Capacitive Reactance Calculator

Understanding Capacitive Reactance Calculator

Capacitive reactance is the opposition to current flow in a capacitor in an AC circuit. It decreases with increasing frequency.

How to use this calculator

1. Enter the frequency \(f\) in hertz \(\text{Hz}\).
2. Enter the capacitance \(C\) in farads \(\text{F}\).
3. Use the formula \(X_C = \frac{1}{2\pi f C}\) to find the reactance.
4. Read the result in ohms \(\Omega\).

The formula explained

The formula \(X_C = \frac{1}{2\pi f C}\) computes capacitive reactance, which is the opposition a capacitor presents to AC. Higher frequency or larger capacitance gives a smaller \(X_C\).

• \(X_C\) = capacitive reactance in ohms \(\Omega\)
• f = frequency of the AC signal in hertz \(\text{Hz}\)
• C = capacitance in farads \(\text{F}\)
• \(\pi\) = the constant pi, about \(3.14159\)

Step by step method

1. Write down the frequency \(f\) and capacitance \(C\).
2. Multiply \(2\pi\), \(f\), and \(C\).
3. Take the reciprocal of that product to get \(X_C\).

Worked example

Problem. Find the capacitive reactance of a \(47\,\mu\text{F}\) capacitor at \(60\,\text{Hz}\).

1. Convert the capacitance: \(47\,\mu\text{F} = 47 \times 10^{-6}\,\text{F}\).
2. Substitute into the formula: \(X_C = \frac{1}{2\pi(60)(47 \times 10^{-6})}\).
3. Calculate the result: \(X_C \approx 56.4\,\Omega\).

Tips and common mistakes

• Make sure the capacitance is in farads before calculating, because microfarads and nanofarads must be converted.
• As frequency increases, capacitive reactance decreases, so a capacitor passes higher frequency signals more easily.

Frequently asked questions