How to Calculate AC Resistance of a Conductor

AC Resistance with Skin Effect Formula:

\[ R_{ac} = R_{dc} \left[1 + \left(\frac{f}{f_s}\right)^4\right] \]

AC Resistance (R_ac):

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1. What is AC Resistance with Skin Effect?

AC resistance accounts for the skin effect phenomenon where alternating current tends to flow near the surface of a conductor at high frequencies. This increases the effective resistance compared to DC resistance due to reduced current-carrying cross-section.

2. How Does the Calculator Work?

The calculator uses the skin effect approximation formula:

\[ R_{ac} = R_{dc} \left[1 + \left(\frac{f}{f_s}\right)^4\right] \]

Where:

\( R_{ac} \) — AC resistance (Ω)
\( R_{dc} \) — DC resistance (Ω)
\( f \) — Operating frequency (Hz)
\( f_s \) — Skin frequency (Hz)

Explanation: The formula approximates how AC resistance increases with frequency due to the skin effect, becoming significant when frequency approaches the skin frequency.

3. Importance of AC Resistance Calculation

Details: Accurate AC resistance calculation is crucial for power transmission systems, high-frequency circuits, transformer design, and determining conductor losses in electrical systems.

4. Using the Calculator

Tips: Enter DC resistance in ohms, operating frequency in Hz, and skin frequency in Hz. All values must be positive numbers with frequency and skin frequency greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is skin frequency?
A: Skin frequency is the frequency at which the skin depth equals the conductor radius, marking where skin effect becomes significant.

Q2: How accurate is this approximation?
A: This is a simplified approximation. For precise calculations, use the full skin effect equations that account for conductor geometry and material properties.

Q3: When does skin effect become important?
A: Skin effect becomes significant when operating frequency approaches or exceeds the skin frequency, typically in high-frequency applications above 1 kHz.

Q4: What factors affect skin frequency?
A: Skin frequency depends on conductor material (conductivity), diameter, and temperature. It's lower for larger conductors and higher conductivity materials.

Q5: How can skin effect be minimized?
A: Use stranded conductors (Litz wire), hollow conductors, or conductive coatings to reduce skin effect losses in high-frequency applications.