REVIEW OF FUNDAMENTALS OF ELECTRICITY WITH TELECOMMUNICATION APPLICATIONS
The phase relationship between current
) and emf (voltage, V
) for an ac capaci-
is equal to the square root of the average of the squares of the instantaneous values over
1 cycle (2
radians). This results in 0.707 times the maximum value or
I = 0.707(I
E = 0.707(E
E and I without subscripts are effective values. Unless otherwise stated, ac voltages
and currents are always given in terms of their effective values.
Calculating Power in ac Circuits
Equation (A.14) provided an expression for power in a dc circuit. The problem with ac
circuits is that the voltage and current are constantly changing their values as a function
of time. At any moment in time the power generated or dissipated by a circuit is
P = EI
P is expressed in watts, E in volts, and I in amperes.
Also, Eqs. (A.15) and
(A.16), Ohm's law variants of Eq. (A.14), are also valid here.
Across a resistive circuit, such as in Figure A.18a, where by definition, the ac voltage
and current are in phase, Eq. (A.29) expresses the power. Here, voltage and current are
Now if the circuit that the ac generator looks into is inductive (Figure A.19a) or
capacitive (Figure A.20a), the calculation of power is somewhat more complicated. The
problem is that the voltage and current are out of phase one with the other, as illus-
trated in Figures A.19b and A.20b. The true power in such circuits will be less than
the power calculated with Eq. (A.29) if the circuit were purely resistive. The power
in such circumstances can be calculated by applying the power factor. Equation (A.29)
P = EI cos ,
is the phase angle, the angle that voltage leads or lags current. Earlier we were
expressing phase angle in radians (see Figure A.17 and its discussion). Again, there are
This equation is identical to Eq. (A.14).