Define Resistance and Conductance | SI Unit and Dimensions

Define Resistance and Conductance | SI Unit , Dimensions

Resistance of a conductor is the opposition offered by the conductor to the flow of electric charge in the conductor.

Resistance of a conductor is defined as the ratio of the potential difference across the ends of the conductor to the current flowing through it.

That is,

$R = \frac{V}{I}$

It's S.I unit is ohm ($\Omega$)

$1 \text{ ohm } (\Omega) = \frac{1 \text{ volt } (V)}{1 \text{ ampere } (A)} \quad \text{ or } 1 \Omega = 1 VA^{-1}$

Resistance of a conductor is said to be 1 ohm, if current of 1 A flows through it, when potential difference of 1 V is applied across it.

$[R] = \frac{[V]}{[I]}$

$[R]= \frac{[\text{Work}]}{[\text{Charge}] \times [\text{Current}]}$

$[R]=\frac{[\text{Work}]}{[\text{Current}] \times [\text{Time}] \times [\text{Current}]}$

$= \frac{[ML^2T^{-2}]}{[A^2T]}$

$= [ML^T^{-3}A^{-2}]$

Conductance:

Conductance of a substance is equal to the inverse of its resistance.

That is,

$G = \frac{1}{R}$

ohm$^{-1}$ ($\Omega^{-1}$) or mho or siemen (S).

$[G] = \frac{1}{[R]} = [M^{-1}L^{-2}T^3A^2]$

Note :Conductance of a substance is also denoted by letter S.