PHYSICS

the potential difference across the horizontal plates which varies
in time with a sawtooth waveform. The field across the vertical
plates is controlled by the potential difference across the source
under investigation, hence a two dimensional image is formed on
the screen.
15.3. CURRENT ELECTRICITY
15.3.1. Electric Current
The term electric current is used to describe the rate of flow of
charge through some region of space. If L1q is the amount of
charge that passes through the area (S) in a time interval L1t, the
average current « I » is equal to the ratio of the charge to the
time interval:
< I > = ~q (15.16)
~t
If the rate at which the charge flows varies in time, the
current also varies in time and we define the instantaneous current
(I) as the differential limit of the expression above:
1= dq
dt
The unit of current is the ampere (1 A = 1 Cis).
(15.17)
The current density (J) in the conductor is defined as the
current per unit area:
. I
J = S (15.18)
where I is a current, and S is the cross-sectional area of the
conductor.
This expression is valid only if the current density is uniform
and the surface is perpendicular to the direction of the current. In
general, the current density is a vector quantity. That is:
J = nq < V > (15.19)
where n represents the number of mobile charge carriers per unit
volume which move with an average speed « V».
The unit of current density is A/m 2 •
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15.3.2. Current Circuits
A closed circuit consists of a source of energy (e.g., a battery),
called an electromotive force (E. M. F.) , and a resistor (fig. 15.4).
Assuming that the connecting
wires have no resistance, the
source of E.M.F., E, has its
own internal resistance (r). The
external resistance (R), is often
called the load resistance. The
I
voltage (U) is the difference in
R electric charge between two
points in a circuit.
The unit of E.M.F. and
voltage is the volt; resistance
Fig. 15.4. Diagram of simple has units of volt per ampere
electric circuit (iQ = IVIA).
15.3.3. Ohm's Law
Ohm's Law for Part of a Circuit: The electric current (I) flowing
through a given resistance (R) is equal to the applied voltage (U)
divided by the resistance, or:
1= U (15.20)
R
Ohm's Law for a Closed Circuit: The amount of current flowing in
a circuit made up of pure resistance is directly proportional to the
electromotive forces impressed on the circuit and inversely
proportional to the total resistance of the circuit:
1= E/(R + r) (15.21)
15.3.4. Kirchhoff's Rules
Complex circuits (fig. 15.5) involving more then one loop are
conveniently analyzed using Kirchhoff's rules:
1. The sum of currents entering any junction must equal the sum
of the currents leaving that junction:
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