Introduction to Electric Circuits

86 Single-phase a.c. circuits the real and imaginary axes. Note that V- IVIL_~: Vcos~+ j V sin ~b = a + jb say (with a = V cos ~ ...

Example 4.12 4.4 Complex notation 87 Determine the sum of the two voltages V 1 = (10 + j50) g and V2 = (15 -j25) V. Solution Let ...

88 Single-phase a.c. circuits Example 4.14 The voltages at two points A and B are given by VA = 100/-20~ and VB- 200/_- 25 ~ V. ...

In polar form A = V/(5 2 --I-- 6 2) /tan -~ (6/5) - 7.81/_50.2~ V and B = ~/(72 + 102)/_ - tan -~ (10//7) = 12.21/_-55~ A A x B ...

90 Single-phase a.c. circuits ahead of the reference axis. The total circuit voltage V is the phasor sum of these two. In comple ...

Example 4.18 4.5 Parallel a.c. circuits 91 A coil having a resistance of 2.5 1) and the inductance of 60 mH is connected in seri ...

92 Single-phase a.c. circuits I I tO (a) IL I, [R I (b) v (reference) Figure 4.29 Dividing through by V we see that 1/Z = ~/[(1/ ...

Example 4.19 4.5 Parallel a.c. circuits 93 Determine the magnitude and phase of the current drawn from the supply in the circuit ...

94 Single-phase a.c. circuits The magnitude of I is thus u + Ic 2) and the phase angle 4~ is tan (Ic/IR). Since I- V/Z, I R -- V ...

4.6 Series-parallel a.c. circuits 95 and Bc = 1/Xc = 1/(1/2".'fC) = 2rrfC = 27r 4 x 10 3 x 10 x 10 -6 = 0.25 S so that Y = (0.2 ...

96 Single-phase a.c. circuits 12 --" (IL COS (])L) 2 q- (/L sin q~c -- Ic) 2 (4.35) and ~b = tan -1 [(Ic sin qSC -- IC)/IL COS q ...

4.7 Power in single-phase a.c. circuits 97 2 We have already calculated the phase angle of the inductive branch to be 63.4 ~ and ...

98 Single-phase a.c. circuits Note that this indicates a frequency of twice that of the supply voltage, confirming the evidence ...

v,i,p 0 P 4.7 Power in single-phase a.c. circuits 99 Figure 4.39 Purely capacitive circuits For the circuit of Fig. 4.11 the vol ...

100 Single-phase a.c. circuits In general, then, in a single-phase sinusoidal a.c. circuit for which the rms value of the supply ...

4.7 Power in single-phase a.c. circuits 101 and = cos-'(P/S) Since V- IZ and cos & = R/Z then n = VI cos 4)= (IZ)I(R/Z) = I2 ...

102 Single-phase a.c. circuits 8f~ t! lOOV 10s 7fl 9fl f 1 5~ I! 2f~ II Figure 4.43 Example 4.23 For the series-parallel circuit ...

4.8 Self-assessment test 103 Z,Z2/(Z, + Z2)= [(12.81 • 11.4)/24.2]/_(51.34 + 52.13 - 51.7) = 6.03/_51.77 ~ lI = 6.03(cos 51.77 + ...

104 Single-phase a.c. circuits 8 Determine the form factor of an alternating waveform whose rms value is 50 and whose ~ average ...

4.9 PROBLEMS 4.9 Problems 105 1 A circuit is supplied from 50 Hz mains whose voltage has a maximum value of 250 V and takes a cu ...