Building Design and Construction Handbook - Merritt - Ventech!

15.4 SECTION FIFTEEN
E � IR E � IR ���E � IR (15.4)
1 1 2 2 n n
Kirchhoff’s law for series circuits states that the total voltage drop in a circuit
is the sum of the voltage drops:
E � E � E � E � ���� E
T 1 2 3 n
� IR � IR � IR � ���� IR (15.5)
1 2 3 n
� I(R � R � R � ���� R )
1 2 3 n
By Ohm’s law the total resistance in a series circuit then is
R � R � R � R � ���� R (15.6)
1 2 3 n
Parallel Circuits. These are, by definition, circuits in which the same voltage drop
is applied to each circuit (Fig. 15.1b). The resistance of each circuit is obtained by
multiplying the resistance per foot by the length, ft.
Kirchhoff’s law for parallel circuits states that the total current in a circuit is
equal to the sum of the currents in each part:
I � I � I � I � ���� I
T 1 2 3 n
E E E E
� � � � ���� (15.7)
R R R R
� �
1 2 3 n
1 1 1 1
� E � � � ����
R R R R
1 2 3 n
By Ohm’s law, then, the total resistance R in a parallel circuit is given by
1 1 1 1 1
� � � � ���� (15.8)
R R R R R
1 2 3 n
It is sometimes convenient to use conductance G, siemens (formerly mhos), which
is the reciprocal of resistance R:
By Ohm’s law,
1
G � (15.9)
R
I � EG � EG � EG � ���� EG (15.10)
T 1 2 3 n
Series circuits are most commonly used in street, airport runway, and subway
lighting. Most building systems use parallel circuits for both motor and lighting
distribution.
Network systems consisting of a combination of series and parallel circuits are
used for municipal distribution.