Conductance of Coaxial Cable Calculator

Formula Used:

\[ G_c = \frac{2 \pi \sigma_c}{\ln\left(\frac{b_r}{a_r}\right)} \]

Electrical Conductivity (σc):

S/m

Outer Radius of Coaxial Cable (b_r):

Inner Radius of Coaxial Cable (a_r):

Conductance of Coaxial Cable (G_c):

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1. What is the Conductance of Coaxial Cable?

The Conductance of a Coaxial Cable is a measure of how easily electric current can flow through the cable. It is the reciprocal of resistance and depends on the material properties and geometric dimensions of the cable.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ G_c = \frac{2 \pi \sigma_c}{\ln\left(\frac{b_r}{a_r}\right)} \]

Where:

\( G_c \) — Conductance of Coaxial Cable (S)
\( \sigma_c \) — Electrical Conductivity (S/m)
\( b_r \) — Outer Radius of Coaxial Cable (m)
\( a_r \) — Inner Radius of Coaxial Cable (m)
\( \pi \) — Archimedes' constant (≈3.14159)
\( \ln \) — Natural logarithm function

Explanation: The formula calculates the conductance based on the electrical conductivity of the material and the geometric ratio of the outer to inner radius.

3. Importance of Conductance Calculation

Details: Accurate conductance calculation is crucial for designing efficient coaxial cable systems, minimizing signal loss, and ensuring proper impedance matching in telecommunications and RF applications.

4. Using the Calculator

Tips: Enter electrical conductivity in S/m, outer and inner radii in meters. All values must be positive, and the outer radius must be greater than the inner radius.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between conductance and resistance?
A: Conductance is the reciprocal of resistance. Higher conductance means lower resistance to current flow.

Q2: Why does the formula use natural logarithm?
A: The natural logarithm accounts for the radial distribution of the electric field in the coaxial cable geometry.

Q3: What are typical values for electrical conductivity?
A: Copper has conductivity of about 5.96×10⁷ S/m, while aluminum is about 3.5×10⁷ S/m at room temperature.

Q4: How does cable geometry affect conductance?
A: Conductance increases with larger cross-sectional area and decreases with longer cable length. The radius ratio affects the field distribution.

Q5: Are there limitations to this formula?
A: This formula assumes uniform material properties, perfect cylindrical symmetry, and neglects skin effect at high frequencies.