ABSTRACT
In parallel circuits, such as those shown in Figures 18.1 and 18.2, 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 = I 2RR watts
Apparent power, S = VI voltamperes (VA) Reactive power,Q = VI sinφ reactive
voltamperes (var)
Power factor= true power apparent power
= P S
= cosφ
(These formulae are the as used in Chapter 17.)
In the two-branch parallel R and inductance L flowing in the resistance, I voltage V and the current L, lags the supply voltage by is the phasor sum of IR and I the applied voltage V by 90◦ (depending on the as angle φ in the phasor
I = √(I 2R + I 2L) (by Pythagoras’ theorem)
where IR = V R
and IL = VXL tanφ = IL
IR ,sinφ = IL
I and
cosφ = IR I
(by trigonometric ratios)
Circuit impedance,Z = V I
Problem 1. A 20 resistor is connected in parallel with an inductance of 2.387mH across a 60V, 1kHz supply. Calculate (a) the current in each branch, (b) the supply current, (c) the circuit phase angle, (d) the circuit impedance, and (e) the power consumed.
