Building Design and Construction Handbook - Merritt - Ventech!

ELECTRICAL SYSTEMS 15.9
E � IZ cos � (15.16)
C
R � Z cos � (15.17)
C
Note that the phasors for inductance and capacitance are in opposite directions.
Thus, when a circuit contains both inductance and capacitance, they can be added
algebraically. If they are equal, they cancel each other, and the Z value is the same
as R. If the inductance is greater, Z will be in the upper quadrant. A greater value
of capacitance will throw Z into the lower quadrant.
The diagram indicates that
L � C
tan � � (15.18)
R
Kirchhoff’s laws are applicable to alternating current circuits containing any
combinations of resistance, inductance, and capacitance by means of phasor analysis:
In a series circuit, the current I is equal in all parts of the circuit, but the total
voltage drop is the phasor sum of the voltage drops in the parts. If the circuit has
resistance R, inductance L, and capacitance C, the voltage drops must be added
phasorially as described in the preceding. Equations (15.14) to (15.18) hold for ac
series circuits. To find the voltage drop in each part of the circuit, compute
E � IR E � IX E � IX
R L L C C
E � E � E � E (phasorially) (15.19)
Z R L C
In a parallel circuit, the voltage E across each part is the same and the total
current I Z is the vector sum of the currents in the branches,
E E E
� I � I � I
R X X
R L C
L C
For parallel circuits, it is convenient to use the reciprocals of the resistance and
reactances, or susceptances, respectively S R, S L, and S C. To find the current in each
branch then, compute
ES � I ES � I ES � I
R R L L C C
I � I � I � I (phasorially) (15.20)
Z R L C
Power in AC Circuits. Pure inductance or capacitance circuits store energy in
either electric or magnetic fields and, when the field declines to zero, this energy
is restored to the electric circuit.
Power is consumed in an ac circuit only in the resistance part of the circuit and
equals E R, the effective voltage across the resistance, times I R the effective current.