Capacitance to Resistance Calculator

How to Use the Capacitance to Resistance Calculator

To analyze capacitive circuits and determine the electrical opposition of a capacitor at a specific operating frequency, follow these steps:

1. 1
   Enter Capacitance: Input the rated capacitance value of the component.
2. 2
   Select Capacitance Unit: Choose Farad (F), millifarad (mF), microfarad (µF), nanofarad (nF), or picofarad (pF).
3. 3
   Enter Frequency: Input the AC frequency of the system.
4. 4
   Select Frequency Unit: Choose Hertz (Hz), kilohertz (kHz), or megahertz (MHz).
5. 5
   Calculate: Click the "Calculate to Resistance" button to run the conversion.

How to Calculate Capacitance to Resistance

In alternating current (AC) power systems and filters, capacitors present a frequency-dependent opposition to current flow. This opposition is technically referred to as capacitive reactance, which acts as the AC equivalent of electrical resistance. Reactance is inversely proportional to both capacitance and frequency. A larger capacitor or higher operating frequency offers less opposition to current, resulting in lower equivalent resistance (reactance) values in Ohms. Sizing power grids, timing loops, or filter paths requires calculating capacitance to resistance.

Real-Life Sizing Scenarios

Scenario 1: Sizing AC Opposition for a 10 µF Motor Run Capacitor at 50 Hz
An HVAC technician determines the nominal AC opposition (reactance) of a 10 µF motor run capacitor operating on a standard 50 Hz line supply:
R = 1 ÷ (2 × π × f × C) = 1 ÷ (2 × 3.14159 × 50 Hz × (10 × 10^−6 F)) = 318.31 Ohms

Scenario 2: Sizing AC Opposition for a 100 nF High-Frequency Decoupling Capacitor at 200 kHz
A hardware engineer calculates the AC reactance of a 100 nF noise bypass capacitor operating at a switching frequency of 200 kHz:
R = 1 ÷ (2 × π × f × C) = 1 ÷ (2 × 3.14159 × (200 × 10^3 Hz) × (100 × 10^−9 F)) = 7.96 Ohms

Step-by-Step Manual Sizing Guide

1. 1
   Identify circuit parameters: Settle the capacitance (C) and the grid frequency (f).
2. 2
   Scale to base physical units: Convert capacitance to Farads (F) (e.g. 10 µF = 10 × 10^−6 F) and frequency to Hertz (Hz).
3. 3
   Solve the reciprocal product: Apply the formula: R = 1 ÷ (2 × π × f × C) to compute resistance in Ohms.

Capacitance to Resistance Chart

The table below displays typical capacitance values and their corresponding AC resistance (reactance) values in Ohms (Ω) calculated at standard frequencies of 50 Hz and 60 Hz:

Capacitance Resistance Dimensional Formula

In dimensional analysis, the product of resistance (R) and capacitance (C) yields time (T), which defines the RC time constant:
[R] = [M L² T^−3 A^−2]
[C] = [M^−1 L^−2 T^4 A²]
[R] × [C] = [T] (seconds). Therefore, equivalent resistance has the dimensional formula [M L² T^−3 A^−2].

Capacitance Resistance Voltage Formula

In a transient series RC circuit connected to a DC source voltage (V_s), the instantaneous voltage across the capacitor plates is related to capacitance and series resistance by:
v(t) = V_s × (1 − e^(−t ÷ RC))
where R limits charging current flow, slowing down voltage build-up.

Capacitance Resistance Unit

The standard International System of Units (SI) unit for resistance is the Ohm (Ω), and the standard unit for capacitance is the Farad (F). The product of these two base units (1 Ohm × 1 Farad) defines a time constant of exactly 1 second.

Frequently Asked Questions (FAQs)