Ohm's Law Basic Concepts, Parallel and Series Resistance

The Ohm's Law states that for a metallic conductor, at constant temperature, the ratio of the potential difference ratio V to the electrical current I is constant.

When an electric field is applied to an insulator like a dielectric, a polarization of the dielectric results. But if the field is applied where free charges exist, the charges are set in motion and an electric current is generated instead of a polarization of the medium.

With no external applied field, when free charges are present, such as electrons in a metal, their motion is hindered by the interaction with the atoms that form the crystal lattice of the metal. Because the electrons are moving in all directions, no net charge transport or electric current results.

However, if an external electric field is applied, a drift motion is superposed on the natural random motion of the electrons and an electric current results. This drift motion can be compared to a body falling through a viscous fluid ,where the effect of the crystal lattice may be represented by a similar “viscous” force acting on the conduction electrons.

Experimental results show that in metallic conductors the ratio of the potential difference V between two points to the electric current I is constant. This constant is named as the electrical resistance R of the conductor between the two points. This is the Ohm’s Law that can be expressed by

V/I = R or V = RI

The Ohm's Law, formulated by the German physicist Georg Ohm, applies to many conductors over a wide range of values of V, I, and temperatures of the conductor. However, for many substances, especially the semiconductors, the Ohm’s Law do not apply.

From the above Ohm's Law equation we see that R is expressed in volts/ampere, a unit called an ohm. Thus, one ohm is the resistance of a conductor through which there is a current of one ampere when a potential difference of one volt is maintained across its ends.

To maintain a current in a conductor requires an amount of energy. In a conductor, because of the interaction of the electrons and the atoms of the crystal lattice, the energy of the electron is transferred to the lattice increasing its vibration energy. This leads to an increase in the temperature of the material, which is the well known heating effect of a current called the Joule effect.

The rate at which energy is transferred to the crystal lattice can be calculated using the equation P = VI, valid for any material, where P is the power. For conductors who follow Ohm’s law,
V = IR, and the power may be written in the alternative form
P = I²R.

Resistors can be combined in two kinds of arrangements: series and parallel. In the series combination the same current "I" flows along each resistor. The potential drop across each resistor, according to Ohm’s law, is V₁ = R₁I, V₂ = R₂I,….., V_n = R_nI. The overall potential difference is

V = V₁ + V₂ + ……. + V_n = (R₁ + R₂ + ….. + R_n)I

The system can be replaced for a single resistor R satisfying V = IR. Therefore,

R = R₁ + R₂ + …..+ R_n

In the parallel combination the resistors are connected in such a way that the potential difference V is the same for all of them. The current through each resistor, according to Ohm’s law, is
I₁ = V/R₁, I₂ = V/R₂, ……, I_n = V/R_n. The total current "I" supplied to the system is

I = I₁ + I₂ +……+ I_n = (1/R₁ + 1/R₂ + …… + 1/R_n)V

The system can be replaced for a single resistor R satisfying
I = V/R. Therefore,

1/R = (1/R₁ + 1/R₂ + …… + 1/R_n)

Ohm's Law Exercises