AC_Notes

 2015 Yeow Kok Han Page 1 Alternating Current 11 BBaassiiccss ooff AACC An alternating current is a current whose magnitude and direction varies periodically. We focus on sinusoidal a.c. because any given non-sinusoidal current can be synthesised from a selection of sinusoidal alternating currents of appropriate weightings and frequencies. Period T the time taken for one cycle of variation. Frequency f the number of cycles per unit time. Peak value the maximum magnitude of current I0 or voltage V0. Peak to peak value the magnitude of the interval between the positive peak and negative peak. 2I0 or 2V0. 22 PPoowweerr && RRMMSS vvaalluuee TThhee rreepprreesseennttaattiivvee mmeeaann ppoowweerr P = IV, hence if I and V both vary with time as shown (in phase for resistive load), the resultant power is given by the product of I and V moment by moment, resulting in a sin2 variation. A typical a.c. has frequency 50 Hz, so the instantaneous power fluctuates at 100 Hz. For many applications such as lighting or heating, the fluctuation is not noticeable. What we observe is the mean effect, hence it is more useful to measure the mean power and regard it as representative or effective power of an a.c.. An alternating current is a current whose magnitude and direction varies periodically. In contrast, a d.c. doesn’t change direction. For a fluctuating power of an a.c., the mean power is more useful & representative. I t I0 -I0 2T T 0 t V0 V -V0 2T T 0 t I0V0 P 2T T 0 P0 I0V0 I = I0 sint V = V0 sint P = I0V0 sin2t time I0, V0 Current or voltage -I0, - V0 2T T 0

 2015 Yeow Kok Han Page 2 TThhee rr..mm..ss.. vvaalluuee ffoorr ccuurrrreenntt aanndd vvoollttaaggee For sinusoidal a.c. current or voltage, is the mean value a use ful representative value? No, because the mean is zero for any amplitude so it cannot t ell us its effectiveness in producing useful work . What value then should we look at? Consider the rate of heating in a resistor, P = I2R (note P and I2 are time varying). The representative mean power <P> is = < I2>R, where <I2> is the mean square current. For the same resistance R, i f a constant current Ic gives a power Pc which is = <P>, then we can take Ic to be a good representative or effective current of the a.c. since Ic essentially produces the same outcome. As Pc = <P>, Ic 2 = <I2> and so Ic =  2I . This constant Ic that is representative of the effectiveness of the a.c. is formally known as root mean square or r.m.s current. A similar consideration using P = V2/R leads to the r.m.s. voltage  2V . Hence, the r.m.s. value of an alternating current is defined as How is the r.m.s. value calculated? Looking at the origin of r .m.s. value, it is not difficult to see that it is calculated b