Page 62 - Mechanical Engineers Reference Book

Basic electrical technology 2/3
asis electrical technology 2.1.3 Electromotive force and potential difference
2.1.1 ]Flux and potential difference In a metallic conductor which has a potential difference
applied across opposite ends. free electrons are attracted to
The concept of flux and potential dnfference enables a unified the more positive end of the conductor. It is this drift of
approach to be adopted for virtually all the ‘field’ type of electrons which constitutes the electric current. and the effect
problems. Generally, the flowing quantity is termed the flux is simply Nature’s attempt to redress an energy imbalance.
and the quantity which drives the flow is called the potential Although the negatively charged electrons actually drift to-
difference. This consistency of method is equally applicable to wards the positive end of the conductor, traditional conven-
problems in fluid flow, heat transfer, electrical conduction. tion gives the direction of the current flow from positive to
electrostatics and electromagnetisn, to name but a few. negative. There is nothing really at issue here, since it is only a
In general terms, the flux may be written as simple sign convention which was adopted long before the true
nature of the atom and its associated electrons were postu-
(Field characteristic) x (Cross-sectional area) x (Potential difference)
Flux = - lated.
(Length) A current of 1 A is associated with the passage of
6.24 x 10“ electrons across any cross-section of the conductor
(2.1)
per second. The quantity of charge is the coulomb, Q, and
In specific terms, for the flow of an electric current through a Q=I.t (2.9)
conducting medium, equation (2.1) takes the form:
where 1 coulomb of charge is passed when a current of 1 A
ua V flows for a period of 1 s.
I=-
I (2.2) The electromotive force (e.m.f.1 is that which tends to
produce an electric current in a circuit, and is associated with
where I is the current in amperes (A), the energy source. Potential difference is simply the product of
n is the conductivity of the medium (siemensim), i.e. current and resistance across any resistive element in a circuit,
the field characteristic, irrespective of the energy source. For circuit elements other
a is the cross-sectional area of the medium (m2), than purely resistive, the potential difference across the ele-
1 is the length of the medium (m), and ment becomes a time-dependent function.
Vis the applied potential difference, or voltage (V).
The gr0u.p (mil) is termed the conductance, denoted by G and 2.1.4 Power and energy
measured in siemens, thus:
Power is the rate at which energy is expended, or suppiied.
I=GV (2.3) The potential difference across any two points in a circuit is
The reciprocal of conductance is referred to as the resist- defined as the work done in moving unit charge from a lower
ance, R and is measured in ohms (a). Hence to a higher potential. Thus the work done in moving Q
coulombs of charge across a constant potential difference of V
I = ViR (2.4) volts is:
Equation (2.4) is the familiar ‘Ohm’s law’, which defines a W=Q.V (2.10)
linear relationship between voltage and current in a conduct- Therefore
ing medium. If the resistance, R, varies with the magnitude of
the voltage, or the current, then the resistance is non-linear. dW dQ
Rectifiers constitute one particular class of non-linear res- Power = - = - V
dt
dt
istors.
Comparing equations (2.4) and (2.2) gives: From equation (2.9) (dQidt) = I. thus
R = l/(aa) (2.5) Power = IV (2.11)
It is mor15 usual, however, to quote the ‘resistivity’ as opposed Using Ohm’s law, the power dissipated across a simple
to the conductivity, and resistance is generally written as: resistive circuit element is
R = plla (2.6) Power = IV = I(I. R) = 12R (2.12)
where p is the resistivity of the conductor in ohm-metres.
The resistame of all pure metals is temperature dependent, 2.1.5 Network theorems
increasing linearly for moderate increases in temperature. A network consists of a number of electrical elements con-
Orher materials, including carbon and many insulators, exhi- nected up in a circuit. If there is no source of electromotive
bit a decreasing resistance for an increase in temperature. force in the circuit it is said to be passive. When the network
contains one or more sources of electromotive force it is said
2.1.2 Simple resistive circuits to be active.
A number of well-established theorems have been deve-
The effective total resistance of a series arrangement is the loped for the analysis of complex resistive networks and are
algebraic sum of all the resistances in series, i.e. listed below:
R, = Ri + R2 + R3 (2.7) Kirchhoffs first law: The algebraic sum of the currents
where R, is the total resistance of the circuit. entering (+ve) and leaving (-ve) a junction is zero.
For resistors in parallel the effective total resistance obeys Kirchhoffs second law: The algebraic sum of potential differ-
an inverse summation law, i.e. ences and e.m.f.’s around any closed circuit is zero.
Superposition theorem: In a linear resistive network containing
more than one source of e.m.f. the resultant current in any
branch is the algebraic sum of the currents that would be