What are the intrinsic safety cable parameters?

1. Parameters: Resistance (R), Inductance (L), and Capacitance (C)

In intrinsically safe (IS) systems, the cable parameters—resistance (R), inductance (L),
and capacitance (C)—are critical to ensure safe operation by limiting the energy stored and transmitted through the cable.

2. Resistance (R): Formula and Calculation

Resistance (R) depends on the conductor's material, cross-section, and length.
The formula for resistance is:
R = ρ * (Lk / A)
Where:
- ρ: Resistivity of the conductor material (e.g., copper = 0.0175 Ω·mm²/m).
- Lk: Total cable length (round trip) in meters.
- A: Cross-sectional area of the conductor in mm².
Example Calculation:
- Cable Length (Lk): 100 m
- Conductor Cross-Section (A): 1.5 mm²
- Resistivity (ρ): 0.0175 Ω·mm²/m

R = 0.0175 * (100 / 1.5) = 1.167 Ω

3. Inductance (L): Formula and Calculation

Inductance (L) determines the cable's ability to store energy in a magnetic field.
For single-core cables, inductance is calculated as:
L = 2 * 10^(-7) * ln(2D / d)
Where:
- D: Center-to-center distance between conductors (in meters).
- d: Diameter of the conductor (in meters).

For standard IS cables, typical inductance values are 0.6–0.8 mH/m.
Total inductance for a given length is calculated as:
L_total = L_m * Lk, where L_m is inductance per meter and Lk is the cable length.

4. Capacitance (C): Formula and Calculation

Capacitance (C) refers to the cable's ability to store energy in an electric field.
It is crucial for IS systems to limit the maximum capacitance to avoid unintended energy storage.

For a parallel wire pair, capacitance per unit length can be estimated as:
C = (πε / ln(D/d))
Where:
- ε: Permittivity of the insulating material.
- D: Center-to-center distance between conductors (m).
- d: Diameter of the conductor (m).

Total capacitance:
C_total = C_m * Lk
Where C_m is capacitance per meter.
5. Example: Full Parameter Calculation
Given an IS system with:
- Maximum Resistance (R_max): 5 Ω
- Maximum Inductance (L_max): 1 mH
- Maximum Capacitance (C_max): 80 nF
- Cable Length: 50 m
- Cable Specifications: 1 mm² copper conductor, L_m = 0.02 mH/m, C_m = 150 pF/m

Calculation:
1. Resistance: R = 0.0175 * (50 / 1) = 0.875 Ω
2. Inductance: L_total = 0.02 * 50 = 1.0 mH
3. Capacitance: C_total = 150 * 10^(-12) * 50 = 7.5 nF

Results:
- R = 0.875 Ω < R_max = 5 Ω
- L_total = 1.0 mH = L_max
- C_total = 7.5 nF < C_max = 80 nF

The cable meets IS safety requirements.

Intrinsic Safety Cable Parameters
1.   Resistance (R)

Resistance is the opposition to the flow of electrical current in the cable. It depends on the resistivity of the conductor material, the cross-sectional area of the conductor, and the cable length.

Formula:

R = ρ * (Lk / A)

Where:
- ρ: Resistivity of the conductor material (e.g., copper = 0.0175 Ω·mm²/m).
- Lk: Total cable length (including round trip, in meters).
- A: Cross-sectional area of the conductor (in mm²).
2.   Inductance (L)

Inductance represents the ability of the cable to store energy in a magnetic field. It depends on the geometry of the conductors, their separation, and the magnetic permeability of the surrounding medium.

Formula for two parallel conductors:

L = 2 * 10^(-7) * ln(2D / d)

Where:
- D: Center-to-center distance between conductors (m).
- d: Diameter of the conductor (m).

3.   Capacitance (C)

Capacitance is the ability of the cable to store energy in an electric field.  It arises from the insulating material between conductors and the geometry of the cable.

Formula for a parallel conductor cable:

C = (π * ε) / ln(D / d)

Where:
- ε: Permittivity of the insulating material.
- D: Center-to-center distance between conductors (m).
- d: Diameter of the conductor (m).
4.   Example Calculations

Given an IS system with:
- Maximum Resistance (R_max): 5 Ω
- Maximum Inductance (L_max): 1 mH
- Maximum Capacitance (C_max): 80 nF
- Cable Length: 50 m
- Cable Specifications: 1 mm² copper conductor, L_m = 0.02 mH/m, C_m = 150 pF/m

Results:
1. Resistance: R = 0.0175 * (50 / 1) = 0.875 Ω
2. Inductance: L_total = 0.02 * 50 = 1.0 mH
3. Capacitance: C_total = 150 * 10^(-12) * 50 = 7.5 nF

Compliance Check:
- R = 0.875 Ω < R_max = 5 Ω
- L_total = 1.0 mH = L_max
- C_total = 7.5 nF < C_max = 80 nF

The cable meets IS requirements.