Question 8.1: The following parameters are available for a 60-Hz four-pole......
The following parameters are available for a 60-Hz four-pole single-phase 110-V 1/2-hp induction motor.
R_{1} = 1.5 Ω R_{2}^{\prime}= 3 Ω
X_{1} = 2.4 Ω X_{2}^{\prime}= 2.4 Ω
X_{m} = 73.4 ΩCalculate Z_{f}, Z_{b}, and the input impedance of the motor at a slip of 0.05.
The result obtained above is a direct application of Eq. (8.17). Similarly, using Eq. (8.18), we get
Z_{f}=\frac{j(X_{m}/2)[(R_{2}^{\prime}/2s)+j(X_{2}^{\prime}/2)]}{(R_{2}^{\prime}/2s)+j[(X_{m}+X_{2}^{\prime})/2]} (8.17)
Z_{b}=\frac{j(X_{m}/2)\{[(R_{2}^{\prime}/2(2-s))+j(X_{2}^{\prime}/2)]\}}{[R_{2}^{\prime}/2(2-s)]+j[(X_{m}+X_{2}^{\prime})/2]} (8.18)
Z_{b}=\frac{j36.7[(1.5/1.95)+j1.2]}{(1.5/1.95)+j37.9}=1.38\angle58.502\ \mathrm{deg}\,\Omega \\ =0.721+j1.1766\;\OmegaWe observe here that |Z_{f}| is much larger than |Z_{b}| at this slip, in contrast to the situation
at starting (s = I), for which \mathrm{Z}_{i}=\mathrm{Z}_{b}.