Page 14 - Schaum's Outline of Theory and Problems of Electric Circuits

INTRODUCTION
CHAP. 1]

Fig. 1-1 3

Of more importance in electric circuit analysis is the current in metallic conductors which takes place
through the motion of electrons that occupy the outermost shell of the atomic structure. In copper, for
example, one electron in the outermost shell is only loosely bound to the central nucleus and moves
freely from one atom to the next in the crystal structure. At normal temperatures there is constant,
random motion of these electrons. A reasonably accurate picture of conduction in a copper conductor
is that approximately 8:5 10 28 conduction electrons per cubic meter are free to move. The electron
charge is e ¼ 1:602 10 19 C, so that for a current of one ampere approximately 6:24 10 18 elec-
trons per second would have to pass a fixed cross section of the conductor.

EXAMPLE 1.2. A conductor has a constant current of five amperes. How many electrons pass a fixed point on
the conductor in one minute?
5A ¼ð5C=sÞð60 s=minÞ¼ 300 C=min
300 C=min 21
¼ 1:87 10 electrons=min
1:602 10 19 C=electron

1.4 ELECTRIC POTENTIAL
An electric charge experiences a force in an electric field which, if unopposed, will accelerate the
particle containing the charge. Of interest here is the work done to move the charge against the field as
suggested in Fig. 1-2(a). Thus, if 1 joule of work is required to move the charge Q, 1 coulomb from
position 0 to position 1, then position 1 is at a potential of 1 volt with respect to position 0; 1 V ¼ 1J=C.
This electric potential is capable of doing work just as the mass in Fig. 1-2(b), which was raised against
the gravitational force g to a height h above the ground plane. The potential energy mgh represents an
ability to do work when the mass m is released. As the mass falls, it accelerates and this potential energy
is converted to kinetic energy.

Fig. 1-2