Q. Define Resistance in lumped-circuit?

An ideal resistor is a circuit element with the property that the current through it is linearly proportional to the potential difference across its terminals,

i = v/R = G_v, or v = iR

which is known as Ohm's law, published in 1827. R is known as the resistance of the resistor with the SI unit of ohms (), and G is the reciprocal of resistance called conductance, with the SI unit of siemens (S). The circuit symbols of fixed and variable resistors are shown in Figure, along with an illustration of Ohm's law. Most resistors used in practice are good approximations to linear resistors for large ranges of current, and their i-v characteristic (current versus voltage plot) is a straight line.

The value of resistance is determined mainly by the physical dimensions and the resistivity ρ of the material of which the resistor is composed. For a bar of resistive material of length l and cross-sectional area A the resistance is given by

where ρ is the resistivity of the material in ohm-meters ( · m), and σ is the conductivity of the material in S/m, which is the reciprocal of the resistivity.Metal wires are often considered as ideal