Question (d) A three-phase, 60-Hz induction motor runs at (700+ a) rpm at no load and at (700 - 3a) rpm at full load, where a is your group number. i. How many poles does this motor have? What is the slip at rated load? ii. iii. What is the speed at one-quarter of the rated load? iv. What is the rotor's electrical frequency at one-quarter of the rated load? (d) A three-phase, 60-Hz induction motor runs at (700+ a) rpm at no load and at (700 - 3a) rpm at full load, where a is your group number. i. How many poles does this motor have? What is the slip at rated load? ii. iii. What is the speed at one-quarter of the rated load? iv. What is the rotor's electrical frequency at one-quarter of the rated load? Open-circuit characteristic 20 18 16 14 12 10 5 6 Field current (A) Open-circuit voltage (kV) 00 9 4 2 2 3 7 8 9 10

Given, f=60 \mathrm{~Hz}At No lond the motor will rua close to synchronous speed.i)\begin{array}{c}\text { Syachinuous specel } \cong 700+\alpha \quad\left[\begin{array}{c}\text { iet's take } \\\alpha=5\end{array}\right] \\N_{s} \cong 705 \\N_{s}=\frac{1.20 \mathrm{f}}{p} \Rightarrow p=\frac{120 \mathrm{f}}{\mathrm{Ns}_{s}} \\N_{0} \text { of Poles }(p)=\frac{120 \times 60}{705}=10.21\end{array}since the number of poles shenld be an integer lets take P=10ii)\begin{array}{l}\text { specd of Full Lond [Rated Speed] } \mathrm{N}_{2}=700-3 \alpha \\=685 \mathrm{rpm} \\S_{\text {ful }}[\text { slip efillgade }]=\frac{N_{s}-N_{2}}{N_{s}}=\frac{705-685}{705} \\S_{\text {fuy }}=0.0283 \\\end{array}jii) Since the load is poopetional to slip Slip@One qwerter of full load =\frac{5 \text { full }}{4}Specd (a that ship\begin{array}{c}s^{\prime}=\frac{N_{s}-N_{\gamma}^{\prime}}{N_{s}} \Rightarrow s^{\prime}=1-\frac{N_{\gamma}^{\prime}}{N_{s}} \\N_{\gamma}^{\prime}=N_{s}\left(1-s^{\prime}\right)=705\left(1-\frac{0.0283}{4}\right) \\N_{\gamma}^{\prime}=700 \text { spM }\end{array}iv) Rotors electrical Erequency.\begin{aligned}\text { Rotor Frequency } & =\text { Slip } \times \text { Supply Frequeny } \\& =S^{\prime} \times \mathrm{F} \\& =\frac{0.0283}{4} \times 60 \\& =0.4245 \mathrm{~Hz}\end{aligned} ...