By C.H. Laycock
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4 at 33° 49' Use of the j Operator While the use of the above formulae with phasor diagrams is satisfactory for simpler series and parallel circuit problems, more complex examples require a less laborious method. The reader will be aware that any phasor can be expressed in cartesian form as well as by the polar co-ordinates used above. The rectangular cartesian co-ordinates may be quoted in complex form allowing the phasor to be drawn on an Argand diagram. 8a shows the phasor whose polar co-ordinates are R L() drawn on an Argand diagram.
1 Thevenin's Theorem Any two-terminal network may be replaced by a voltage generator equal to the open -circuit output voltage in series with an impedance equal to the input impedance of the network when all voltage and current sources have been replaced by their internal impedances. 18b . 18a. 18c) . 18d. 18b where VTh = 10 V and ZTh = 5 n resistive. c. c. sources and impedances. Another similar theorem allows any network to be simplified in another way . 2 Norton's Theorem Any two-terminal network may be replaced by a current generator equal to the short-circuit output current of the network in parallel with an impedance equal to the input impedance of the network when all voltage and current sources have been replaced by their internal impedances.
For example , in the RL case merely put Xc to zero and for the RC case put XL to zero. 7 ; since R , L and C are in parallel it is the voltage V that is common to all three. The voltage phasor V is thus made the reference phasor which is conventionally drawn horizontally. The resistor current I R will have a magnitude VIR and will be in phase with V. Similarly h and Ie will have magnitudes V/XL and V/Xe respectively in the directions shown. Phasor addition of h and Ie gives (h - Ie) which when combined with IR gives the total current I as shown (assuming Xc> XL).
Applied Electrotechnology for Engineers by C.H. Laycock