3.19 POINTS TO PONDER

1. Current is a scalar although we represent current with an arrow. Currents do not obey the law of vector addition. That current is a scalar also follows from it’s definition. The current I through an area of cross-section is given by the scalar product of two vectors:


I = j vector ⋅Δ S vector


where j and Δ S are vectors.

2. Refer to V-I curves of a resistor and a diode as drawn in the text. A resistor obeys Ohm’s law while a diode does not. The assertion that V = IR is a statement of Ohm’s law is not true. This equation defines resistance and it may be applied to all conducting devices whether they obey Ohm’s law or not. The Ohm’s law asserts that the plot of I versus V is linear i.e., R is independent of V.

Equation E vector = ρ j vector leads to another statement of Ohm’s law, i.e., a conducting material obeys Ohm’s law when the resistivity of the material does not depend on the magnitude and direction of applied electric field.

3. Homogeneous conductors like silver or semiconductors like pure germanium or germanium containing impurities obey Ohm’s law within some range of electric field values. If the field becomes too strong, there are departures from Ohm’s law in all cases.

4. Motion of conduction electrons in electric field E vector is the sum of (i) motion due to random collisions and (ii) that due to E vector. The motion due to random collisions averages to zero and does not contribute to vd (Chapter 11, Textbook of Class 11). vd , thus is only due to applied electric field on the electron.

5. The relation j vector = ρ v vector should be applied to each type of charge carriers separately. In a conducting wire, the total current and charge density arises from both positive and negative charges:


j vector = (ρ+) (v+ vector) + (ρ−) (v− vector)


ρ = (ρ+) + (ρ−)


Now in a neutral wire carrying electric current,


(ρ+) = − (ρ−)

Further, v+ ~ 0 which gives


ρ = 0

j vector = (ρ−) v vector

Thus, the relation j vector = ρ v vector does not apply to the total current charge density.

6. Kirchhoff’s junction rule is based on conservation of charge, and states that the outgoing currents add up and are equal to incoming currents at a junction.


Bending or reorienting the wire does not change the validity of Kirchhoff’s junction rule.