Impedance Calculator

Impedance Formula:

\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \]

Impedance (Z):

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1. What is Impedance?

Impedance (Z) is the total opposition that a circuit presents to alternating current. It combines resistance (R) and reactance (X) and is measured in ohms. Impedance is a complex quantity that includes both magnitude and phase angle.

2. How Does the Calculator Work?

The calculator uses the impedance formula:

\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \]

Where:

\( Z \) — Total impedance (ohms)
\( R \) — Resistance (ohms)
\( X_L \) — Inductive reactance (ohms)
\( X_C \) — Capacitive reactance (ohms)

Explanation: The formula calculates the magnitude of impedance in an AC circuit by considering the resistive and reactive components. The term (X_L - X_C) represents the net reactance in the circuit.

3. Importance of Impedance Calculation

Details: Accurate impedance calculation is crucial for circuit design, power system analysis, audio engineering, and telecommunications. It helps determine how circuits will behave with AC signals and is essential for impedance matching to maximize power transfer.

4. Using the Calculator

Tips: Enter resistance in ohms, inductive reactance in ohms, and capacitive reactance in ohms. All values must be valid numerical values. Resistance must be non-negative.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between impedance and resistance?
A: Resistance opposes DC current, while impedance opposes AC current and includes both resistive and reactive components.

Q2: When is impedance purely resistive?
A: When X_L = X_C (resonance condition), the net reactance becomes zero, and impedance equals resistance.

Q3: Can impedance be negative?
A: The magnitude of impedance is always positive, but the reactive component can be positive (inductive) or negative (capacitive).

Q4: How does frequency affect impedance?
A: Inductive reactance increases with frequency (X_L = 2πfL), while capacitive reactance decreases with frequency (X_C = 1/(2πfC)).

Q5: What is impedance matching?
A: The process of making the output impedance of a source equal to the input impedance of the load to maximize power transfer and minimize signal reflection.