Current Electricity and Equivalent Resistance

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CURRENT ELECTRICITY - 1
(electric current, drift velocity, resistivity & resistance, effect of temperature on resistivity & resistance, ohm's law, resistances in series & parallel, equivalent resistance)
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1. Current electricity (or electric current): Charges in motion are called "current electricity" or "electric current". Obviously, a suitable conducting medium (conductor) and a driving force have to be available for the charges to flow.

2. Conductors and insulators: Conductors are the materials which have large numbers of free (to move) electrons, the electrons which are not attached to their atoms. On the other hand, insulators which have few such free electrons. Since flow of electric current requires motion of charge (free electrons), a conductor is a suitable medium for the flow of electric current.

3. Driving force for flow of electrons in a conductor: We have learnt in electrostatics, a charge placed in an electrostatic field experiences a force; a positive charge in the direction of the field (E vector) and a negative charge opposite to it. Hence, in order to make the free electrons in a conductor move, we must create an electrostatic field within the conductor. To do so, a potential difference (V) is applied across the conductor (of length L) say by connecting it to a battery. An electric field of magnitude E = V/L (as dE = - dV/dl) is set up within the conductor. Electric field vector E points from the +ve potential towards the -ve potential. Each free electron experiences a force equal to eE in the direction -ve potential to +ve potential (being negatively charged) and starts moving in that direction. The potential difference applied across a conductor is therefore the "driving force" for flow of current in a conductor.

Why does the electric field vector E point from +ve to -ve potential within the conductor?

This is because, a positive charge placed at any point in the conductor, repelled by the +ve potential and attracted by the -ve potential will move in the direction +ve to -ve and as the direction of motion of a positive charge in an electric field must correspond to the direction of ...