ects of alternating and direct currents are different. This is known as the effective value and REVIEW OF FUNDAMENTALS OF ELECTRICITY WITH TELECOMMUNICATION APPLICATIONS Phase Figure A.20b The phase relationship between current (lc) and emf (voltage, Vc) for an ac capaci- tive circuit. 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(Imax), (A.28a) E = 0.707(Emax), (A.28b) where E and I without subscripts are effective values. Unless otherwise stated, ac voltages and currents are always given in terms of their effective values. A.8.1 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 (A.29) where P is expressed in watts, E in volts, and I in amperes. 7 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 effective values. 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) now becomes P = El cos A, (A.30) where O 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 7 This equation is i