By Theodore V. Karman and Maurice A. Biot
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22b . Number the meshes and insert clockwise circulating currents as shown . For mesh 1 +6 For mesh 2 -4 = II (2 + 10) - 12 (10) - 13 (2) -II (10) + 12 (10 + 3) - 13 (3) o = -- II For mesh 3 (2) - h (3) + h (2 + 3 + 6) We may check these equations for errors in two ways (i) The positive signs should proceed in one diagonal line , all other terms on the right-hand side being negative. 24 is by the use of determinants. 24. When arranged in this systematic way they are eminently suitable, of course, for computer solution.
3 showed that a current multiplication effect can occur in parallel circuits. At the resonant frequency, the current multiplication factor Qo is given by Ie I Qo = - = Qo = tan e tc sin rp h cosrp woL = -- R Thus the voltage multiplication factor for series resonance and the current multiplication factor for parallel resonance are numerically equal and equal to the Q-factor. 17 shows a set of current response curves for an RLC series circuit at various values of R when fed with a constant voltage V.
0 One of the phase currents in the load is then sketched 45 behind (lagging) rise to Ip I') 1P3 its appropriate subscript voltage. (For example VB R gives 0 0 and IP2 are then included at 120 intervals always 45 behind the voltage. Selecting one of the line currents , say I B Hence sketchin/& - IP I and summing with IP 2 gives lB ' Then I R and I y may be included at 120 intervals. Always check that the phase sequence is correct. For example, an observer standing at X would see IR,Iy and I B come past in that order as the diagram rotated.