ABSTRACT
At the end of this chapter you should be able to: • draw phasor diagrams and current and voltagewaveforms for (a) purely resistive (b) purely inductive and (c) purely capacitive a.c. circuits
• perform calculations involving XL = 2πfL and XC = 12πfC• draw circuit diagrams, phasor diagrams and voltage and impedance triangles for R-L, R-C and R-L-C series a.c. circuits and perform calculations using Pythagoras’ theorem, trigonometric ratios and Z = V
I• understand resonance • derive the formula for resonant frequency and use it in calculations
• understand Q-factor and perform calculations using VL(or VC)
V or
ωrL R
or 1
ωrCR or
1 R
√( L C
)
• understand bandwidth and half-power points • perform calculations involving ( f2 − f1)= frQ• understand selectivity and typical values of Q-factor • appreciate that power P in an a.c. circuit is given by
P=VI cosφ or I2RR and perform calculations using these formulae
• understand true, apparent and reactive power and power factor and perform calculations involving these quantities
15.1 Purely resistive a.c. circuit
In a purely resistive a.c. circuit, the current IR and applied voltage VR are in phase. See Figure 15.1.
