Chapter 11: Problem 2
For each set of voltages, state whether or not the voltages form a balanced three-phase set. If the set is balanced, state whether the phase sequence is positive or negative. If the set is not balanced, explain why. a) \(v_{\mathrm{a}}=339 \cos 377 t \mathrm{V}\) \(v_{\mathrm{b}}=339 \cos \left(377 t-120^{\circ}\right) \mathrm{V}\) \(v_{\mathrm{c}}=339 \cos \left(377 t+120^{\circ}\right) \mathrm{V}\) b) \(v_{\mathrm{a}}=622 \sin 377 t \mathrm{V}\) \(v_{b}=622 \sin \left(377 t-240^{\circ}\right) \mathrm{V}\) \(v_{\mathrm{c}}=622 \sin \left(377 t+240^{\circ}\right) \mathrm{V}\) c) \(v_{\mathrm{a}}=933 \sin 377 t \mathrm{V}\) \(v_{b}=933 \sin \left(377 t+240^{\circ}\right) \mathrm{V}\) \(v_{\mathrm{c}}=933 \cos \left(377 t+30^{\circ}\right) \mathrm{V}\) d) \(v_{a}=170 \sin \left(\omega t+60^{\circ}\right) \mathrm{V}\) \(v_{b}=170 \sin \left(\omega t+180^{\prime \prime}\right) V\) \(v_{c}=170 \cos \left(\omega t-150^{\circ}\right) \mathrm{V}\) e) \(v_{a}=339 \cos \left(\omega t+30^{\circ}\right) \mathrm{V}\) \(v_{b}=339 \cos \left(\omega t-90^{\circ}\right) V\) \(v_{c}=393 \cos \left(\omega t+240^{\circ}\right) \mathrm{V}\) f) \(v_{\mathrm{a}}=3394 \sin \left(\omega t+70^{\circ}\right) \mathrm{V}\) \(v_{b}=3394 \cos \left(\omega t-140^{\circ}\right) \mathrm{V}\) \(v_{c}=3394 \cos \left(\omega t+180^{\circ}\right) \mathrm{V}\)
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