V

Result: Supply Current = 1.037 mA

Typical

Given: Line Frequency 1 kHz, Dropper Capacitor 100 µF, Line Voltage 12 V

Result: Supply Current = 7.54 A

High range

Given: Line Frequency 20 kHz, Dropper Capacitor 1 mF, Line Voltage 0.23 kV

Result: Supply Current = 28.9 kA

Maximum range

Given: Line Frequency 0.2 MHz, Dropper Capacitor 10 mF, Line Voltage 2.3 kV

Result: Supply Current = 28900 kA

Solving for each variable

Solve for Supply Current

Line Frequency 5 Hz, Dropper Capacitor 100 nF, Line Voltage 0.33 V → 1.037 µA

Solve for Line Frequency

Supply Current 100 µA, Dropper Capacitor 100 nF, Line Voltage 0.33 V → 0.4823 kHz

Solve for Dropper Capacitor

Supply Current 100 µA, Line Frequency 5 Hz, Line Voltage 0.33 V → 9.646 µF

Solve for Line Voltage

Supply Current 100 µA, Line Frequency 5 Hz, Dropper Capacitor 100 nF → 31.83 V

How Supply Current changes with Line Frequency

Line Frequency (input)	Supply Current (result)
100 Hz	0.754 A
0.25 kHz	1.885 A
0.5 kHz	3.77 A
0.75 kHz	5.655 A
1 kHz	7.54 A
1.5 kHz	11.31 A
2 kHz	15.08 A
4 kHz	30.16 A
7 kHz	52.78 A
10 kHz	75.4 A

The same result in other units

Unit	Value
µA	7540000
mA	7540
A	7.54
kA	0.00754

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Frequently asked questions

How do you calculate Capacitive Dropper Supply Current?

Use I = 2π × f × C × Vrms = Vrms / Xc. With Line Frequency 1 kHz, Dropper Capacitor 100 µF, Line Voltage 12 V, Supply Current works out to 7.54 A.

How do you calculate capacitive dropper current formula 230v 50hz 3.3uf capacitor 238ma?

Rearrange for Supply Current: with Line Frequency 50 Hz, Dropper Capacitor 1 µF, Line Voltage 3.3 V, Supply Current is 1.037 mA.

What is the formula for Capacitive Dropper Supply Current?

The formula is I = 2π × f × C × Vrms = Vrms / Xc. A capacitive dropper (X-rated capacitor) supplies a small DC current from the mains by using the capacitor’s reactance to limit current without dissipating heat.

How do you find Line Frequency when you know the other values?

Rearrange for Line Frequency: with Supply Current 100 µA, Dropper Capacitor 100 nF, Line Voltage 0.33 V, Line Frequency is 0.4823 kHz.

How do you find Dropper Capacitor when you know the other values?

Rearrange for Dropper Capacitor: with Supply Current 100 µA, Line Frequency 5 Hz, Line Voltage 0.33 V, Dropper Capacitor is 9.646 µF.

What units does Capacitive Dropper Supply Current use?

Supply Current is shown in µA, mA, A, kA. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

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