ABSTRACT
At the end of this chapter you should be able to:
• calculate unknown currents, impedances and circuit phase angle from phasor diagrams for (a) R-L (b) R-C (c) L-C (d) LR-C parallel a.c. circuits
• state the condition for parallel resonance in an L R-C circuit • derive the resonant frequency equation for an LR-C parallel a.c. circuit • determine the current and dynamic resistance at resonance in an LR-C parallel circuit • understand and calculate Q-factor in an LR-C parallel circuit • understand how power factor may be improved
In parallel circuits, such as those shown in Figs 16.1 and 16.2, the voltage is common to each branch of the network and is thus taken as the reference phasor when drawing phasor diagrams. For any parallel a.c. circuit:
True or active power, P=VI cosφ watts (W) or P =I2R R watts Apparent power, S=VI voltamperes (VA) Reactive power, Q=VI sinφ reactive
voltamperes(var)
Power factor = true power apparent power
= PS = cosφ
(These formulae are the same as for series a.c. circuits as used in Chapter 15.)
In the two branch parallel circuit containing resistance R and inductance L shown in Fig. 16.1, the current flowing in the resistance, IR, is in-phase with the supply voltage V and the current flowing in the inductance, IL, lags the supply voltage by 90◦. The supply current I is the phasor sum of IR and IL and thus the current I lags the applied voltage V by an angle lying between 0◦ and 90◦ (depending on the values of IR and IL), shown as angle φ in the phasor diagram.
