Introduction to Electric Circuits

106 Single-phase a.c. circuits a coil of impedance (5 + j7) 1~. Calculate for each case (i) the current drawn from the supply, ( ...

5 Three-phase a.c. circuits 5.1 INTRODUCTION Three-phase has a number of advantages over single-phase: 9 A three-phase machine ...

108 Three-phase a.c. circuits Coil A has two ends labelled a and a" coil B has two ends b and b'; coil C has ends c and c'. End ...

Figure 5.4 03 a b' c C a' (a) 5.4 Balanced three-phase systems 109 EatsE c Eb (b) 5.4 BALANCED THREE-PHASE SYSTEMS It is importa ...

110 Three-phase a.c. circuits 9 EB = -E cos 60 ~ - jE sin 60 ~ = E(-0.5 - j0.866) 9 Ec = -E cos 60 ~ + jE sin 60 ~ = E(-0.5 + ...

5.4 Balanced three-phase systems 111 Three-wire star system If the system is balanced the current in each phase can be represent ...

112 Three-phase a.c. circuits Now VAB = 2 VAN COS 0 = 2 VAN COS 30 ~ = 2 VAN ~/3/2 : ~/3 VAN But VAB = VL and VAN = Vpn SO that ...

5.4 Balanced three-phase systems 113 1 The voltage across each resistor is the phase voltage, and from Equation (5.1) VpH = VL/X ...

114 Three-phase a.c. circuits Delta system EpH = : c Figure 5.12 A IA = IL X > - Ic :' la~ ZA ZB If, instead of connecting to ...

5.5 Power in balanced three-phase circuits 115 Also there is a phase difference of 30 ~ between the line and phase currents. Exa ...

116 Three-phase a.c. circuits where VpH is the rms value of the phase voltage,/PH is the rms value of the phase current, and cb ...

5.5 Power in balanced three-phase circuits 117 Measurement of power in balanced three-phase circuits For a four-wire system it i ...

118 Three-phase a.c. circuits cos ~b so that the phase currents are lagging the phase voltages by ~b. Wattmeter W~ reads VAclA c ...

5.5 Power in balanced three-phase circuits 119 Since the phase angle ~b is given by tan -~ (reactive power/real power) then 4~ = ...

120 Three-phase a.c. c#'cuits Example 5.6 A 440 V three-phase motor has a useful output of 50 kW and operates at a power factor ...

5.6 Self-assessment test 121 7 State the phase sequence of a system for which E~ = 240 sin ~ot; E b = 240 (sin ~ot + 120~ Ec = 2 ...

122 Three-phase a.c. circuits 5.7 PROBLEMS 1 A balanced delta-connected load is supplied from a symmetrical three- phase, 400 V ...

6 Resonance 6.1 SERIES RESONANCE We saw in Chapter 4 that under certain conditions a series RLC circuit such as that shown in Fi ...

124 Resonance 9 The voltage phasor VR = IR is drawn in phase with the current phasor. The voltage V is the phasor sum of VL, Vc ...

1 Series resonance 125 9 the phase angle is 4' = 0 and the power factor is cos 4> = 1; 9 the frequency is f~ - 1,/27rk/(L ...