# Resistance, Conductance, Impedance and Admittance Formulas

## Formulas & Equations for Resistance, Conductance, Impedance & Admittance

Table of Contents

**Resistance **Formulas

Resistance is the opposition to the flow of electrical current denoted by “R” and measured in ohms “Ω”. For any metal conductor “R” is given by:

**R = ρl / A**

Where

- R is the resistance
- ρ (Greek word Rho)is
*specific electrical resistance*of the conductor - l is the length of the conductor
- A is the cross-sectional area of the conductor

**Resistance Formulas in DC Circuits**

**R = V / I****R = P / I**^{2}**R = V**^{2}/ P

Where:

- R is the resistance
- I is the electric current
- V is the voltage
- P is the electrical power

Keep in mind that in pure resistive circuit (Where only and only resistors are used), electric resistance “R” is equal to the impedance “Z”. In other words, Resistance and impedance is the same thing in pure resistive circuits.

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**Conductance Formulas**

The conductance is the inverse of resistance. It is the allowance of the electrical current through a conductor, denoted by “G” and measured in Siemens represented by the symbol of “Mho” (℧).

**G = σA / l**

Where

- G is the Conductance
- A is the area
- l is the length
- σ (Greek word sigma) is the electrical conductivity

### Impedance Formulas

The opposition of a circuit to the current when voltage is applied is impedance, denoted by “Z” and it is measured in Ohms (Ω).

**Z = R + jX**

Where

- Z is the Impedance
- R is the real part, resistance of the circuit
- X is the imaginary part, reactance of the circuit.

Impedance in Pure resistive circuits:

**Z ^{2} = R^{2} + X^{2}**

Impedance in inductive circuits:

**Z = √(R ^{2} + X_{L}^{2})**

Impedance in capacities circuits:

**Z = √(R ^{2} + X_{C}^{2})**

Impedance in capacities and inductive circuits:

**Z = √(R ^{2} + (X_{L}– X_{C})^{2}**

Where:

- Z is the impedance in ohms
- R is the resistance in ohms
- X
_{L}is the inductive reactance in ohms - X
_{C}is the capacitive reactance in ohms

In addition,

- Inductive reactance = X
_{L }= 2π*f*L…Where L = Inductance in Henry - Capacitive reactance = X
_{C}= 1/2π*f*C… Where C = Capacitance in Farads.

Also;

- ω = 2π
*f*

### Admittance Formulas

The inverse of Impedance is Admittance denoted by “Y” and it is measured in “Siemens” represented by the symbol of “℧” (Mho). Components of admittance can be calculated by the following formulas.

**Y = 1 / Z**

**Y = G + JB**

Where

- Y is the Admittance
- G is the real part known as Conductance of the circuit
- B is the imaginary part of admittance known as
**Susceptance**

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