Duality Between Series and Parallel Circuits

There is a certain peculiar pattern of relationship between series and parallel circuits. For example,
in a series circuit. current is the same whereas in a parallel circuit. voltage is the same. Also, in a
series circuit, individual voltages are added and in a parallel circuit, individual currents are added. It
is seen that while comparing series and parallel circuits, voltage takes the place of current and current
takes tha place of voltage. Such a pattern is known as "duality" and the two circuits are said to be
duals of each other.
As arranged in Table 1.4 the equations involving voltage, current and resistance in a series
circuit have a corresponding dual counterparts in terms of current, voltage and conductance for a
parallel circuit. It is the voltage of one point in a circuit with respect to that of another point (usually called the
reference or common point).
Consider the circuit of Fig. 1.83 (a) where the most negative end-point C has been taken as the
reference. With respect to point C, both points A and B are positive thoughA is more positive than B.
The voltage of point B with respect to that of C i.e. VBC=+ 30 V.
Similarly, VAC=+ (20 + 30) =+ 50 V.
This point is often called ground or earth because originally it meant a point in a
circuit which was actually connected to earth either for safety in power
systems or for efficient radio reception and transmission. Although, this
meaning still exists, yet it has become usual today for 'ground' to mean
any point in the circuit which is connected to a large metallic object such
as the metal chassis of a transmitter, the aluminium chassis of a receiver, a
wide strip of copper plating on a printed circuit board, frame or cabinet
which supports the whose equipment. Sometimes, reference point is also
called common point. The main advantage of using a ground system is to
simplify our circuitry by saving on the amount of wiring because ground is used as the return path
for may circuits. The three commonly-used symbols for grounnd are shownVE = V0 - voltage fall across 4 Q restors =20 - 8 =+ 12 V
Also VA = VE - fall across 6 Q resistor =12 (2 x 6) =0 V
(ii) In Fig. 1.87, point D has been taken as the ground. Starting from point D, as we go to E
there is a fall of 8 V. Hence, VE = - 8 V. Similarly, VA=- (8 + 12) =- 20 V.
As we go from A to B, there is a sudden increase of 34 V because we are going from negative
terminal of the battery to its positive tenninal.
:. VB = - 20 + 34 =+ 14 V
Ve = VB - voltage fall across 2 Q resistor = \4 - 4 = + 10 V.
It should be so because C is connected directly to the positive terminal of the 10 V battery.
Choice of a reference point does not in any way affect the operation of a circuit. Moreover, it
also does not change the voltage across any resistor or between any pair of points (as shown below)
because the ground current ig=O.